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  • 251.
    Lindell, Hugo
    Linköpings universitet, Matematiska institutionen, Optimeringslära.
    Methods for optimizing large scale thermal imaging camera placement problems2019Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Syftet med detta examensarbete är att modellera och lösa kameraplaceringsproblemet då IR-kameror ska användas för brandövervakning av fastbränslehögar. Problemet består i att givet ett antal kamera modeller och monteringsstolpar bestämma de kombinationer av placeringar och modeller sådana att övervakningen av högarna är maximal, för alla möjliga kostnadsnivåer.

    I den första delen av examensarbetet presenteras en modell för detta kameraplaceringsproblem. Modellen använder sig av en diskret formulering, där området om ska övervaras är representerad av ett rutnät. De möjliga kameravalen beskrivas med en diskret mängd av möjliga kameraplaceringar. För att utröna vilka celler inom rutnätet som en kameraplacering övervakar används metoden ray-casting. Utifrån mängden av möjliga kameraplaceringar kan en optimeringsmodell med två målfunktioner formuleras. Målet i den första målfunktionen är att minimera kostnaden för övervakningen och i den andra att maximera storleken på det övervakade området.

    Utgående från denna modell presenteras därefter ett antal algoritmer för att lösa modellen. Dessa är: Greedy Search, Random Greedy Search, Fear Search, Unique Search, Meta-RaPS och Weighted Linear Neighbourhood Search. Algoritmerna utvärderas på två konstgjorda testproblem och ett antal problem från verkliga fastbränslelager. Utvärderingen baseras på lösningsfronter (grafer över de icke-dominerade lösningarna med de bästa kombinationerna av kostnad och täckning) samt ett antal resultatmått som tid, lägsta kostnad för lösning med full täckning, etc...

    Vid utvärderingen av resultaten framkom att för de konstgjorda testinstanserna presterade ingen av heuristikerna jämförbart med en standardlösare, varken i termer av kvalitén på lösningarna eller med hänsyn tagen till tidsåtgången. De heuristiker som presterade bäst på dessa problem var framförallt Fear Search och Greedy Search. Även på de mindre probleminstanserna från existerande fastbränslelager hittade standardlösaren optimala lösningsfronter och en lösning med full täckning, men tidsåtgången var här flera gånger större jämfört med vissa av heuristikerna. På en hundra- respektive en tiondel av tiden kan Greedy Search eller Random Greedy Search heuristikerna finna en lösningsfront som är jämförbar med standardlösare, upp till 70-80% täckning. För de största probleminstanserna är tidsåtgången vid användning av standardlösare så pass stor att det i många fall är praktiskt svårt att lösa problemen, både för att generera fronten och att hitta en lösning med full täckning. I dessa fall är heuristiker oftast de enda möjliga alternativen. Vi fann att Greedy Search och Random Greedy Search var de heuristiker som, liksom för de mindre probleminstanserna, genererade de bästa lösningsfronterna. Ofta kunde dock en bättre lösning för full täckning hittas med hjälp av Fear Search eller Unique Search.

    Ladda ner fulltext (pdf)
    Methods_for_optimizing_large_scale_thermal_imaging_camera_placement_problems
  • 252.
    Lindholm, Anna
    et al.
    Lund University, Sweden.
    Giselsson, Pontus
    Lund University, Sweden.
    Quttineh, Nils-Hassan
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Lidestam, Helene
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Johnsson, Charlotta
    Lund University, Sweden.
    Forsman, Krister
    Perstorp AB, Sweden.
    Production Scheduling in the Process Industry2013Ingår i: Proceedings for 22nd International Conference on Production Research, 2013, 2013Konferensbidrag (Refereegranskat)
    Abstract [en]

    The purpose of this paper is to formulate an optimization model for the production scheduling problem at continuous production sites. The production scheduling activity should produce a monthly schedule that accounts for orders and forecasts of all products. The plan should be updated every day, with feedback on the actual production the previous day. The actual daily production may be lower than the planned production due to disturbances, e.g. disruptions in the supply of a utility. The work is performed in collaboration with Perstorp, a world-leading company within several sectors of the specialty chemicals market. Together with Perstorp, a list of specifications for the production scheduling has been formulated. These are formulated mathematically in a mixed-integer linear program that is solved in receding horizon fashion. The formulation of the model aims to be general, such that it may be used for any process industrial site.

  • 253.
    Lindholm, Anna
    et al.
    Lund University, Sweden.
    Johnsson, Charlotta
    Lund University, Sweden.
    Quttineh, Nils-Hassan
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Lidestam, Helene
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Henningsson, Mathias
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Wikner, Joakim
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Tang, Ou
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Nytzén, Nils-Petter
    Perstorp AB, Sweden.
    Forsman, Krister
    Perstorp AB, Sweden.
    Hierarchical Scheduling and Utility Disturbance Management in the Process Industry2013Ingår i: Proceedings for IFAC Conference on Manufacturing Modelling, Management and Control (MIM2013), 2013, Elsevier, 2013, s. 140-145Konferensbidrag (Refereegranskat)
    Abstract [en]

    The integration of scheduling and control in the process industry is a topic that has been frequently discussed during the recent years, but many challenges remain in order to achieve integrated solutions that can be implemented for large-scale industrial sites. In this paper we consider production control under disturbances in the supply of utilities at integrated sites together with the integration towards production scheduling. Utilities, such as steam and cooling water, are often shared between the production areas of a site, which enables formulation of an optimization problem for determining the optimal supply of utilities to each area at the occurrence of a disturbance. Optimization in two timescales is suggested to handle the scheduling and disturbance management problems in a hierarchical fashion. The suggested structure has been discussed with companies within the chemical process industry. A simple example is provided to show how the structure may be used

  • 254.
    Lindholm, Anna
    et al.
    Lund University, Sweden.
    Quttineh, Nils-Hassan
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Lidestam, Helene
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Hierarchical Production Scheduling: A Case Study at Perstorp2014Ingår i: 24th European Symposium on Computer Aided Process Engineering / [ed] Jiří Jaromír Klemeš, Petar Sabev Varbanov and Peng Yen Liew, Elsevier, 2014, s. 511-516Konferensbidrag (Refereegranskat)
    Abstract [en]

    Planning and scheduling are functions that have large economic impact in the chemical process industry. For integrated sites with many interconnected production areas, obtaining production schedules that respect all production-related constraints is a complex task. One important issue is the constraints due to disturbances in utilities, such as steam and cooling water. These are often site-wide disturbances that may make it impossible to maintain desired production rates in several production areas at a site. In this study, scheduling at two levels of the functional hierarchy at a site of a world lead chemical industry, Perstorp, is handled. The activities are denoted production scheduling (PS) and detailed production scheduling (DPS). Real data of incoming orders and utility disturbances are used to produce a production schedule and detailed production schedule for one month. The PS and DPS problems are formulated as optimization problems, where production-related constraints such as production rate constraints, inventory limitations, and start-up costs are included. The objective functions of the PS and DPS problems are formulated to reflect the importance of different issues at the site. The procedure aims to show how the hierarchical optimization framework may be used to provide decision support for how to operate the production at a site in order to maximize profit while minimizing the effects of site-wide disturbances.

  • 255.
    Lundberg, Kristian
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Effect Oriented Planning in Military Mission Support Systems: Models and Heuristic Approaches2013Licentiatavhandling, monografi (Övrigt vetenskapligt)
    Abstract [en]

    Today there are many aspects of model based planning, probably much more than for just 20 years ago. Today data is not the problem, data is everywhere, but the big issue is to understand how to gain advantage of data in decision making - a growing focus is now on modeling!

    This work is devoted to this task and can be seen as a three part study. First a general problem of multi-resource routing with sequence dependent costs is studied both in terms of models, as well as the development of methods to solve this class of problems efficiently. Sequence dependent costs among resources arise in situations where for instance, one resource is allocated to a task which influence another task and makes that easier in the sense that it can be conducted to a lower cost or shorter time or some other measured effort. This is a useful building block in military decision making when making plans for troops, attacks or missions in general.

    The next part is founded by Vinnova via the research project “Effect Oriented Planning in Dynamic Scenarios”, and deals with a military ground attack problem with simultaneous attacks against a plurality of targets. This part deals with the difficulties of the attacker-defender problem which is modeled in a Nonlinear Mixed Integer Programming formulation. Suggestions are given how to refine and transform this into robust solution methods.

    The last part, also included in the Vinnova research project, deals with mission support modeling of Air to Ground missions including multiple aircrafts and a plurality of targets. In this case, sequencing is most important and a strong effort has been put in the understanding and transformation of the problem into models and methods.

    In these last two parts implementations of models and heuristics as well as computer runs and simulations, originates from the work in [19] and [20] which has been an invaluable contribution to this work.

    The results are very promising where fast execution and sufficient planning accuracy have drawn the attention as a foundation for future work and research in model based decision making applicable to industry needs and ambitions.

    Ladda ner (pdf)
    omslag
  • 256.
    Lundgren, Jan
    et al.
    Linköpings universitet, Institutionen för teknik och naturvetenskap.
    Rönnqvist, Mikael
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Optimeringslära.
    Värbrand, Peter
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för teknik och naturvetenskap.
    Optimeringslära2003Övrigt (Övrig (populärvetenskap, debatt, mm))
  • 257.
    Lundén, Anna
    Linköpings universitet, Matematiska institutionen, Optimeringslära.
    Taktisk bemanningsplanering av läkare: modellutveckling och en pilotstudie2010Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Inom vården utförs ofta schemaläggning av personal manuellt, vilket kräver mycket tid och resurser. Att planera arbetet för en grupp läkare, med dess ofta mycket komplexa sammansättning vad gäller exempelvis arbetsuppgifter och kompetenser, är ingen lätt uppgift. Detta examensarbete studerar huruvida en automatiserad taktisk bemanningsplanering med en tidshorisont på ett halvår till ett år, skulle kunna underlätta denna uppgift.

    I rapporten presenteras en måloptimeringsmodell som implementerats i AMPL för att med CPLEX som lösare generera förslag till bemanningsplaner. För att utveckla en matematisk modell som väl representerar de förutsättningar som råder vid bemanningsplanering av läkare har alternativa formuleringar provats och utvärderats. Den mest lovande av modellerna, som baseras på måloptimering, har i en pilotstudie testats på data från Onkologiska kliniken vid Linköpings universitetssjukhus. Flexibiliteten i modellen gjorde att den enkelt kunde användas på de data som erhölls därifrån. Resultatet från pilotstudien indikerar att den utvecklade modellen har kapacitet att ge förslag till rimliga bemanningsplaner.

    Ladda ner fulltext (pdf)
    Taktisk bemanningsplanering av läkare
  • 258. Mattias, Forsberg
    et al.
    Rönnqvist, Mikael
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Optimeringslära.
    Decision support system/tools: Integrated logistics management in the forest supply chain2003Ingår i: 2nd Forest Engineering Conference,2003, 2003, s. 64-73Konferensbidrag (Övrigt vetenskapligt)
  • 259.
    Mayambala, Fred
    et al.
    Department of Mathematics, Makerere University, Kampala, Uganda.
    Rönnberg, Elina
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Eigendecomposition of the mean-variance portfolio optimization model2015Ingår i: Optimization, control, and applications in the information age / [ed] Athanasios Migdalas and Athanasia Karakitsiou, Springer, 2015, s. 209-232Kapitel i bok, del av antologi (Refereegranskat)
    Abstract [en]

    We provide new insights into the mean-variance portfolio optimization problem, based on performing eigendecomposition of the covariance matrix. The result of this decomposition can be given an interpretation in terms of uncorrelated eigenportfolios. When only some of the eigenvalues and eigenvectors are used, the resulting mean-variance problem is an approximation of the original one. A solution to the approximation yields lower and upper bounds on the original mean-variance problem; these bounds are tight if sufficiently many eigenvalues and eigenvectors are used in the approximation. Even tighter bounds are obtained through the use of a linearized error term of the unused eigenvalues and eigenvectors.

    We provide theoretical results for the upper bounding quality of the approximate problem and the cardinality of the portfolio obtained, and also numerical illustrations of these results. Finally, we propose an ad hoc linear transformation of the mean-variance problem, which in practice significantly strengthens the bounds obtained from the approximate mean-variance problem.

  • 260.
    Mayambala, Fred
    et al.
    Department of Mathematics, Makerere University, Kampala, Uganda.
    Rönnberg, Elina
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Tight Upper Bounds on the Cardinality Constrained Mean-Variance Portfolio Optimization Problem Using Truncated Eigendecomposition2016Ingår i: Operations Research Proceedings 2014: Selected Papers of the Annual International Conference of the German Operations Research Society (GOR), RWTH Aachen University, Germany, September 2-5, 2014 / [ed] Marco Lübbecke, Arie Koster, Peter Letmathe, Reinhard Madlener, Britta Peis and Grit Walther, Springer, 2016, s. 385-392Konferensbidrag (Refereegranskat)
    Abstract [en]

    The mean-variance problem introduced by Markowitz in 1952 is a fundamental model in portfolio optimization up to date. When cardinality and bound constraints are included, the problem becomes NP-hard and the existing optimizing solution methods for this problem take a large amount of time.

    We introduce a core problem based method for obtaining upper bounds to the meanvariance portfolio optimization problem with cardinality and bound constraints. The method involves performing eigendecomposition on the covariance matrix and then using only few of the eigenvalues and eigenvectors to obtain an approximation of the original problem. A solution of this approximate problem has a relatively low cardinality and is used to construct a core problem. When solved, the core problem provides an upper bound. We test the method on large scale problems of up to 1000 assets. The obtained upper bounds are of high quality and the time required to obtain them is much less than what state-of-the-art mixed integer softwares use, which makes it practically useful.

  • 261.
    Melin, Kennet
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Optimization modelling and methods for freight transportation in scheduled railways2002Licentiatavhandling, monografi (Övrigt vetenskapligt)
    Abstract [en]

    In the planning process of a freight railway transportation company, a number of optimization problems arise. In this thesis, we study two of them; empty freight car distribution and line planning.

    The empty freight car distribution process is the planning and realization of empty freight car movement in order to remedy spatial imbalances of cargo flows. An efficient utilization of empty cars helps keeping investment costs low. One objective of the empty freight car distribution process is to group empty cars in suitable blocks. In this context, the multicommodity network flow problem with fixed path costs is applicable. The problem is a difficult mixed integer programming problem, and we develop and implement a Lagrangean heuristic for solving the problem. Numerical results are also presented.

    Line planning is the first stage in the process of making a time table. The aim is to decide paths for trains to follow, and frequencies with which trains run in the paths. A model for the line planning problem for freight transportation in scheduled railways is presented. We also present a mode! for a special case of this problem where only direct trains are used. For the mode! in the direct train case of line planning. two heuristics are developed and evaluated: the first one is a rounding heuristic and the other is a tabu search algorithm.

  • 262. Beställ onlineKöp publikationen >>
    Mitradjieva-Daneva, Maria
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Feasible Direction Methods for Constrained Nonlinear Optimization: Suggestions for Improvements2007Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This thesis concerns the development of novel feasible direction type algorithms for constrained nonlinear optimization. The new algorithms are based upon enhancements of the search direction determination and the line search steps.

    The Frank-Wolfe method is popular for solving certain structured linearly constrained nonlinear problems, although its rate of convergence is often poor. We develop improved Frank--Wolfe type algorithms based on conjugate directions. In the conjugate direction Frank-Wolfe method a line search is performed along a direction which is conjugate to the previous one with respect to the Hessian matrix of the objective. A further refinement of this method is derived by applying conjugation with respect to the last two directions, instead of only the last one.

    The new methods are applied to the single-class user traffic equilibrium problem, the multi-class user traffic equilibrium problem under social marginal cost pricing, and the stochastic transportation problem. In a limited set of computational tests the algorithms turn out to be quite efficient. Additionally, a feasible direction method with multi-dimensional search for the stochastic transportation problem is developed.

    We also derive a novel sequential linear programming algorithm for general constrained nonlinear optimization problems, with the intention of being able to attack problems with large numbers of variables and constraints. The algorithm is based on inner approximations of both the primal and the dual spaces, which yields a method combining column and constraint generation in the primal space.

    Delarbeten
    1. The Stiff is Moving - Conjugate Direction Frank -Wolfe Methods with Applications to Traffic Assignment
    Öppna denna publikation i ny flik eller fönster >>The Stiff is Moving - Conjugate Direction Frank -Wolfe Methods with Applications to Traffic Assignment
    2013 (Engelska)Ingår i: Transportation Science, ISSN 0041-1655, E-ISSN 1526-5447, Vol. 47, nr 2, s. 280-293Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    We present versions of the Frank-Wolfe method for linearly constrained convex programs, in which consecutive search directions are made conjugate. Preliminary computational studies in a MATLAB environment applying pure Frank-Wolfe, conjugate direction Frank-Wolfe (CFW), bi-conjugate Frank-Wolfe (BFW), and "partanized" Frank-Wolfe methods to some classical Traffic Assignment Problems show that CFW and BFW compare favorably to the other methods. This spurred a more detailed study, comparing our methods to an origin-based algorithm. This study indicates that our methods are competitive for accuracy requirements ensuring link flow stability. We also show that CFW is globally convergent. We further point at independent studies by other researchers that show that our methods compare favorably with recent bush-based and gradient projection algorithms on computers with several cores

    Nationell ämneskategori
    Matematik
    Identifikatorer
    urn:nbn:se:liu:diva-14437 (URN)10.1287/trsc.1120.0409 (DOI)000318852300010 ()
    Tillgänglig från: 2007-04-27 Skapad: 2007-04-27 Senast uppdaterad: 2017-12-13
    2. Multi-Class User Equilibria under Social Marginal Cost Pricing
    Öppna denna publikation i ny flik eller fönster >>Multi-Class User Equilibria under Social Marginal Cost Pricing
    2002 (Engelska)Ingår i: Operations Research 2002, 2002, s. 174-179Konferensbidrag, Publicerat paper (Övrigt vetenskapligt)
    Abstract [en]

    In the congested cities of today, congestion pricing is a tempting alternative. With a single user class, already Beckmann et al. showed that ``system optimal'' traffic flows can be achieved by social marginal cost (SMC) pricing where users have to pay for the delays the incur on others. However different user classes can have widly differing time values. Hence, when introducing tolls, one should consider multi-class user equilibria, where the classes have different time values. In the single class case, the equilibrium conditions can be viewn as optimality conditions of an equivalent optimization problem. In the multi-class case, however, netter claims that this is not possible. We show that, depending on the formulation, the multi-class SMC-pricing equilibrium problem (with different time values) can be stated either as an asymmetric or as a symmetric equilibrium problem. In the latter case, the corresponding optimization problems is in general non-convex. For this non-convex problem, we devise descent methods of Frank-Wolfe type. We apply the methods and study a synthetic case based on Sioux Falls.

    Nationell ämneskategori
    Matematik
    Identifikatorer
    urn:nbn:se:liu:diva-14438 (URN)978-3-540-00387-8 (ISBN)
    Tillgänglig från: 2007-04-27 Skapad: 2007-04-27 Senast uppdaterad: 2009-05-11
    3. A Conjugate Direction Frank-Wolfe Method for Nonconvex Problems
    Öppna denna publikation i ny flik eller fönster >>A Conjugate Direction Frank-Wolfe Method for Nonconvex Problems
    2003 (Engelska)Rapport (Refereegranskat)
    Abstract [en]

    In this paper we propose an algorithm for solving problems with nonconvex objective function and linear constraints. We extend the previously suggested Conjugate direction Frank–Wolfe algorithm to nonconvex problems. We apply our method to multi-class user equilibria under social marginal cost pricing. Results of numerical experiments on Sioux Falls and Winnipeg are reported.

    Serie
    LiTH-MAT-R, ISSN 0348-2960 ; 2003:09
    Nationell ämneskategori
    Matematik
    Identifikatorer
    urn:nbn:se:liu:diva-14439 (URN)
    Tillgänglig från: 2007-04-27 Skapad: 2007-04-27 Senast uppdaterad: 2016-07-01Bibliografiskt granskad
    4. A Comparison of Feasible Direction Methods for the Stochastic Transportation Problem
    Öppna denna publikation i ny flik eller fönster >>A Comparison of Feasible Direction Methods for the Stochastic Transportation Problem
    2010 (Engelska)Ingår i: Computational optimization and applications, ISSN 0926-6003, E-ISSN 1573-2894, Vol. 46, nr 3, s. 451-466Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    The feasible direction method of Frank and Wolfe has been claimed to be efficient for solving the stochastic transportation problem. While this is true for very moderate accuracy requirements, substantially more efficient algorithms are otherwise diagonalized Newton and conjugate Frank–Wolfe algorithms, which we describe and evaluate. Like the Frank–Wolfe algorithm, these two algorithms take advantage of the structure of the stochastic transportation problem. We also introduce a Frank–Wolfe type algorithm with multi-dimensional search; this search procedure exploits the Cartesian product structure of the problem. Numerical results for two classic test problem sets are given. The three new methods that are considered are shown to be superior to the Frank–Wolfe method, and also to an earlier suggested heuristic acceleration of the Frank–Wolfe method.

    Nyckelord
    Stochastic transportation problem, Frank–Wolfe method, Descent methods, Cartesian product sets
    Nationell ämneskategori
    Matematik
    Identifikatorer
    urn:nbn:se:liu:diva-14440 (URN)10.1007/s10589-008-9199-0 (DOI)000278736100004 ()
    Tillgänglig från: 2007-04-27 Skapad: 2007-04-27 Senast uppdaterad: 2017-12-13
    5. A Sequential Linear Programming Algorithm with Multi-dimensional Search: Derivation and Convergence
    Öppna denna publikation i ny flik eller fönster >>A Sequential Linear Programming Algorithm with Multi-dimensional Search: Derivation and Convergence
    Visa övriga...
    2007 (Engelska)Artikel i tidskrift (Övrigt vetenskapligt) Submitted
    Abstract [en]

    We present a sequential linear programming, SLP, algorithm in which the traditional line-search step is replaced by a multi-dimensional search. The algorithm is based on inner approximations of both the primal and dual spaces, which yields a method which in the primal space combines column and constraint generation. The algorithm does not use a merit function, and the linear programming subproblem of the algorithm differs from the one obtained in traditional methods of this type, in the respect that linearized constraints are taken into account only implicitly in a Lagrangiandual fashion. Convergence to a point that satisfies the Karush-Kuhn-Tucker conditions is established. We apply the new method to a selection of the Hoch-Schittkowski’s nonlinear test problems and report a preliminary computational study in a Matlab environment. Since the proposed algorithmcombines column and constraint generation, it should be advantageous with large numbers of variables and constraints.

    Nationell ämneskategori
    Matematik
    Identifikatorer
    urn:nbn:se:liu:diva-14441 (URN)
    Tillgänglig från: 2007-04-27 Skapad: 2007-04-27 Senast uppdaterad: 2016-07-01Bibliografiskt granskad
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    FULLTEXT01
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    POPULARSUMMARY01
  • 263.
    Morén, Björn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet.
    Icke-triviala billigaste väg-ruttningskonflikter - klassificering och sökmetoder2010Självständigt arbete på grundnivå (kandidatexamen), 15 poäng / 22,5 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Inom telekommunikation och ruttning av datatrafik i IP-nätverk så används oftaett protokoll som kallas “Open Shortest Path First” (OSPF). Det innebär att enserver sköter ruttningen över ett nätverk genom att utifrån givna bågkostnaderberäkna billigaste vägar som används för ruttningen. Frågeställningen utgårfrån att vi har ett önskat ruttningsschema och vi vill ta reda på om det gåratt sätta bågkostnader så att det önskade ruttningsschemat ingår i en billigasteväg-graf. I det här examensarbetet splittas inte trafik utan varje billigaste vägär unik mellan två noder. Att söka efter bågkostnader som löser problemet geren krävande LP-modell och ett alternativ är att utgå från LP-dualen undervissa restriktioner. Dessa lösningar till LP-dualen benämns konflikter och enkonflikt motsvarar att det inte finns några bågkostnader så att det önskaderuttningsschemat fås. Målet med examensarbetet är att studera, klassificeraoch söka efter konflikter. En algoritm har tagits fram som hittar vissa typer avsådana konflikter i polynomiell tid, sett till storleken på grafen.

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    FULLTEXT01
  • 264.
    Morén, Björn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Mathematical Modelling of Dose Planning in High Dose-Rate Brachytherapy2019Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    Cancer is a widespread type of diseases that each year affects millions of people. It is mainly treated by chemotherapy, surgery or radiation therapy, or a combination of them. One modality of radiation therapy is high dose-rate brachytherapy, used in treatment of for example prostate cancer and gynecologic cancer. Brachytherapy is an invasive treatment in which catheters (hollow needles) or applicators are used to place the highly active radiation source close to or within a tumour.

    The treatment planning problem, which can be modelled as a mathematical optimization problem, is the topic of this thesis. The treatment planning includes decisions on how many catheters to use and where to place them as well as the dwell times for the radiation source. There are multiple aims with the treatment and these are primarily to give the tumour a radiation dose that is sufficiently high and to give the surrounding healthy tissue and organs (organs at risk) a dose that is sufficiently low. Because these aims are in conflict, modelling the treatment planning gives optimization problems which essentially are multiobjective.

    To evaluate treatment plans, a concept called dosimetric indices is commonly used and they constitute an essential part of the clinical treatment guidelines. For the tumour, the portion of the volume that receives at least a specified dose is of interest while for an organ at risk it is rather the portion of the volume that receives at most a specified dose. The dosimetric indices are derived from the dose-volume histogram, which for each dose level shows the corresponding dosimetric index. Dose-volume histograms are commonly used to visualise the three-dimensional dose distribution.

    The research focus of this thesis is mathematical modelling of the treatment planning and properties of optimization models explicitly including dosimetric indices, which the clinical treatment guidelines are based on. Modelling dosimetric indices explicitly yields mixedinteger programs which are computationally demanding to solve. The computing time of the treatment planning is of clinical relevance as the planning is typically conducted while the patient is under anaesthesia. Research topics in this thesis include both studying properties of models, extending and improving models, and developing new optimization models to be able to take more aspects into account in the treatment planning.

    There are several advantages of using mathematical optimization for treatment planning in comparison to manual planning. First, the treatment planning phase can be shortened compared to the time consuming manual planning. Secondly, also the quality of treatment plans can be improved by using optimization models and algorithms, for example by considering more of the clinically relevant aspects. Finally, with the use of optimization algorithms the requirements of experience and skill level for the planners are lower.

    This thesis summary contains a literature review over optimization models for treatment planning, including the catheter placement problem. How optimization models consider the multiobjective nature of the treatment planning problem is also discussed.

    Delarbeten
    1. Mathematical optimization of high dose-rate brachytherapy-derivation of a linear penalty model from a dose-volume model
    Öppna denna publikation i ny flik eller fönster >>Mathematical optimization of high dose-rate brachytherapy-derivation of a linear penalty model from a dose-volume model
    2018 (Engelska)Ingår i: Physics in Medicine and Biology, ISSN 0031-9155, E-ISSN 1361-6560, Vol. 63, nr 6, artikel-id 065011Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    High dose-rate brachytherapy is a method for cancer treatment where the radiation source is placed within the body, inside or close to a tumour. For dose planning, mathematical optimization techniques are being used in practice and the most common approach is to use a linear model which penalizes deviations from specified dose limits for the tumour and for nearby organs. This linear penalty model is easy to solve, but its weakness lies in the poor correlation of its objective value and the dose-volume objectives that are used clinically to evaluate dose distributions. Furthermore, the model contains parameters that have no clear clinical interpretation. Another approach for dose planning is to solve mixed-integer optimization models with explicit dose-volume constraints which include parameters that directly correspond to dose-volume objectives, and which are therefore tangible. The two mentioned models take the overall goals for dose planning into account in fundamentally different ways. We show that there is, however, a mathematical relationship between them by deriving a linear penalty model from a dose-volume model. This relationship has not been established before and improves the understanding of the linear penalty model. In particular, the parameters of the linear penalty model can be interpreted as dual variables in the dose-volume model.

    Ort, förlag, år, upplaga, sidor
    IOP PUBLISHING LTD, 2018
    Nyckelord
    high dose-rate brachytherapy; mathematical optimization; linear penalty model; dose-volume histogram; dwell time optimization; linear programming; dosimetric index
    Nationell ämneskategori
    Radiologi och bildbehandling
    Identifikatorer
    urn:nbn:se:liu:diva-147128 (URN)10.1088/1361-6560/aaab83 (DOI)000427702800002 ()29380746 (PubMedID)
    Anmärkning

    Funding Agencies|Swedish Research Council [VR-NT 2015-04543]; Swedish Cancer Foundation [CAN 2015/618]

    Tillgänglig från: 2018-04-20 Skapad: 2018-04-20 Senast uppdaterad: 2019-05-01
    2. Preventing Hot Spots in High Dose-Rate Brachytherapy
    Öppna denna publikation i ny flik eller fönster >>Preventing Hot Spots in High Dose-Rate Brachytherapy
    2018 (Engelska)Ingår i: Operations Research Proceedings 2017 / [ed] Kliewer, Natalia; Ehmke, Jan Fabian; Borndörfer, Ralf, Springer International Publishing , 2018, s. 369-375Konferensbidrag, Publicerat paper (Refereegranskat)
    Abstract [en]

    High dose-rate brachytherapy is a method of radiation cancer treatment, where the radiation source is placed inside the body. The recommended way to evaluate dose plans is based on dosimetric indices which are aggregate measures of the received dose. Insufficient spatial distribution of the dose may however result in hot spots, which are contiguous volumes in the tumour that receive a dose that is much too high. We use mathematical optimization to adjust a dose plan that is acceptable with respect to dosimetric indices to also take spatial distribution of the dose into account. This results in large-scale nonlinear mixed-binary models that are solved using nonlinear approximations. We show that there are substantial degrees of freedom in the dose planning even though the levels of dosimetric indices are maintained, and that it is possible to improve a dose plan with respect to its spatial properties.

    Ort, förlag, år, upplaga, sidor
    Springer International Publishing, 2018
    Serie
    Operations Research Proceedings, ISSN 0721-5924 ; 2017
    Nationell ämneskategori
    Radiologi och bildbehandling
    Identifikatorer
    urn:nbn:se:liu:diva-154967 (URN)10.1007/978-3-319-89920-6_50 (DOI)978-3-319-89919-0 (ISBN)978-3-319-89920-6 (ISBN)
    Konferens
    Annual International Conference of the German Operations Research Society (GOR), Freie Universiät Berlin, Germany, September 6-8, 2017
    Tillgänglig från: 2019-03-07 Skapad: 2019-03-07 Senast uppdaterad: 2019-03-07
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    Mathematical Modelling of Dose Planning in High Dose-Rate Brachytherapy
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  • 265.
    Morén, Björn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Utilizing problem specic structures in branch and bound methods for manpower planning2012Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [en]

    This thesis is about solving the manpower planning problem concerning stangand transitioning of pilots. The objective of the planning is to have enoughpilots to satisfy the demand while minimizing the cost. The main decisions totake are how many pilots to hire, which pilots to train and which courses toschedule. The planning problems that arise are both large and dicult whichmakes it important to use ecient solution methods. Seniority rules betweenpairs of pilots are the most complicating factor.A major part in the solution process is the solving of mixed integer programs.The emphasis in the thesis is to develop and test adaptations of the branch andbound algorithm to solve mixed integer programs faster. One of these is abranching principle that takes a problem specic structure into account. Agraph of implications is constructed from the seniority rules and this graph isthen used to estimate the impact of each branching candidate. The implementedmethods outperform the software XPRESS on some instances, while for mostinstances the performance is comparable.

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    Master Thesis Björn Morén
  • 266.
    Morén, Björn
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Carlsson Tedgren, Åsa
    Linköpings universitet, Institutionen för medicin och hälsa, Avdelningen för radiologiska vetenskaper. Linköpings universitet, Medicinska fakulteten. Region Östergötland, Diagnostikcentrum, Medicinsk strålningsfysik. Karolinska Univ Hosp, Sweden; Karolinska Inst, Sweden.
    A mathematical optimization model for spatial adjustments of dose distributions in high dose-rate brachytherapy2019Ingår i: Physics in Medicine and Biology, ISSN 0031-9155, E-ISSN 1361-6560, Vol. 64, nr 22, artikel-id 225012Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    High dose-rate brachytherapy is a modality of radiation therapy used for cancer treatment, in which the radiation source is placed within the body. The treatment goal is to give a high enough dose to the tumour while sparing nearby healthy tissue and organs (organs-at-risk). The most common criteria for evaluating dose distributions are dosimetric indices. For the tumour, such an index is the portion of the volume that receives at least a specified dose level (e.g. the prescription dose), while for organs-at-risk it is instead the portion of the volume that receives at most a specified dose level. Dosimetric indices are aggregate criteria and do not consider spatial properties of the dose distribution. Further, there are neither any established evaluation criteria for characterizing spatial properties, nor have such properties been studied in the context of mathematical optimization of brachytherapy. Spatial properties are however of clinical relevance and therefore dose plans are sometimes adjusted manually to improve them. We propose an optimization model for reducing the prevalence of contiguous volumes with a too high dose (hot spots) or a too low dose (cold spots) in a tentative dose plan. This model is independent of the process of constructing the tentative plan. We conduct computational experiments with tentative plans obtained both from optimization models and from clinical practice. The objective function considers pairs of dose points and each pair is given a distance-based penalty if the dose is either too high or too low at both dose points. Constraints are included to retain dosimetric indices at acceptable levels. Our model is designed to automate the manual adjustment step in the planning process. In the automatic adjustment step large-scale optimization models are solved. We show reductions of the volumes of the largest hot and cold spots, and the computing times are feasible in clinical practice.

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    fulltext
  • 267.
    Morén, Björn
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Carlsson Tedgren, Åsa
    Linköpings universitet, Institutionen för medicin och hälsa, Avdelningen för radiologiska vetenskaper. Linköpings universitet, Medicinska fakulteten. Region Östergötland, Diagnostikcentrum, Medicinsk strålningsfysik. Karolinska University Hospital, Stockholm, Sweden.
    An extended dose-volume model in high dose-rate brachytherapy: Using mean-tail-dose to reduce tumor underdosage2019Ingår i: Medical physics (Lancaster), ISSN 0094-2405, Vol. 46, nr 6, s. 2556-2566Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Purpose High dose-rate brachytherapy is a method of radiotherapy for cancer treatment in which the radiation source is placed within the body. In addition to give a high enough dose to a tumor, it is also important to spare nearby healthy organs [organs at risk (OAR)]. Dose plans are commonly evaluated using the so-called dosimetric indices; for the tumor, the portion of the structure that receives a sufficiently high dose is calculated, while for OAR it is instead the portion of the structure that receives a sufficiently low dose that is of interest. Models that include dosimetric indices are referred to as dose-volume models (DVMs) and have received much interest recently. Such models do not take the dose to the coldest (least irradiated) volume of the tumor into account, which is a distinct weakness since research indicates that the treatment effect can be largely impaired by tumor underdosage even to small volumes. Therefore, our aim is to extend a DVM to also consider the dose to the coldest volume. Methods An improved DVM for dose planning is proposed. In addition to optimizing with respect to dosimetric indices, this model also takes mean dose to the coldest volume of the tumor into account. Results Our extended model has been evaluated against a standard DVM in ten prostate geometries. Our results show that the dose to the coldest volume could be increased, while also computing times for the dose planning were improved. Conclusion While the proposed model yields dose plans similar to other models in most aspects, it fulfils its purpose of increasing the dose to cold tumor volumes. An additional benefit is shorter solution times, and especially for clinically relevant times (of minutes) we show major improvements in tumour dosimetric indices.

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    fulltext
  • 268.
    Morén, Björn
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Carlsson Tedgren, Åsa
    Linköpings universitet, Institutionen för medicin och hälsa, Avdelningen för radiologiska vetenskaper. Linköpings universitet, Medicinska fakulteten. Karolinska Univ Hosp, Sweden; Karolinska Inst, Sweden.
    Mathematical optimization of high dose-rate brachytherapy-derivation of a linear penalty model from a dose-volume model2018Ingår i: Physics in Medicine and Biology, ISSN 0031-9155, E-ISSN 1361-6560, Vol. 63, nr 6, artikel-id 065011Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    High dose-rate brachytherapy is a method for cancer treatment where the radiation source is placed within the body, inside or close to a tumour. For dose planning, mathematical optimization techniques are being used in practice and the most common approach is to use a linear model which penalizes deviations from specified dose limits for the tumour and for nearby organs. This linear penalty model is easy to solve, but its weakness lies in the poor correlation of its objective value and the dose-volume objectives that are used clinically to evaluate dose distributions. Furthermore, the model contains parameters that have no clear clinical interpretation. Another approach for dose planning is to solve mixed-integer optimization models with explicit dose-volume constraints which include parameters that directly correspond to dose-volume objectives, and which are therefore tangible. The two mentioned models take the overall goals for dose planning into account in fundamentally different ways. We show that there is, however, a mathematical relationship between them by deriving a linear penalty model from a dose-volume model. This relationship has not been established before and improves the understanding of the linear penalty model. In particular, the parameters of the linear penalty model can be interpreted as dual variables in the dose-volume model.

    Ladda ner fulltext (pdf)
    fulltext
  • 269.
    Morén, Björn
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten. Linköpings universitet, Institutionen för medicin och hälsa.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Carlsson Tedgren, Åsa
    Medical Radiation Physics and Nuclear Medicine, Department of Oncology Pathology, Karolinska University Hospital, Solna Sweden.
    Preventing Hot Spots in High Dose-Rate Brachytherapy2018Ingår i: Operations Research Proceedings 2017 / [ed] Kliewer, Natalia; Ehmke, Jan Fabian; Borndörfer, Ralf, Springer International Publishing , 2018, s. 369-375Konferensbidrag (Refereegranskat)
    Abstract [en]

    High dose-rate brachytherapy is a method of radiation cancer treatment, where the radiation source is placed inside the body. The recommended way to evaluate dose plans is based on dosimetric indices which are aggregate measures of the received dose. Insufficient spatial distribution of the dose may however result in hot spots, which are contiguous volumes in the tumour that receive a dose that is much too high. We use mathematical optimization to adjust a dose plan that is acceptable with respect to dosimetric indices to also take spatial distribution of the dose into account. This results in large-scale nonlinear mixed-binary models that are solved using nonlinear approximations. We show that there are substantial degrees of freedom in the dose planning even though the levels of dosimetric indices are maintained, and that it is possible to improve a dose plan with respect to its spatial properties.

  • 270. Beställ onlineKöp publikationen >>
    Mwakisisile, Andongwisye John
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Asset Liability Management for Tanzania Pension Funds2018Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This thesis presents a long-term asset liability management for Tanzania pension funds. As an application, the largest pension fund in Tanzania is considered. This is a pay-as-you-go pension fund where the contributions are used to pay current benefits. The Pension plan analyzed is a final salary defined benefit. Two kinds of pension benefit are considered, a commuted (at retirement) and a monthly (old age) pension. A decision factor in the analysis is the increased life expectancy of the members of the pension fund.

    The presentation is divided into two parts. First is a long-term projection of the fund using a fixed and relatively low return on asset value. Basing on the number of members in 2015, a 50 years projection of members and retirees is done. The corresponding amount of contributions, asset values, benefit payouts, and liabilities are also projected. The evaluation of some possible reforms of the fund is done. Then, the growth of asset values using different asset returns is studied. The projection shows that the fund will not be fully sustainable in a long future due to the increase in life expectancy of its members. The contributions will not cover the benefit payouts and the asset value will not fully cover liabilities. Evaluation of some reforms of the fund shows that they cannot guarantee a long-term sustainability. Higher returns on asset value will improve the asset to liability ratio, but contributions are still insufficient to cover benefit payouts.

    Second is a management based on stochastic programming. This approach allocates investment in assets with the best return to raise the asset value closer to the level of liabilities. The model is based on work by Kouwenberg in 2001 includes some features from Tanzania pension system. In contrast with most asset liability management models for pension funds by stochastic programming, liabilities are modeled by number of years of life expectancy. Scenario trees are generated by using Monte Carlo simulation. Two models according to different investment guidelines are built. First is using the existing investment guidelines and second is using modified guidelines which are practical and suitable for modeling. Numerical results suggest that, in order to improve a long-term sustainability of the Tanzania pension fund system, it is necessary to make reforms concerning the contribution rate, investment guidelines and formulate target levels (funding ratios) to characterize the pension funds’ solvency situation. These reforms will improve the sustainability of the system.

    Delarbeten
    1. Projecting Tanzania Pension Fund System
    Öppna denna publikation i ny flik eller fönster >>Projecting Tanzania Pension Fund System
    2017 (Engelska)Ingår i: African Journal of Applied Statistics, ISSN 2316-0861, Vol. 4, nr 1, s. 193-218Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    A mandatory Tanzania pension fund with a final salary defined benefit is analyzed. This fund is a contributory pay-as-you-go defined benefit pension system which is much affected by the change in demography. Two kinds of pension benefit, a commuted (at retirement) and a monthly (old age) pension are considered. A decisive factor in the analysis is the increased life expectancy of members of the fund. The projection of the fund’s future members and retirees is done using expected mortality rates of working population and expected longevity. The future contributions, benefits, asset values and liabilities are analyzed. The projection shows that the fund will not be fully sustainable on a long term due to the increase in life expectancy of its members. The contributions will not cover the benefit payouts and the asset value will not fully cover liabilities. Evaluation of some possible reforms of the fund shows that they cannot guarantee a long-term sustainability. Higher returns on asset value will improve the funding ratio, but contributions are still insufficient to cover benefit payouts.

    Ort, förlag, år, upplaga, sidor
    Afrika Statistika - SPAS, 2017
    Nyckelord
    Pension fund; Pay-as-you-go; Defined benefit; Demography
    Nationell ämneskategori
    Sannolikhetsteori och statistik
    Identifikatorer
    urn:nbn:se:liu:diva-143272 (URN)10.16929/ajas/2017.193.210 (DOI)
    Anmärkning

    A mandatory Tanzania pension fund with a final salary defined benefit is an- alyzed. This fund is a contributory pay-as-you-go defined benefit pension system which is much affected by the change in demography. Two kinds of pension benefit, a commuted (at retirement) and a monthly (old age) pension are considered. A decisive factor in the anal- ysis is the increased life expectancy of members of the fund. The projection of the fund’s future members and retirees is done using expected mortality rates of working population and expected longevity. The future contributions, benefits, asset values and liabilities are analyzed. The projection shows that the fund will not be fully sustainable on a long term due to the increase in life expectancy of its members. The contributions will not cover the benefit payouts and the asset value will not fully cover liabilities. Evaluation of some possi- ble reforms of the fund shows that they cannot guarantee a long-term sustainability. Higher returns on asset value will improve the funding ratio, but contributions are still insufficient to cover benefit payouts. 

    Tillgänglig från: 2017-11-28 Skapad: 2017-11-28 Senast uppdaterad: 2018-08-31Bibliografiskt granskad
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    Asset Liability Management for Tanzania Pension Funds
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    omslag
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    presentationsbild
  • 271.
    Ndengo, Marcel
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Blomvall, Jörgen
    Linköpings universitet, Institutionen för ekonomisk och industriell utveckling, Produktionsekonomi. Linköpings universitet, Tekniska högskolan.
    Optimal Investment in the Fixed-Income Market with Focus on the Term PremiumManuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    A good estimation of expected returns is imperative when optimal investments are determined with Stochastic Programming model. However, existing Stochastic Programming models do not include a model for the time-varying term premium. In this paper Duffee’s essentially affine model is used to capture the randomness in interest rates and the time-varying term premium. To determine optimal investments, a two-stage Stochastic Programming model without recourse is proposed which models borrowing, shorting and proportional transaction costs. The proposed model is evaluated over the period 1961-2011 and the Sharpe ratio is better than the one’s that corresponds to the market index, and Jensen’s alpha is positive.

  • 272. Beställ onlineKöp publikationen >>
    Ndengo Rugengamanzi, Marcel
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Term structure estimation based on a generalized optimization framework2013Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    The current work is devoted to estimating the term structure of interest rates based on a generalized optimization framework. To x the ideas of the subject, we introduce representations of the term structure as they are used in nance: yield curve, discount curve and forward rate curve.

    Yield curves are used in empirical research in nance and macroeconomic to support nancial decisions made by governments and/or private nancial institutions. When governments (or nancial corporations) need fundings, they issue to the public (i.e. the market) debt securities (bills, bonds, notes, etc ) which are sold at the discount rate at the settlement date and promise the face value of the security at the redemption date, known as maturity date. Bills, notes and bonds are usually sold with maximum maturity of 1 year, 10 years and 30 years respectively.

    Let us assume that the government issues to the market zero-coupon bonds, which provide a single payment at maturity of each bond. To determine the price of the security at time of settlement, a single discount factor is used. Thus, the yield can be dened as the discount rate which makes the present value of the security issued (the zero-coupon bond) equal to its initial price. The yield curve describes the relationship between a particular yield and a bond's maturity. In general, given a certain number of bonds with dierent time to maturity, the yield curve will describe the one-to-one relationship between the bond yields and their corresponding time to maturity. For a realistic yield curve, it is important to use only bonds from the same class of issuer or securities having the same degree of liquidity when plotting the yields.

    Discount factors, used to price bonds, are functions of the time to maturity. Given that yields are positive, these functions are assumed to be monotonically decreasing as the time to maturity increases. Thus, a discount curve is simply the graph of discount factors for dierent maturities associated with dierent securities.

    Another useful curve uses the forward rate function which can be deduced from both the discount factor and the yield function. The forward rate is the rate of return for an investment that is agreed upon today but which starts at some time in the future and provides payment at some time in the future as well. When forward rates are used, the resulting curve is referred to as the forward rate curve. Thus, any of these curves, that is, the yield curve, the discount curve or the forward rate curve, can be used to represent what is known as the term structure of interest rate. The shapes that the term structure of interest rates can assume include upward sloping, downward sloping,  atness or humped, depending on the state of the economy. When the expectations of market participants are incorporated in the construction of these curves representing the term structure, their shapes capture and summarize the cost of credit and risks associated with every security traded.

    However, constructing these curves and the choice of an appropriate representation of the term structure to use is not a straightforward task. This is due to the complexity of the market data, precisely, the scarcity of zero-coupon bonds which constitutes the backbone of the term structure. The market often provides coupons alongside market security prices for a small number of maturities. This implies that, for the entire maturity spectrum, yields can not be observed on the market. Based on available market data, yields must be estimated using traditional interpolation methods. To this end, polynomial splines as well as parsimonious functions are the methods mostly used by nancial institutions and in research in nance. However, it is observed in literature that these methods suer from the shape constraints which cause them to produce yield curves that are not realistic with respect to the market observations. Precisely, the yield curves produced by these methods are characterized by unrealistic t of the market data, either in the short end or in the long end of the term structure of interest rate.

    To ll the gap, the current research models the yield curve using a generalized optimization framework. The method is not shape constrained, which implies that it can adapt to any shape the yield curve can take across the entire maturity spectrum. While estimating the yield curve using this method in comparison with traditional methods on the Swedish and US markets, it is shown that any other traditional method used is a special case of the generalized optimization framework. Moreover, it is shown that, for a certain market consistency, the method produces lower variances than any of the traditional methods tested. This implies that the method produces forward rate curve of higher quality compared to the existing traditional methods.

    Interest rate derivatives are instruments whose prices depend or are derived from the price of other instruments. Derivatives instruments that are extensively used include the forward rate agreement (FRA) contracts where forward rate is used and the interest rate swap (IRS) where LIBOR rate is used as  oating rate. These instruments will only be used to build up the term structure of interest rates. Since the liquidity crisis in 2007, it is observed that discrepancies in basis spread between interest rates applied to dierent interest rate derivatives have grown so large that a single discount curve is no longer appropriate to use for pricing securities consistently. It has been suggested that the market needs new methods for multiple yield curves estimation to price securities consistently with the market. As a response, the generalized optimization framework is extended to a multiple yield curves estimation. We show that, unlike the cubic spline for instance, which is among the mostly used traditional method, the generalized framework can produce multiple yield curves and tenor premium curves that are altogether smooth and realistic with respect to the market observations.

    U.S. Treasury market is, by size and importance, a leading market which is considered as benchmark for most xed-income securities that are traded worldwide. However, existing U.S. Treasury yield curves that are used in the market are of poor quality since they have been estimated by traditional interpolation methods which are shape constrained. This implies that the market prices they imply contain lots of noise and as such, are not safe to use. In this work, we use the generalized optimization framework to estimate high-quality forward rates for the U.S. Treasury yield curve. Using ecient frontiers, we show that the method can produce low pricing error with low variance as compared to the least squares methods that have been used to estimate U.S. Treasury yield curves.

    We nally use the high-quality U.S. Treasury forward rate curve estimated by the generalized optimization framework as input to the essentially ane model to capture the randomness property in interest rates and the time-varying term premium. This premium is simply a compensation that is required for additional risks that investors are exposed to. To determine optimal investment in the U.S. Treasury market, a two-stage stochastic programming model without recourse is proposed, which model borrowing, shorting and proportional transaction cost. It is found that the proposed model can provide growth of wealth in the long run. Moreover, its Sharpe ratio is better than the market index and its Jensen's alpha is positive. This implies that the Stochastic Programming model proposed can produce portfolios that perform better than the market index.

    Delarbeten
    1. High Quality Yield Curves from a Generalized Optimization Framework
    Öppna denna publikation i ny flik eller fönster >>High Quality Yield Curves from a Generalized Optimization Framework
    (Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    Traditional methods for estimating yield curves are special cases of a generalized optimization framework. For pricing out-of-sample in both the Swedish and U.S. interest rate swap (IRS) markets, it is shown that the framework dominates or is close to dominating the traditional methods in the comparison by first order stochastic dominance. When measuring the perceived variance for each traditional method, it is shown that, for the same level of market consistency, the framework produces lower variance. For these new yield curves, PCA of innovations in forward rates shows that the first three loadings (shift, twist and butterfly) do not explain movements in the short end, and that the subsequent loadings explain uncorrelated movements in the short end.

    Nyckelord
    Term structure estimation, Forward rate, Principal Components Analysis (PCA)
    Nationell ämneskategori
    Matematik
    Identifikatorer
    urn:nbn:se:liu:diva-97405 (URN)
    Tillgänglig från: 2013-09-12 Skapad: 2013-09-12 Senast uppdaterad: 2013-09-12Bibliografiskt granskad
    2. Multiple Yield Curves Estimation Using A Generalized Optimization Framework
    Öppna denna publikation i ny flik eller fönster >>Multiple Yield Curves Estimation Using A Generalized Optimization Framework
    (Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    After the credit crunch which started in 2007, significant basis spreads for exchanging floating payments of different tenors appeared. To deal with the problem, multiple yield curves estimation methods have been suggested. In this paper, a generalized optimization framework is extended to a multiple yield curve framework. As has been observed by practitioners, extending traditional cubic splines to multiple yield curves, though consistent with the market prices, does not provide smooth and realistic yield curves. When the parameters in the generalized optimization framework are selected to exactly match market prices, the yield curves are much more realistic, but small waves still remain due to noise in the input data. To avoid having a rough yield curve, we also study the least squares parameter setting in the generalized optimization framework. This method gives much smoother and more realistic yield curves with adjustments to market prices that are less than 0.2 basis points. When exact traditional methods are extended to estimate multiple yield curves, then even tiny pricing errors can cause a situation where the shape constraints prevent the method from finding realistic yield curves.

    Nyckelord
    Multiple yield curve estimation, Overnight Index Swap (OIS), Basis spread, Tenor Swap (TS)
    Nationell ämneskategori
    Matematik
    Identifikatorer
    urn:nbn:se:liu:diva-97406 (URN)
    Tillgänglig från: 2013-09-12 Skapad: 2013-09-12 Senast uppdaterad: 2013-09-12Bibliografiskt granskad
    3. Estimating U.S. Treasury Yield Curves By A Generalized Optimization Framework
    Öppna denna publikation i ny flik eller fönster >>Estimating U.S. Treasury Yield Curves By A Generalized Optimization Framework
    (Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    We show that traditional data sets for the U.S. Treasury yield curves contain large amounts of noise, in e.g. the Fama-Bliss discount file already the second factor loading for innovations in forward rates is a consequence of noise. We implement the quadratic and cubic McCulloch splines, Nelson-Siegel and Svensson models and compare these traditional models with a recently developed generalized optimization framework using daily CRSP data from 1961 to 2011. In out-of-sample tests, it is shown that the generalized optimization framework produces smaller pricing errors compared to the traditional methods. Factor loadings from the generalized optimization framework show that the short and long end of the forward rate curve move independently, where principal component 1-3 explain the long end, and subsequent principal components explain the short end. This is consistent with the behavior of the market where short rates are governed by central bank while long rates are dependent on e.g. the expectation of future inflation.

    Nyckelord
    structure estimation, U.S. Treasury, Principal component analysis, Forward rates
    Nationell ämneskategori
    Matematik
    Identifikatorer
    urn:nbn:se:liu:diva-97407 (URN)
    Tillgänglig från: 2013-09-12 Skapad: 2013-09-12 Senast uppdaterad: 2013-09-12Bibliografiskt granskad
    4. Optimal Investment in the Fixed-Income Market with Focus on the Term Premium
    Öppna denna publikation i ny flik eller fönster >>Optimal Investment in the Fixed-Income Market with Focus on the Term Premium
    (Engelska)Manuskript (preprint) (Övrigt vetenskapligt)
    Abstract [en]

    A good estimation of expected returns is imperative when optimal investments are determined with Stochastic Programming model. However, existing Stochastic Programming models do not include a model for the time-varying term premium. In this paper Duffee’s essentially affine model is used to capture the randomness in interest rates and the time-varying term premium. To determine optimal investments, a two-stage Stochastic Programming model without recourse is proposed which models borrowing, shorting and proportional transaction costs. The proposed model is evaluated over the period 1961-2011 and the Sharpe ratio is better than the one’s that corresponds to the market index, and Jensen’s alpha is positive.

    Nyckelord
    Realized premium, Term premium, Forward rates, Stochastic programming
    Nationell ämneskategori
    Matematik Ekonomi och näringsliv
    Identifikatorer
    urn:nbn:se:liu:diva-97409 (URN)
    Tillgänglig från: 2013-09-12 Skapad: 2013-09-12 Senast uppdaterad: 2013-09-12Bibliografiskt granskad
    Ladda ner fulltext (pdf)
    Term structure estimation based on a generalized optimization framework
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    omslag
  • 273.
    Norell, Björn
    et al.
    Philips Digital Mammography Sweden AB.
    Burdakov, Oleg
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Andersson, Mats
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Knutsson, Hans
    Linköpings universitet, Institutionen för medicinsk teknik, Medicinsk informatik. Linköpings universitet, Tekniska högskolan.
    Approximate spectral factorization for design of efficient sub-filter sequences2011Rapport (Övrigt vetenskapligt)
    Abstract [en]

    A well-known approach to the design of computationally efficient filters is to use spectral factorization, i.e. a decomposition of a filter into a sequence of sub-filters. Due to the sparsity of the sub-filters, the typical processing speedup factor is within the range 1-10 in 2D, and for 3D it achieves10-100. The design of such decompositions consists in choosing the proper number of sub-filters, their individual types and sparsity. We focus here on finding optimal values of coefficients for given sequences of sparse sub-filters. It is a non-convex large scale optimization problem. The existing approaches are characterized by a lack of robustness - a very slow convergence with no guarantee of success. They are typically based on generating random initial points for further refinement with the use of local search methods. To deal with the multi-extremal nature of the original problem, we introduce a new constrained optimization problem. Its solution is then used as an initial point in the original problem for further refinement. Our approach is applicable to designing multi-dimensional filters. Its efficiency and robustness is illustrated by designing sub-filter sequences for 2D low-pass, band-pass and high-pass filters of approximately the same quality as with the use of a standard approach, but with the overall design speedup factor of several hundred.

    Ladda ner fulltext (pdf)
    Approximate spectral factorization for design of efficient sub-filter sequences
  • 274.
    Olsson, Jonas
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Solving a highly constrained multi-level container loading problem from practice2017Självständigt arbete på grundnivå (kandidatexamen), 10,5 poäng / 16 hpStudentuppsats (Examensarbete)
    Abstract [en]

    The container loading problem considered in this thesis is to determine placements of a set of packages within one or multiple shipping containers. Smaller packages are consolidated on pallets prior to being loaded in the shipping containers together with larger packages. There are multiple objectives which may be summarized as fitting all the packages while achieving good stability of the cargo as well as the shipping containers themselves.

    According to recent literature reviews, previous research in the field have to large extent been neglecting issues relevant in practice. Our real-world application was developed for the industrial company Atlas Copco to be used for sea container shipments at their Distribution Center (DC) in Texas, USA. Hence all applicable practical constraints faced by the DC operators had to be treated properly. A high variety in sizes, weights and other attributes such as stackability among packages added complexity to an already challenging combinatorial problem.

    Inspired by how the DC operators plan and perform loading manually, the batch concept was developed, which refers to grouping of boxes based on their characteristics and solving subproblems in terms of partial load plans. In each batch, an extensive placement heuristic and a load plan evaluation run iteratively, guided by a Genetic Algorithm (GA). In the placement heuristic, potential placements are evaluated using a scoring function considering aspects of the current situation, such as space utilization, horizontal support and heavier boxes closer to the floor. The scoring function is weighted by coefficients corresponding to the chromosomes of an individual in the GA population. Consequently, the fitness value of an individual in the GA population is the rating of a load plan.

    The loading optimization software has been tested and successfully implemented at the DC in Texas. The software has been proven capable of generating satisfactory load plans within acceptable computation times, which has resulted in reduced uncertainty and labor usage in the loading process. Analysis using real sea container shipments shows that the GA is able to tune the scoring coefficients to suit the particular problem instance being solved.

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    ContainerLoadingJonasOlsson
  • 275.
    Olsson, Jonas
    et al.
    Linköpings universitet, Matematiska institutionen. Linköpings universitet, Tekniska fakulteten.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Quttineh, Nils-Hassan
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Automating the planning of container loading for Atlas Copco: Coping with real-life stacking and stability constraints2019Ingår i: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 280, nr 3, s. 1018-1034Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The Atlas Copco* distribution center in Allen, TX, supplies spare parts and consumables to mining and construction companies across the world. For some customers, packages are shipped in sea containers. Planning how to load the containers is difficult due to several factors: heterogeneity of the packages with respect to size, weight, stackability, positioning and orientation; the set of packages differs vastly between shipments; it is crucial to avoid cargo damage. Load plan quality is ultimately judged by shipping operators. This container loading problem is thus rich with respect to practical considerations. These are posed by the operators and include cargo and container stability as well as stacking and positioning constraints. To avoid cargo damage, the stacking restrictions are modeled in detail. For solving the problem, we developed a two-level metaheuristic approach and implemented it in a decision support system. The upper level is a genetic algorithm which tunes the objective function for a lower level greedy-type constructive placement heuristic, to optimize the quality of the load plan obtained. The decision support system shows load plans on the forklift laptops and has been used for over two years. Management has recognized benefits including reduction of labour usage, lead time, and cargo damage risk. (C) 2019 Elsevier B.V. All rights reserved.

    Publikationen är tillgänglig i fulltext från 2021-07-27 08:31
  • 276. Beställ onlineKöp publikationen >>
    Olsson, Per-Magnus
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Methods for Network Optimization and Parallel Derivative-free Optimization2014Doktorsavhandling, monografi (Övrigt vetenskapligt)
    Abstract [en]

    This thesis is divided into two parts that each is concerned with a specific problem.

    The problem under consideration in the first part is to find suitable graph representations, abstractions, cost measures and algorithms for calculating placements of unmanned aerial vehicles (UAVs) such that they can keep one or several static targets under constant surveillance. Each target is kept under surveillance by a surveillance UAV, which transmits information, typically real time video, to a relay UAV. The role of the relay UAV is to retransmit the information to another relay UAV, which retransmits it again to yet another UAV. This chain of retransmission continues until the information eventually reaches an operator at a base station.

    When there is a single target, then all Pareto-optimal solutions, i.e. all relevant compromises between quality and the number of UAVs required, can be found using an efficient new algorithm. If there are several targets, the problem becomes a variant of the Steiner tree problem and to solve this problem we adapt an existing algorithm to find an initial tree. Once it is found, we can further improve it using a new algorithm presentedin this thesis.

    The second problem is optimization of time-consuming problems where the objective function is seen as a black box, where the input parameters are sent and a function valueis returned. This has the important implication that no gradient or Hessian information is available. Such problems are common when simulators are used to perform advanced calculations such as crash test simulations of cars, dynamic multibody simulations etc. It is common that a single function evaluation takes several hours.

    Algorithms for solving such problems can be broadly divided into direct search algorithms and model building algorithms. The first kind evaluates the objective function directly, whereas the second kind builds a model of the objective function, which is then optimized in order to find a new point where it is believed that objective function has agood value. Then the objective function is evaluated in that point.

    Since the objective function is very time-consuming, it is common to focus on minimizing the number of function evaluations. However, this completely disregards the possibility to perform calculations in parallel and to exploit this we investigate different ways parallelization can be used in model-building algorithms. Some of the ways to do this is to use several starting points, generate several new points in each iteration, new ways of predicting a point’s value and more.

    We have implemented the parallel extensions in one of the state of the art algorithms for derivative-free optimization and report results from testing on synthetic benchmarksas well as from solving real industrial problems.

    Ladda ner fulltext (pdf)
    Methods for Network Optimization and Parallel Derivative-free Optimization
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    omslag
  • 277.
    Olsson, Per-Magnus
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för datavetenskap, KPLAB - Laboratoriet för kunskapsbearbetning. Linköpings universitet, Matematiska institutionen, Optimeringslära.
    Practical Pathfinding in Dynamic Environments2008Ingår i: AI Game Programming Wisdom 4 / [ed] Steve Rabin, Boston: Charles River , 2008, 1, s. -699Kapitel i bok, del av antologi (Övrigt vetenskapligt)
    Abstract [en]

    Welcome to the latest volume of AI Game Programming Wisdom! AI Game Programming Wisdom 4 includes a collection of more than 50 new articles featuring cutting-edge techniques, algorithms, and architectures written by industry professionals for use in commercial game development. Organized into 7 sections, this comprehensive volume explores every important aspect of AI programming to help you develop and expand your own personal AI toolbox. You'll find ready-to-use ideas, algorithms, and code in all key AI areas including general wisdom, scripting and dialogue, movement and pathfinding, architecture, tactics and planning, genre specific, and learning and adaptation. New to this volume are articles on recent advances in realistic agent, squad, and vehicle movement, as well as dynamically changing terrain, as exemplified in such popular games as Company of Heroes.You'll also find information on planning as a key game architecture, as well as important new advances in learning algorithms and player modeling. AI Game Programming Wisdom 4 features coverage of multiprocessor architectures, Bayesian networks, planning architectures, conversational AI, reinforcement learning, and player modeling.These valuable and innovative insights and issues offer the possibility of new game AI experiences and will undoubtedly contribute to taking the games of tomorrow to the next level.

  • 278.
    Olsson, Per-Magnus
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Test Results from Parallelization of Model Building Algorithms for Derivative-free Optimization2014Rapport (Övrigt vetenskapligt)
    Abstract [en]

    We present results from testing of parallel versions of algorithms for derivativefree optimization. Such algorithms are required when an analytical expression for the objective function is not available, which often happens in simulator-driven product development. Since the objective function is unavailable, we cannot use the common algorithms that require gradient and Hessian information. Instead special algorithms for derivative-free optimization are used. Such algorithms are typically sequential, and here we present the rst test results of parallelization of such algorithms. The parallel extensions include using several start points, generating several points from each start point in each iteration, alternative model building, and more. We also investigate whether we can generate synergy between the di erent start points through information sharing. Examples of this include using several models to predict the objective function value of a point in order to prioritize the order in which points are sent for evaluation. We also present results for higher-level control of the optimization algorithms.

    Ladda ner fulltext (pdf)
    LiTH-MAT-R--2014/02--SE
  • 279.
    Olsson, Per-Magnus
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Holmberg, Kaj
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Exploiting parallelization and synergy in derivative free optimization2020Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Real life optimization often concerns difficult objective functions, in two aspects, namely that gradients are unavailable, and that evaluation of the objective function takes a long time. Such problems are often attacked with model building algorithms, where an approximation of the function is constructed and solved, in order to find a new promising point to evaluate. We study several ways of saving time by using parallel calculations in the context of model building algorithms, which is not trivial, since such algorithms are inherently sequential. We present a number of ideas that has been implemented and tested on a large number of known test functions, and a few new ones. The computational results reveal that some ideas are quite promising.

    Ladda ner fulltext (pdf)
    fulltext
  • 280.
    Olsson, Per-Magnus
    et al.
    Linköpings universitet, Institutionen för datavetenskap, KPLAB - Laboratoriet för kunskapsbearbetning. Linköpings universitet, Tekniska högskolan.
    Kvarnström, Jonas
    Linköpings universitet, Institutionen för datavetenskap, KPLAB - Laboratoriet för kunskapsbearbetning. Linköpings universitet, Tekniska högskolan.
    Doherty, Patrick
    Linköpings universitet, Institutionen för datavetenskap, KPLAB - Laboratoriet för kunskapsbearbetning. Linköpings universitet, Tekniska högskolan.
    Burdakov, Oleg
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Holmberg, Kaj
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Generating UAV Communication Networks for Monitoring and Surveillance2010Ingår i: Proceedings of the 11th International Conference on Control, Automation, Robotics and Vision (ICARCV 2010), IEEE conference proceedings , 2010, s. 1070-1077Konferensbidrag (Refereegranskat)
    Abstract [en]

    An important use of unmanned aerial vehicles is surveillance of distant targets, where sensor information must quickly be transmitted back to a base station. In many cases, high uninterrupted bandwidth requires line-of-sight between sender and transmitter to minimize quality degradation. Communication range is typically limited, especially when smaller UAVs are used. Both problems can be solved by creating relay chains for surveillance of a single target, and relay trees for simultaneous surveillance of multiple targets. In this paper, we show how such chains and trees can be calculated. For relay chains we create a set of chains offering different trade-offs between the number of UAVs in the chain and the chain’s cost. We also show new results on how relay trees can be quickly calculated and then incrementally improved if necessary. Encouraging empirical results for improvement of relay trees are presented.

  • 281.
    Olsson, Sam
    Linköpings universitet, Matematiska institutionen, Optimeringslära.
    Klassificeringsmodeller för transportproblemet2019Självständigt arbete på grundnivå (kandidatexamen), 10,5 poäng / 16 hpStudentuppsats (Examensarbete)
    Abstract [sv]

    Det klassiska transportproblemet är ett linjärt och kontinuerligt optimeringsproblem vilket vanligtvis kan lösas till optimalitet snabbt och effektivt med t.ex. simplex-metoden. Men väldigt stora instanser (> 10 000 000 variabler) är minneskrävande och tar lång tid att lösa även för state-of-the-art lösare.Syftet med undersökningen är att hitta ett eller flera sätt att skatta det optimala målfunktionsvärdet för transportproblemet utan att lösa problemet. Olika nyckeltal och karakteristika för probleminstanser till transportproblemet har tagits fram, och dessa har sedan använts för att ta fram linjära regressionsmodeller. För att få en helhetsbild av hur funktionerna och nyckeltalen fungerar på transportproblemet skapas ett antal extremfall. Dessa extremfall är olika sätt att placera ut noder. Resultatet visar att linjär regression inte är tillräckligt för att lösa problemet i samtliga fall. Vi ser dock att det är möjligt att hitta bra skattningar till det optimala målfuntionsvärdet i vissa specialfall.

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    fulltext
  • 282.
    Onnheim, Magnus
    et al.
    Chalmers, Sweden; University of Gothenburg, Sweden.
    Gustavsson, Emil
    Chalmers, Sweden; University of Gothenburg, Sweden.
    Stromberg, Ann-Brith
    Chalmers, Sweden; University of Gothenburg, Sweden.
    Patriksson, Michael
    Chalmers, Sweden; University of Gothenburg, Sweden.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Ergodic, primal convergence in dual subgradient schemes for convex programming, II: the case of inconsistent primal problems2017Ingår i: Mathematical programming, ISSN 0025-5610, E-ISSN 1436-4646, Vol. 163, nr 1-2, s. 57-84Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Consider the utilization of a Lagrangian dual method which is convergent for consistent convex optimization problems. When it is used to solve an infeasible optimization problem, its inconsistency will then manifest itself through the divergence of the sequence of dual iterates. Will then the sequence of primal subproblem solutions still yield relevant information regarding the primal program? We answer this question in the affirmative for a convex program and an associated subgradient algorithm for its Lagrange dual. We show that the primal-dual pair of programs corresponding to an associated homogeneous dual function is in turn associated with a saddle-point problem, in which-in the inconsistent case-the primal part amounts to finding a solution in the primal space such that the Euclidean norm of the infeasibility in the relaxed constraints is minimized; the dual part amounts to identifying a feasible steepest ascent direction for the Lagrangian dual function. We present convergence results for a conditional epsilon-subgradient optimization algorithm applied to the Lagrangian dual problem, and the construction of an ergodic sequence of primal subproblem solutions; this composite algorithm yields convergence of the primal-dual sequence to the set of saddle-points of the associated homogeneous Lagrangian function; for linear programs, convergence to the subset in which the primal objective is at minimum is also achieved.

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    fulltext
  • 283. Beställ onlineKöp publikationen >>
    Palmgren, Myrna
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Optimal Truck Scheduling: Mathematical Modeling and Solution by the Column Generation Principle2005Doktorsavhandling, monografi (Övrigt vetenskapligt)
    Abstract [en]

    We consider the daily transportation problem in forestry which arises when transporting logs from forest sites to customers such as sawmills and pulp and paper mills. Each customer requires a specific amount of a certain assortment, and the deliveries to the customers can be made within time intervals, known as time windows. Further, there are a number of supply points, each with a certain assortment, and a number of vehicles of a given capacity, to be used for transport.

    The log truck scheduling problem consists of finding a set of minimal costs routes, one for each vehicle, such that the customers’ demands are satisfied without exceeding the supplies available at the supplies. Each route has to satisfy a number of constraints concerning time windows, truck capacity, timetable of the driver, lunch breaks, et cetera. The model used to describe the log truck scheduling problem is based on the route concept, and each variable, or column, represents one feasible route. Since the number of feasible routes is huge, we work only with restricted versions of this problem, which are similar to restricted master problems in a Dantzig-Wolfe decomposition scheme.

    We use three solution methods based on the column generation principle, together with a pool strategy which allows us to deal with the feasible routes outside the restricted master problem. The three methods proposed have a common structure; they use branch-andprice together with a column generator, followed by branch-and-bound. The column generators in the three methods differ. In the first method, the subproblem is based on a cluster-first-route-second strategy. The column generator in the second method involves solving a constrained shortest path problem, and finally, the third method builds on a repeated generation of clusters and routes.

    The three methods are tested on real cases from Swedish forestry companies, and the third method has been adapted to a computerised system that utilises the Swedish national road data base, for computing travelling distances. The results obtained show that the optimisation methods succeed in finding significantly better solutions than those obtained by manual planning, and in a reasonable computing time.

    Ladda ner fulltext (pdf)
    FULLTEXT01
  • 284.
    Palmgren, Myrna
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Optimeringslära.
    Rönnqvist, Mikael
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Optimeringslära.
    RuttOpt - an operative transportation planning system2003Ingår i: The 2003 Symposium for Systems Analysis in Forest Resources,2003, 2003Konferensbidrag (Övrigt vetenskapligt)
  • 285.
    Palmgren, Myrna
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Optimeringslära.
    Rönnqvist, Mikael
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Optimeringslära.
    Ryan, David
    A hybrid column generation method for log truck scheduling2003Ingår i: ROUTE2003,2003, 2003Konferensbidrag (Övrigt vetenskapligt)
  • 286.
    Palmgren, Myrna
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Optimeringslära.
    Rönnqvist, Mikael
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Optimeringslära.
    Ryan, David
    Solving truck scheduling problems with branch and price2003Ingår i: ISMP 2003,2003, 2003Konferensbidrag (Övrigt vetenskapligt)
  • 287.
    Palmgren, Myrna
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Optimeringslära.
    Rönnqvist, Mikael
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Optimeringslära.
    Värbrand, Peter
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för teknik och naturvetenskap.
    A near-exact method for solving the log-truck scheduling problem2004Ingår i: International Transactions in Operational Research, ISSN 0969-6016, E-ISSN 1475-3995, Vol. 11, nr 4, s. 447-464Artikel i tidskrift (Refereegranskat)
  • 288.
    Palmgren, Myrna
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Optimeringslära.
    Rönnqvist, Mikael
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Optimeringslära.
    Värbrand, Peter
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för teknik och naturvetenskap.
    A solution approach for log truck scheduling based on composite pricing and branch and bound2003Ingår i: International Transactions in Operational Research, ISSN 0969-6016, E-ISSN 1475-3995, Vol. 10, s. 433-447Artikel i tidskrift (Refereegranskat)
  • 289.
    Pavski, Johann Joachim
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Handover Optimization in GSM2015Självständigt arbete på avancerad nivå (masterexamen), 20 poäng / 30 hpStudentuppsats (Examensarbete)
    Abstract [en]

    In telecommunications in general and in GSM in particular, the handover is a feature that guarantees a smooth transition of a call from one base station - that is for the purpose of this project an antenna - to another. In the recent ten years, the amount of data traffic through mobile telecommunications has doubled annually, putting an enormous strain on the network and forcing operators to upgrade with more and more base stations and new features. Although 3G and 4G are responsible for data traffic in most countries, GSM still provides more than 80% of the coverage for mobile devices around the world. Due to the increase in data traffic, 3G and 4G need to use more and more frequencies at the expense of GSM. An optimization of the GSM network is thus vital. In this project, we research two methods to automatically choose the parameters of interest (PoI) that govern the handover feature in each cell which is, roughly speaking, the area of coverage of one antenna. In one of these methods, the choice of cell- and cell-to-cell-specific parameters has its origins in control theory while the other method is based on mathematical optimization. In the mathematical sense, our goal is to optimize the quality of service over PoIs. Extensive simulations have been run using these PoIs in order to evaluate if and how the two different methods can effectively be used in reality. Several useful insights have been gained that will provide the basis for future work. The optimization approach in particular has proved to deliver good results within the limitations of the simulated environment used for testing.

    Ladda ner fulltext (pdf)
    Handover Optimization in GSM
  • 290.
    Persson, Fredrik
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Institutionen för teknik och naturvetenskap.
    Engevall, Stefan
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Optimeringslära.
    The Shift from Construction Site to Prefabrication in the Construction Industry: A Case Study2008Ingår i: Advances in Production Management Systems,2008, Espoo, Finland: Espoo , 2008Konferensbidrag (Refereegranskat)
  • 291.
    Persson, Jan A.
    et al.
    Blekinge Institute of Technology.
    Göthe-Lundgren, Maud
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Optimeringslära.
    Shipment planning at oil refineries using column generation and valid inequalities2005Ingår i: European Journal of Operational Research, ISSN 0377-2217, E-ISSN 1872-6860, Vol. 163, nr 3, s. 631-652Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we suggest an optimization model and a solution method for a shipment planning problem. This problem concerns the simultaneous planning of how to route a fleet of ships and the planning of which products to transport in these ships. The ships are used for moving products from oil refineries to storage depots. There are inventory levels to consider both at the refineries and at the depots. The inventory levels are affected by the process scheduling at the refineries and demand at the depots. The problem is formulated using an optimization model including an aggregated representation of the process scheduling at the refineries. Hence, we integrate the shipment planning and the process scheduling at the refineries. We suggest a solution method based on column generation, valid inequalities, and constraint branching. The solution method is tested on data provided by the Nynas oil refinery company and solutions are obtained within 4 hours, for problem instances of up to 3 refineries, 15 depots, and 4 products when considering a time horizon of 42 days. © 2004 Elsevier B.V. All rights reserved.

  • 292.
    Persson, Jan
    et al.
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Optimeringslära.
    Göthe-Lundgren, Maud
    Linköpings universitet, Tekniska högskolan. Linköpings universitet, Matematiska institutionen, Optimeringslära.
    Lundgren, Jan
    Linköpings universitet, Institutionen för teknik och naturvetenskap. Linköpings universitet, Tekniska högskolan.
    Gendron, Bernard
    A tabu search heuristic for scheduling the production processes at an oil refinery2004Ingår i: International Journal of Production Research, ISSN 0020-7543, E-ISSN 1366-588X, Vol. 42, nr 3, s. 445-471Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    In this paper we present a tabu search heuristic which can be used for scheduling the production at an oil refinery. The scheduling problem is to decide which production modes to use at the different processing units at each point in time. The problem is a type of lot-sizing problem where costs of changeovers, inventories and production are considered. In the suggested tabu search heuristic we explore the use of variable neighbourhood, dynamic penalty and different tabu lists. Computational results are presented for different versions of the heuristic and the results are compared to the best-known lower bound for a set of scheduling scenarios.

  • 293.
    Powell, M.J.D.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Derivate Free Optimization2014Rapport (Övrigt vetenskapligt)
    Abstract [en]

    During the last ten years, the speaker has developed Fortran software for minimizing general objective functions when first derivatives are not available. He has released two packages, namely NEWUOA and UOBYQA, for the unconstrained case and for simple upper and lower bounds on the variables, respectively. His current research addresses general linear constraints on the variables, which is intended to provide the new LINCOA package. These algorithms require only of magnitude n squared operations on a typical iteration, where n is the number of variables, which has allowed them to be applied when n is in the hundreds. No attention is given to sparsity.

    Some excellent numerical results have been achieved, which certainly depend on the use of the symmetric Broyden updating formula. That formula when derivatives are not available is the subject of Lecture 1. It supplies the solution to the following variational problem. Some values of the objective function and a quadratic approximation to the objective function are given, where usually the approximation does not interpolate all the given function values. A new quadratic approximation is required that does interpolate the given function values. The freedom that remains in the new approximation is taken up by making as small as possible the Frobenius norm of the change to the second derivative  matrix of the approximation.

    A trust region in the space of the variables is the set of all points that are within a prescribed distance of the best point so far. A typical change to the vector of variables is a move from the best point so far to a new point within the trust region, the new point being chosen to provide a relatively small value of the current quadratic approximation to the objective function. The calculation of the new point is the subject of Lecture 2. A version of truncated conjugate gradients is employed, in order that the amount of work is only of magnitude n2. Several decisions had to be taken to specify an algorithm. They are particularly interesting for the LINCOA software, due to the linear constraints on the variables.

    Lectures 1 and 2 describe vital ingredients of the software that has been mentioned. A few more details are addressed in Lecture 3, to complete an outline of how the algorithms work. The numerical results from several test problems are considered too. The accuracy and efficiency are much better than expected if one takes the view that the second derivative matrix of the quadratic approximation should become close to the second derivative matrix of the objective function. We find clearly that this view is wrong. Also the numerical results show that good accuracy is achieved eventually, although the number of iterations is sometimes very sensitive to effects from computer rounding errors.

    Ladda ner fulltext (pdf)
    LiTH-MAT-R--2014/02--SE
  • 294. Beställ onlineKöp publikationen >>
    Quttineh, Nils-Hassan
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Models and Methods for Costly Global Optimization and Military Decision Support Systems2012Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    The thesis consists of five papers. The first three deal with topics within costly global optimization and the last two concern military decision support systems.

    The first part of the thesis addresses so-called costly problems where the objective function is seen as a “black box” to which the input parameter values are sent and a function value is returned. This means in particular that no information about derivatives is available. The black box could, for example, solve a large system of differential equations or carry out   timeconsuming simulation, where a single function evaluation can take several hours! This is the reason for describing such problems as costly and why they require customized algorithms. The goal is to construct algorithms that find a (near)-optimal solution using as few function evaluations as possible. A good example of a real life application comes from the automotive industry, where the development of new engines utilizes advanced mathematical models that are governed by a dozen key parameters. The objective is to optimize the engine by changing these parameters in such a way that it becomes as energy efficient as possible, but still meets all sorts of demands on strength and external constraints. The first three papers describe algorithms and implementation details for these costly global optimization problems.

    The second part deals with military mission planning, that is, problems that concern logistics, allocation and deployment of military resources. Given a fleet of resource, the decision problem is to allocate the resources against the enemy so that the overall mission success is optimized. We focus on the problem of the attacker and consider two separate problem classes. In the fourth paper we introduce an effect oriented planning approach to an advanced weapon-target allocation problem, where the objective is to maximize the expected outcome of a coordinated attack. We present a mathematical model together with efficient solution techniques. Finally, in the fifth paper, we introduce a military aircraft mission planning problem, where an aircraft fleet should attack a given set of targets. Aircraft routing is an essential part of the problem, and the objective is to maximize the expected mission success while minimizing the overall mission time. The problem is stated as a generalized vehicle routing model with synchronization and precedence side constraints.

    Delarbeten
    1. An adaptive radial basis algorithm (ARBF) for expensive black-box mixed-integer constrained global optimization
    Öppna denna publikation i ny flik eller fönster >>An adaptive radial basis algorithm (ARBF) for expensive black-box mixed-integer constrained global optimization
    2008 (Engelska)Ingår i: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 9, nr 3, s. 311-339Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    Response surface methods based on kriging and radial basis function (RBF) interpolationhave been successfully applied to solve expensive, i.e. computationally costly,global black-box nonconvex optimization problems.In this paper we describe extensions of these methods to handlelinear, nonlinear, and integer constraints.In particular, algorithms for standard RBF and the new adaptive RBF (ARBF) aredescribed.Note, however, while the objective function may be expensive, we assumethat any nonlinear constraints are either inexpensive or are incorporatedinto the objective function via penalty terms.Test results are presented on standard test problems, both nonconvexproblems with linear and nonlinear constraints, and mixed-integernonlinear problems (MINLP). Solvers in the TOMLAB OptimizationEnvironment (http://tomopt.com/tomlab/) have been compared,specifically the three deterministic derivative-free solversrbfSolve, ARBFMIP and EGO with three derivative-based mixed-integernonlinear solvers, OQNLP, MINLPBB and MISQP, as well as the GENOsolver implementing a stochastic genetic algorithm. Results showthat the deterministic derivative-free methods compare well with thederivative-based ones, but the stochastic genetic algorithm solver isseveral orders of magnitude too slow for practical use.When the objective function for the test problems is costly to evaluate,the performance of the ARBF algorithm proves to be superior.

    Ort, förlag, år, upplaga, sidor
    Springer, 2008
    Nyckelord
    Global optimization, radial basis functions, response surface model, surrogate model, expensive function, CPU-intensive, optimization software, splines, mixed-integer nonlinear programming, nonconvex, derivative-free, black-box, linear constraints, nonlinear constraints
    Nationell ämneskategori
    Beräkningsmatematik
    Identifikatorer
    urn:nbn:se:liu:diva-77076 (URN)10.1007/s11081-008-9037-3 (DOI)000259577400002 ()
    Tillgänglig från: 2012-05-04 Skapad: 2012-05-04 Senast uppdaterad: 2017-12-07Bibliografiskt granskad
    2. The Influence of Experimental Designs on the performance of surrogate model based costly global optimization solvers
    Öppna denna publikation i ny flik eller fönster >>The Influence of Experimental Designs on the performance of surrogate model based costly global optimization solvers
    2009 (Engelska)Ingår i: Studies in Informatics and Control, ISSN 1220-1766, E-ISSN 1841-429X, Vol. 18, nr 1, s. 87-95Artikel i tidskrift (Refereegranskat) Published
    Abstract [en]

    When dealing with costly objective functions in optimization, one good alternative is to use a surrogate model approach. A common feature for all such methods is the need of an initial set of points, or "experimental design", in order to start the algorithm. Since the behavior of the algorithms often depends heavily on this set, the question is how to choose a good experimental design. We investigate this by solving a number of problems using different designs, and compare the outcome with respect to function evaluations and a root mean square error test of the true function versus the surrogate model produced. Each combination of problem and design is solved by 3 different solvers available in the TOMLAB optimization environment. Results indicate two designs as superior.

    Ort, förlag, år, upplaga, sidor
    National Institute for R&D in Informatics (ICI), 2009
    Nyckelord
    Black-box, Surrogate model, Costly functions, Latin Hypercube Designs, Experimental Design
    Nationell ämneskategori
    Beräkningsmatematik
    Identifikatorer
    urn:nbn:se:liu:diva-77077 (URN)000269029600010 ()
    Tillgänglig från: 2012-05-04 Skapad: 2012-05-04 Senast uppdaterad: 2017-12-07Bibliografiskt granskad
    3. Implementation of a One-Stage Efficient Global Optimization (EGO) Algorithm
    Öppna denna publikation i ny flik eller fönster >>Implementation of a One-Stage Efficient Global Optimization (EGO) Algorithm
    2009 (Engelska)Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Almost every Costly Global Optimization (CGO) solver utilizes a surrogate model, or response surface, to approximate the true (costly) function. The EGO algorithm introduced by Jones et al. utilizes the DACE framework to build an approximating surrogate model. By optimizing a less costly utility function, the algorithm determines a new point where the original objective function is evaluated. This is repeated until some convergence criteria is fulfilled.The original EGO algorithm finds the new point to sample in a two-stage process. In its first stage, the estimates of the interpolation parameters are optimized with respect to already sampled points. In the second stage, these estimated values are considered true in order to optimize the location of the new point. The use of estimate values as correct introduces a source of error.Instead, in the one-stage EGO algorithm, both the parameters and the location of a new point are optimized at the same time, removing the source of error. This new subproblem becomes more difficult, but eliminates the need of solving two subproblems.Difficulties in implementing a fast and robust One-Stage EGO algorithm in TOMLAB are discussed, especially the solution of the new subproblem.

    Förlag
    s. 26
    Serie
    Research Report 2009, School of Education, Culture and Communication, Division of Applied Mathematics, Mälardalen University, ISSN 1404-4978 ; 2009:2
    Nyckelord
    Global Optimization, Costly, EGO
    Nationell ämneskategori
    Beräkningsmatematik
    Identifikatorer
    urn:nbn:se:liu:diva-77075 (URN)
    Tillgänglig från: 2012-05-04 Skapad: 2012-05-04 Senast uppdaterad: 2015-02-26Bibliografiskt granskad
    4. Effect Oriented Planning
    Öppna denna publikation i ny flik eller fönster >>Effect Oriented Planning
    2012 (Engelska)Rapport (Övrigt vetenskapligt)
    Abstract [en]

    The problem setting concerns the tactical planning of a military operation. Imagine a big wide open area where a number of interesting targets are positioned. It could be radar stations or other surveillance equipment, with or without defensive capabilities, which the attacker wishes to destroy. Moreover, the targets are possibly guarded by defending units, like Surface-to-Air Missile (SAM) units. The positions of all units, targets and defenders, are known. We consider the problem of the attacker, where the objective is to maximize the expected outcome of a joint attack against the enemy, subject to a limited amount of resources (i.e. aircraft, tanks). We present a mathematical model for this problem, together with alternative model versions which provide optimistic and a pessimistic approximations. The model is not efficient for large problem instances, hence we also provide heuristic solution approaches and successfully provide solutions to a number of scenarios.

    Förlag
    s. 90
    Serie
    LiTH-MAT-R, ISSN 0348-2960 ; 2012:6
    Nyckelord
    Targeting Problem, Weapon-Target Assignment, Military Operations Research, Decision Support
    Nationell ämneskategori
    Beräkningsmatematik
    Identifikatorer
    urn:nbn:se:liu:diva-77072 (URN)
    Tillgänglig från: 2012-05-04 Skapad: 2012-05-04 Senast uppdaterad: 2015-02-25Bibliografiskt granskad
    5. Aircraft Mission Planning
    Öppna denna publikation i ny flik eller fönster >>Aircraft Mission Planning
    2012 (Engelska)Rapport (Övrigt vetenskapligt)
    Abstract [en]

    This paper deals with a Military Aircraft Mission Planning Problem, where the problem is to find time efficient flight paths for a given aircraft fleet that should attack a number of ground targets. Due to the nature of the attack, two aircraft need to rendezvous at the target, that is, they need to be synchronized in both space and time. At the attack, one aircraft is launching a guided weapon, while the other is illuminating the target. Each target is associated with multiple attack and illumination options. Further, there may be precedence constraints between targets, limiting the order of the attacks. The objective is to maximize the outcome of the entire attack, while also minimizing the mission time span. We present two mathematical models for this problem and compare their efficiency on some small test cases. We also provide some heuristic approaches since direct application of a general MIP solver to the mathematical model is only practical for smaller scenarios. The heuristics are compared and they successfully provide solutions to a number of scenarios.

    Förlag
    s. 72
    Serie
    LiTH-MAT-R, ISSN 0348-2960 ; 2012:7
    Nyckelord
    Aircraft Routing, Generalized Vehicle Routing Problem, Precedence, Synchronization, Military Operations Research, Decision Support
    Nationell ämneskategori
    Beräkningsmatematik
    Identifikatorer
    urn:nbn:se:liu:diva-77074 (URN)
    Tillgänglig från: 2012-05-04 Skapad: 2012-05-04 Senast uppdaterad: 2015-02-25Bibliografiskt granskad
    Ladda ner fulltext (pdf)
    Models and Methods for Costly Global Optimization and Military Decision Support Systems
    Ladda ner (pdf)
    omslag
  • 295.
    Quttineh, Nils-Hassan
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Holmström, Kenneth
    Division of Applied mathematics, Mälardalen University, SE-721 23 Västerås, Sweden.
    Implementation of a One-Stage Efficient Global Optimization (EGO) Algorithm2009Rapport (Övrigt vetenskapligt)
    Abstract [en]

    Almost every Costly Global Optimization (CGO) solver utilizes a surrogate model, or response surface, to approximate the true (costly) function. The EGO algorithm introduced by Jones et al. utilizes the DACE framework to build an approximating surrogate model. By optimizing a less costly utility function, the algorithm determines a new point where the original objective function is evaluated. This is repeated until some convergence criteria is fulfilled.The original EGO algorithm finds the new point to sample in a two-stage process. In its first stage, the estimates of the interpolation parameters are optimized with respect to already sampled points. In the second stage, these estimated values are considered true in order to optimize the location of the new point. The use of estimate values as correct introduces a source of error.Instead, in the one-stage EGO algorithm, both the parameters and the location of a new point are optimized at the same time, removing the source of error. This new subproblem becomes more difficult, but eliminates the need of solving two subproblems.Difficulties in implementing a fast and robust One-Stage EGO algorithm in TOMLAB are discussed, especially the solution of the new subproblem.

  • 296.
    Quttineh, Nils-Hassan
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Häll, Carl Henrik
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska fakulteten.
    Ekström, Joakim
    Linköpings universitet, Institutionen för teknik och naturvetenskap, Kommunikations- och transportsystem. Linköpings universitet, Tekniska fakulteten.
    Ceder, Avi
    Department of Civil and Environmental Engineering, University of Auckland, New Zealand.
    Combined Timetabling and Vehicle Scheduling for Electric Buses2017Ingår i: Proceedings of the 22nd International Conference of Hong Kong Society for Transportation Studies (HKSTS), December 9-11, 2017, Hong Kong, China, Hong Kong: HKSTS , 2017, , s. 8Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    In this paper we present a novel mathematical model, integrating the timetabling and vehicle schedulingproblems for electric buses. The objective is to minimize the number of buses while satisfying constraintsconcerning routing and charging, including design choices of where to install charging equipment. Weillustrate the different effects of tackling the timetabling and vehicle scheduling of electric buses as separateproblems or as a joint problem, both for fixed and variable headways. To do so, tests are performed with: (i) given timetable, i.e. solving only the vehicle scheduling problem, (ii) fixed headways for each line, (iii) variable headways. For these tests, a small case based on four bidirectional bus lines is used.

  • 297.
    Quttineh, Nils-Hassan
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Military Aircraft Mission Planning: Efficient model-based metaheuristics approaches2015Ingår i: Optimization Letters, ISSN 1862-4472, E-ISSN 1862-4480, Vol. 9, nr 8, s. 1625-1639Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider a military mission planning problem where a given fleet of aircraft should attack a number of ground targets. At each attack, two aircraft need to be synchronized in both space and time. Further, there are multiple attack options against each targets, with different target effects. The objective is to maximize the outcome of the entire attack, while also minimizing the mission timespan. Real-life mission planning instances involve only a few targets and a few aircraft, but are still computationally challenging. We present metaheuristic solution methods for this problem, based on an earlier presented model. The problem includes three types of decisions: attack directions, task assignments and scheduling, and the solution methods exploit this structure in a two-stage approach. In an outer stage, a heuristic search is performed with respect to attack directions, while in an inner stage the other two decisions are optimized, given the outer stage decisions. The proposed metaheuristics are capable of producing high-quality solutions and are fast enough to be incorporated in a decision support tool.

    Ladda ner fulltext (pdf)
    fulltext
  • 298.
    Quttineh, Nils-Hassan
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Lundberg, Kristian
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Holmberg, Kaj
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Effect Oriented Planning of Joint Attacks2013Ingår i: Optimization Theory, Decision Making, and Operations Research Applications / [ed] Athanasios Migdalas, Angelo Sifaleras, Christos K. Georgiadis, Jason Papathanasiou, Emmanuil Stiakakis, Springer-Verlag New York, 2013, s. 49-70Konferensbidrag (Refereegranskat)
    Abstract [en]

    We consider tactical planning of a military operation on a large target scene where a number of specific targets of interest are positioned, using a given number of resources which can be, for example, fighter aircraft, unmanned aerial vehicles, or missiles. The targets could be radar stations or other surveillance equipment, with or without defensive capabilities, which the attacker wishes to destroy. Further, some of the targets are defended, by, for example, Surface-to-Air Missile units, and this defense capability can be used to protect also other targets. The attacker has knowledge about the positions of all the targets and also a reward associated with each target. We consider the problem of the attacker, who has the objective to maximize the expected outcome of a joint attack against the enemy. The decisions that can be taken by the attacker concern the allocation of the resources to the targets and what tactics to use against each target. We present a mathematical model for the attacker’s problem. The model is similar to a generalized assignment problem, but with a complex objective function that makes it intractable for large problem instances. We present approximate models that can be used to provide upper and lower bounds on the optimal value, and also provide heuristic solution approaches that are able to successfully provide near-optimal solutions to a number of scenarios.

  • 299.
    Quttineh, Nils-Hassan
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Lundberg, Kristian
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Holmberg, Kaj
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska högskolan.
    Military aircraft mission planning: a generalized vehicle routing model with synchronization and precedence2013Ingår i: EURO Journal on Transportation and Logistics, ISSN 2192-4376, E-ISSN 2192-4384, Vol. 2, nr 1-2, s. 109-127Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We introduce a military aircraft mission planning problem where agiven fleet of aircraft should attack a number of ground targets. Due to the nature of the attack, two aircraft need to rendez-vous at the target, that is, they need to be synchronized in both space and time. At the attack, one aircraft is launching a guided weapon, while the other is illuminating the target. Each target is associated with multiple attack and illumination options. Further, there may be precedence constraints between targets, limiting the order of the attacks. The objective is to maximize the outcome of the entire attack, while also minimizing the mission timespan. We give a linear mixed integer programming model of the problem, which can be characterized as ageneralized vehicle routing problem with synchronization and precedence side constraints. Numerical results are presented for problem instances of realistic size.

  • 300.
    Quttineh, Nils-Hassan
    et al.
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Larsson, Torbjörn
    Linköpings universitet, Matematiska institutionen, Optimeringslära. Linköpings universitet, Tekniska fakulteten.
    Van den Bergh, Jorne
    Katholieke University of Leuven, Belgium.
    Belien, Jeroen
    Katholieke University of Leuven, Belgium.
    A Time-Indexed Generalized Vehicle Routing Model and Stabilized Column Generation for Military Aircraft Mission Planning2015Ingår i: OPTIMIZATION, CONTROL, AND APPLICATIONS IN THE INFORMATION AGE: IN HONOR OF PANOS M. PARDALOSS 60TH BIRTHDAY, SPRINGER , 2015, Vol. 130, s. 299-314Konferensbidrag (Refereegranskat)
    Abstract [en]

    We introduce a time-indexed mixed-integer linear programming model for a military aircraft mission planning problem, where a fleet of cooperating aircraft should attack a number of ground targets so that the total expected effect is maximized. The model is a rich vehicle routing problem and the direct application of a general solver is practical only for scenarios of very moderate sizes. We propose a Dantzig-Wolfe reformulation and column generation approach. A column here represents a specific sequence of tasks at certain times for an aircraft, and to generate columns a longest path problem with side constraints is solved. We compare the column generation approach with the time-indexed model with respect to upper bounding quality of their linear programming relaxations and conclude that the former provides a much stronger formulation of the problem.

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