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Morén, B., Larsson, T. & Carlsson Tedgren, Å. (2019). An extended dose-volume model in high dose-rate brachytherapy: Using mean-tail-dose to reduce tumor underdosage. Medical physics (Lancaster), 46(6), 2556-2566
Open this publication in new window or tab >>An extended dose-volume model in high dose-rate brachytherapy: Using mean-tail-dose to reduce tumor underdosage
2019 (English)In: Medical physics (Lancaster), ISSN 0094-2405, Vol. 46, no 6, p. 2556-2566Article in journal (Refereed) Published
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.

Place, publisher, year, edition, pages
Wiley-Blackwell Publishing Inc., 2019
Keywords
cold volumes, CVaR, dose-volume model, dosimetric index, dwell time optimization, EUD, mean-tail-dose, TCP
National Category
Computational Mathematics Radiology, Nuclear Medicine and Medical Imaging
Identifiers
urn:nbn:se:liu:diva-157356 (URN)10.1002/mp.13533 (DOI)000471277705311 ()30972758 (PubMedID)2-s2.0-85065984130 (Scopus ID)
Funder
Swedish Research Council, VR-NT 2015-04543Swedish Cancer Society, CAN 2015/618
Note

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

Available from: 2019-06-12 Created: 2019-06-12 Last updated: 2019-07-15Bibliographically approved
Rönnberg, E. & Larsson, T. (2019). An integer optimality condition for column generation on zero-one linear programs. Discrete Optimization, 31, 79-92
Open this publication in new window or tab >>An integer optimality condition for column generation on zero-one linear programs
2019 (English)In: Discrete Optimization, ISSN 1572-5286, E-ISSN 1873-636X, Vol. 31, p. 79-92Article in journal (Refereed) Published
Abstract [en]

Column generation is a linear programming method that, when combined with appropriate integer programming techniques, has been successfully used for solving huge integer programs. The method alternates between a restricted master problem and a column generation subproblem. The latter step is founded on dual information from the former one; often an optimal dual solution to the linear programming relaxation of the restricted master problem is used.

We consider a zero–one linear programming problem that is approached by column generation and present a generic sufficient optimality condition for the restricted master problem to contain the columns required to find an integer optimal solution to the complete problem. The condition is based on dual information, but not necessarily on an optimal dual solution. It is however most natural to apply the condition in a situation when an optimal or near-optimal dual solution is at hand.

We relate our result to a few special cases from the literature, and make some suggestions regarding possible exploitation of the optimality condition in the construction of column generation methods for integer programs.

Place, publisher, year, edition, pages
Elsevier, 2019
Keywords
Zero–one linear programming, Integer linear programming, Discrete optimisation, Column generation, Optimality conditions
National Category
Computational Mathematics
Identifiers
urn:nbn:se:liu:diva-151698 (URN)10.1016/j.disopt.2018.09.001 (DOI)000461538300006 ()2-s2.0-85053921680 (Scopus ID)
Funder
Swedish Research Council, 621- 2005-2874
Note

Funding agencies Swedish Research Council [621-2005-2874]

Available from: 2018-10-02 Created: 2018-10-02 Last updated: 2019-04-01Bibliographically approved
John Mwakisisile, A., Larsson, T., Ohlson, M. & Mushi, A. (2018). Asset liability management for Tanzania pension funds by stochastic programming. Afrika Statistika
Open this publication in new window or tab >>Asset liability management for Tanzania pension funds by stochastic programming
2018 (English)In: Afrika Statistika, ISSN 2316-090XArticle in journal (Refereed) Submitted
National Category
Other Mathematics
Identifiers
urn:nbn:se:liu:diva-152118 (URN)
Available from: 2018-10-17 Created: 2018-10-17 Last updated: 2018-10-26Bibliographically approved
Rönnberg, E. & Larsson, T. (2018). Integral Simplex Methods for the Set Partitioning Problem: Globalisation and Anti-Cycling. In: Panos M. Pardalos, Athanasios Migdalas (Ed.), Open Problems in Optimization and Data Analysis: (pp. 285-303). Cham: Springer
Open this publication in new window or tab >>Integral Simplex Methods for the Set Partitioning Problem: Globalisation and Anti-Cycling
2018 (English)In: Open Problems in Optimization and Data Analysis / [ed] Panos M. Pardalos, Athanasios Migdalas, Cham: Springer, 2018, p. 285-303Chapter in book (Refereed)
Abstract [en]

The set partitioning problem is a generic optimisation model with many applications, especially within scheduling and routing. It is common in the context of column generation, and its importance has grown due to the strong developments in this field. The set partitioning problem has the quasi-integrality property, which means that every edge of the convex hull of the integer feasible solutions is also an edge of the polytope of the linear programming relaxation. This property enables, in principle, the use of solution methods that find improved integer solutions through simplex pivots that preserve integrality; pivoting rules with this effect can be designed in a few different ways. Although seemingly promising, the application of these approaches involves inherent challenges. Firstly, they can get be trapped at local optima, with respect to the pivoting options available, so that global optimality can be guaranteed only by resorting to an enumeration principle. Secondly, set partitioning problems are typically massively degenerate and a big hurdle to overcome is therefore to establish anti-cycling rules for the pivoting options available. The purpose of this chapter is to lay a foundation for research on these topics.

Place, publisher, year, edition, pages
Cham: Springer, 2018
Series
Springer Optimization and Its Applications, ISSN 1931-6828, E-ISSN 1931-6836 ; 141
Keywords
Quasi-integrality, Set partitioning, Integral simplex method, Anti-cycling rules
National Category
Computational Mathematics
Identifiers
urn:nbn:se:liu:diva-153425 (URN)10.1007/978-3-319-99142-9_15 (DOI)9783319991412 (ISBN)9783319991429 (ISBN)
Available from: 2018-12-14 Created: 2018-12-14 Last updated: 2018-12-18Bibliographically approved
Morén, B., Larsson, T. & Carlsson Tedgren, Å. (2018). Preventing Hot Spots in High Dose-Rate Brachytherapy. In: Kliewer, Natalia; Ehmke, Jan Fabian; Borndörfer, Ralf (Ed.), Operations Research Proceedings 2017: . Paper presented at Annual International Conference of the German Operations Research Society (GOR), Freie Universiät Berlin, Germany, September 6-8, 2017 (pp. 369-375). Springer International Publishing
Open this publication in new window or tab >>Preventing Hot Spots in High Dose-Rate Brachytherapy
2018 (English)In: Operations Research Proceedings 2017 / [ed] Kliewer, Natalia; Ehmke, Jan Fabian; Borndörfer, Ralf, Springer International Publishing , 2018, p. 369-375Conference paper, Published paper (Refereed)
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.

Place, publisher, year, edition, pages
Springer International Publishing, 2018
Series
Operations Research Proceedings, ISSN 0721-5924 ; 2017
National Category
Radiology, Nuclear Medicine and Medical Imaging
Identifiers
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)
Conference
Annual International Conference of the German Operations Research Society (GOR), Freie Universiät Berlin, Germany, September 6-8, 2017
Available from: 2019-03-07 Created: 2019-03-07 Last updated: 2019-03-07
John Mwakisisile, A., Larsson, T., Singull, M. & Mushi, A. (2017). Projecting Tanzania Pension Fund System. African Journal of Applied Statistics, 4(1), 193-218
Open this publication in new window or tab >>Projecting Tanzania Pension Fund System
2017 (English)In: African Journal of Applied Statistics, ISSN 2316-0861, Vol. 4, no 1, p. 193-218Article in journal (Refereed) 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.

Place, publisher, year, edition, pages
Afrika Statistika - SPAS, 2017
Keywords
Pension fund; Pay-as-you-go; Defined benefit; Demography
National Category
Probability Theory and Statistics
Identifiers
urn:nbn:se:liu:diva-143272 (URN)10.16929/ajas/2017.193.210 (DOI)
Note

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. 

Available from: 2017-11-28 Created: 2017-11-28 Last updated: 2018-08-31Bibliographically approved
Holm, Å., Carlsson Tedgren, Å. & Larsson, T. (2016). Heuristics for Integrated Optimization of Catheter Positioning and Dwell Time Distribution in Prostate HDR Brachytherapy. Annals of Operations Research, 236(2), 319-339
Open this publication in new window or tab >>Heuristics for Integrated Optimization of Catheter Positioning and Dwell Time Distribution in Prostate HDR Brachytherapy
2016 (English)In: Annals of Operations Research, ISSN 0254-5330, E-ISSN 1572-9338, Vol. 236, no 2, p. 319-339Article in journal (Refereed) Published
Abstract [en]

High dose-rate (HDR) brachytherapy is a kind of radiotherapy used to treat, among others, prostate cancer. When applied to prostate cancer a radioactive source is moved through catheters implanted into the prostate. For each patient a treatment plan is constructed that decide for example catheter placement and dwell time distribution, that is where to stop the radioactive source and for how long.

Mathematical optimization methods has been used to find quality plans with respect to dwell time distribution, however few optimization approaches regarding catheter placement have been studied. In this article we present an integrated optimization model that optimize catheter placement and dwell time distribution simultaneously. Our results show that integrating the two decisions yields greatly improved plans, from 15% to 94% improvement.

Since the presented model is computationally demanding to solve we also present three heuristics: tabu search, variable neighbourhood search and genetic algorithm. Of these variable neighbourhood search is clearly the best, outperforming a state-of-the-art optimization software (CPLEX) and the two other heuristics.

Place, publisher, year, edition, pages
Springer, 2016
Keywords
Brachytherapy, Dose planning, Catheter positioning, Mixed integer programming, Metaheuristics
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-67788 (URN)10.1007/s10479-013-1448-7 (DOI)000368946400003 ()
Available from: 2011-04-26 Created: 2011-04-26 Last updated: 2019-01-28Bibliographically approved
Zhao, Y., Larsson, T., Yuan, D., Rönnberg, E. & Lei, L. (2016). Power efficient uplink scheduling in SC-FDMA: benchmarking by column generation. Optimization and Engineering, 17(4), 695-725
Open this publication in new window or tab >>Power efficient uplink scheduling in SC-FDMA: benchmarking by column generation
Show others...
2016 (English)In: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 17, no 4, p. 695-725Article in journal (Refereed) Published
Abstract [en]

We study resource allocation in cellular systems and consider the problem of finding a power efficient scheduling in an uplink single carrier frequency division multiple access system. Due to the discrete nature of this problem and its computational difficulty, particularly in a real-time setting, the use of suboptimal algorithms is common practice. We aim at an effective way of gauging the performance of suboptimal algorithms by finding tight bounds on the global optimum. Toward this end, we first provide a basic integer linear programming formulation. Then we propose a significantly stronger column-oriented formulation and a corresponding column generation method, as well as an enhanced column generation scheme. The latter extends the first scheme through the inclusion of a stabilization technique, an approximate column generation principle, and a tailored heuristic that is embedded in the column generation scheme to find high-quality though not necessarily global optimal solutions. The computational evaluation demonstrates that compared with a poor performance by the integer linear programming formulation, the column generation method can produce near-optimal schedules that enable a sharp bounding interval. The enhanced column generation method significantly sharpens the bounding interval. Hence the column generation approach serves well for the purpose of benchmarking results for large-scale instances.

Place, publisher, year, edition, pages
Springer-Verlag New York, 2016
Keywords
Localized SC-FDMA, Stabilized column generation, Power minimization, Integer linear programming, Uplink scheduling, Matheuristic
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-127355 (URN)10.1007/s11081-015-9304-z (DOI)000387857500004 ()
Note

Funding agencies: Research School in Interdisciplinary Mathematics at Linkoping University; Excellence Center at Linkoping - Lund in Information Technology, Centrum for Industriell Informationsteknologi, Linkoping University, EC FP7 Marie Curie Project [318992]; Chinese Sc

Available from: 2016-04-22 Created: 2016-04-22 Last updated: 2019-08-06Bibliographically approved
Larsson, T. & Patriksson, M. (2016). Subbens checklist. Computers & Operations Research, 71, 163-164
Open this publication in new window or tab >>Subbens checklist
2016 (English)In: Computers & Operations Research, ISSN 0305-0548, E-ISSN 1873-765X, Vol. 71, p. 163-164Article in journal (Refereed) Published
Abstract [en]

Excellent guides on academic writing and presentation in science in general, and in mathematics and computer science in particular, do abound (see, for example, Refs. [1-8], while guides on the assessment of the results of academic writing are rather more scarce. This short article presents two itemized lists that may be helping hands during the assessment of a scientific article in the field of mathematical optimization and operations research-be it your own, a work by a Master or PhD student of yours, or even a manuscript that you are refereeing for a scientific journal or conference proceedings volume. The first list-"Subbens checklist"-describes necessary ingredients of a complete article. The second list provides criteria for assessing the quality and scientific value of an article. (C) 2016 Elsevier Ltd. All rights reserved.

Place, publisher, year, edition, pages
PERGAMON-ELSEVIER SCIENCE LTD, 2016
Keywords
Academic writing; Editing; Evaluation
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-128918 (URN)10.1016/j.cor.2016.02.004 (DOI)000374602800014 ()
Available from: 2016-06-09 Created: 2016-06-07 Last updated: 2017-11-30
Mayambala, F., Rönnberg, E. & Larsson, T. (2016). Tight Upper Bounds on the Cardinality Constrained Mean-Variance Portfolio Optimization Problem Using Truncated Eigendecomposition. In: Marco Lübbecke, Arie Koster, Peter Letmathe, Reinhard Madlener, Britta Peis and Grit Walther (Ed.), 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. Paper presented at Annual International Conference of the German Operations Research Society (GOR), RWTH Aachen University, Germany, September 2-5, 2014 (pp. 385-392). Springer
Open this publication in new window or tab >>Tight Upper Bounds on the Cardinality Constrained Mean-Variance Portfolio Optimization Problem Using Truncated Eigendecomposition
2016 (English)In: 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, p. 385-392Conference paper, Published paper (Refereed)
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.

Place, publisher, year, edition, pages
Springer, 2016
Series
Operations Research Proceedings, ISSN 0721-5924
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-118359 (URN)10.1007/978-3-319-28697-6_54 (DOI)9783319286952 (ISBN)9783319286976 (ISBN)
Conference
Annual International Conference of the German Operations Research Society (GOR), RWTH Aachen University, Germany, September 2-5, 2014
Available from: 2015-05-27 Created: 2015-05-27 Last updated: 2018-06-25Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-2094-7376

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