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  • 1.
    Blikstad, Mathias
    et al.
    Saab AB, Sweden.
    Karlsson, Emil
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Lööw, Tomas
    Saab AB, Sweden.
    Rönnberg, Elina
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    A constraint generation procedure for pre-runtime scheduling of integrated modular avionic systems2017In: Proceedings of the 13th Workshop on Models and Algorithms for Planning and Scheduling Problems / [ed] Susanne Albers, Nicole Megow, Andreas S. Schulz, Leen Stougie, 2017Conference paper (Other academic)
    Abstract [en]

    In modern integrated modular avionic systems, applications share hardware resources on a common avionic platform. Such an architecture necessitates strict requirements on the spatial and temporal partitioning of the system to prevent fault propagation between different aircraft functions. One way to establish a temporal partitioning is through pre-runtime scheduling of the system, which involves creating a schedule for both tasks and a communication network.

    While the avionic systems are growing more and more complex, so is the challenge of scheduling them. Scheduling of the system has an important role in the development of new avionic systems since functionality typically is added to the system over a period of several years and a scheduling tool is used both to detect if the platform can host the new functionality and, in case this is possible, to create a new schedule. For this reason an exact solution strategy for avionics scheduling is preferred over a heuristic one.

    In this paper we present a mathematical model for an industrially relevant avionic system and present a constraint generation  procedure for scheduling of such systems. We apply our optimisation approach to instances provided by our industrial partner. These instances are of relevance for the development of future avionic systems and contain up to 20 000 tasks to be scheduled. The computational results show that our optimisation approach can be used to create schedules for such instances within reasonable time.

  • 2.
    Blikstad, Mathias
    et al.
    Saab AB, Sweden.
    Karlsson, Emil
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Lööw, Tomas
    Saab AB, Sweden.
    Rönnberg, Elina
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    An Optimisation Approach for Pre-Runtime Scheduling of Tasks and Communication in an Integrated Modular Avionic System2017Report (Other academic)
    Abstract [en]

    In modern integrated modular avionic systems, applications share hardware resources on a common avionic platform. Such an architecture necessitates strict requirements on the spatial and temporal partitioning of the system to prevent fault propagation between different aircraft functions. One way to establish a temporal partitioning is through pre-runtime scheduling of the system, which involves creating a schedule for both tasks and a communication network.

    While the avionic systems are growing more and more complex, so is the challenge of scheduling them. Scheduling of the system has an important role in the development of new avionic systems since functionality typically is added to the system over a period of several years and a scheduling tool is used both to detect if the platform can host the new functionality and, in case this is possible, to create a new schedule. For this reason an exact solution strategy for avionics scheduling is preferred over a heuristic one.

    In this paper we present a mathematical model for an industrially relevant avionic system and present a constraint generation  procedure for scheduling of such systems. We apply our optimisation approach to instances provided by our industrial partner. These instances are of relevance for the development of future avionic systems and contain up to 20 000 tasks to be scheduled. The computational results show that our optimisation approach can be used to create schedules for such instances within reasonable time.

  • 3.
    Blikstad, Mathias
    et al.
    Saab AB, Linköping, Sweden.
    Karlsson, Emil
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering. Saab AB, Linköping, Sweden.
    Lööw, Tomas
    Saab AB, Linköping, Sweden.
    Rönnberg, Elina
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering. Saab AB, Linköping, Sweden.
    An optimisation approach for pre-runtime scheduling of tasks and communication in an integrated modular avionic system2018In: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 19, no 4, p. 977-1004Article in journal (Refereed)
    Abstract [en]

    In modern integrated modular avionic systems, applications share hardware resources on a common avionic platform. Such an architecture necessitates strict requirements on the spatial and temporal partitioning of the system to prevent fault propagation between different aircraft functions. One way to establish a temporal partitioning is through pre-runtime scheduling of the system, which involves creating a schedule for both tasks and a communication network. While avionic systems are growing more and more complex, so is the challenge of scheduling them. The scheduling of the system has an important role in the development of new avionic systems, since functionality is typically added to the system over a period of several years and a scheduling tool is used both to detect if the platform can host the new functionality and, if this is possible, to create a new schedule. For this reason an exact solution strategy for avionics scheduling is preferred over a heuristic one. In this paper we present a mathematical model for an industrially relevant avionic system and present a constraint generation procedure for the scheduling of such systems. We apply our optimisation approach to instances provided by our industrial partner. These instances are of relevance for the development of future avionic systems and contain up to 20,000 tasks to be scheduled. The computational results show that our optimisation approach can be used to create schedules for such instances within a reasonable time.

  • 4.
    Karlsson, Emil
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, The Institute of Technology.
    Explicit Estimators for a Banded Covariance Matrix in a Multivariate Normal Distribution2014Independent thesis Basic level (degree of Bachelor), 10,5 credits / 16 HE creditsStudent thesis
    Abstract [en]

    The problem of estimating mean and covariances of a multivariate normal distributedrandom vector has been studied in many forms. This thesis focuses on the estimatorsproposed in [15] for a banded covariance structure with m-dependence. It presents theprevious results of the estimator and rewrites the estimator when m = 1, thus makingit easier to analyze. This leads to an adjustment, and a proposition for an unbiasedestimator can be presented. A new and easier proof of consistency is then presented.This theory is later generalized into a general linear model where the correspondingtheorems and propositions are made to establish unbiasedness and consistency. In thelast chapter some simulations with the previous and new estimator verifies that thetheoretical results indeed makes an impact.

  • 5.
    Karlsson, Emil
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Optimisation-based scheduling of an avionic system2019Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    Modern computer systems in aircraft are often based on an integrated modular avionic architecture. In this architecture, software applications share hardware resources on a common avionic platform. Many functions in an aircraft are controlled by software and a failure in such software can have severe consequences. In order to avoid malfunction, there are many aspects to consider. One aspect is to ensure that the activities in the system is done at the right time with the right resources. To analyse if this is possible or not is often called schedulability analysis.

    When multiple functions are using the same resources, the schedulability analysis becomes increasingly challenging. This thesis focuses on a pre-runtime scheduling problem of an integrated modular avionic system proposed by our industrial partner Saab. The purpose of this problem is to find a feasible schedule or prove that none exists as part of a schedulability analysis.

    For the system that we study, there are two major challenges. One is that task and communication scheduling are integrated and the other is that there is a large amount of tasks to schedule. For the largest instances, there are more than 10 000 tasks on a single module. In order to solve such problems, we have developed a matheuristic. At the core of this matheuristic is a constraint generation procedure designed to handle the challenges of the scheduling problem.

    The constraint generation procedure is based on first making a relaxed scheduling decision and then evaluating this in a separate problem where a complete schedule is produced. This yields a decomposition where most technical details are considered in the relaxed problem, and the actual scheduling of tasks is handled in a subproblem. Both the relaxed problem and the subproblem are formulated and solved as mixed integer programs.

    The heuristic component of the matheuristic is that the relaxed problem is solved using an adaptive large neighbourhood search method. Instead of solving the relaxed problem as a single mixed integer program, the adaptive large neighbourhood search explores neighbourhoods through solving a series of mixed integer programs. Features of this search method are that it is made over both discrete and continuous variables and it needs to balance feasibility against profitable objective value.

    The matheuristic described in this thesis has been implemented in a scheduling tool. This scheduling tool has been applied to instances provided by our industrial partner and to a set of public instances that we have developed. With this tool, we have solved instances with more than 45 000 tasks.

    List of papers
    1. An optimisation approach for pre-runtime scheduling of tasks and communication in an integrated modular avionic system
    Open this publication in new window or tab >>An optimisation approach for pre-runtime scheduling of tasks and communication in an integrated modular avionic system
    2018 (English)In: Optimization and Engineering, ISSN 1389-4420, E-ISSN 1573-2924, Vol. 19, no 4, p. 977-1004Article in journal (Refereed) Published
    Abstract [en]

    In modern integrated modular avionic systems, applications share hardware resources on a common avionic platform. Such an architecture necessitates strict requirements on the spatial and temporal partitioning of the system to prevent fault propagation between different aircraft functions. One way to establish a temporal partitioning is through pre-runtime scheduling of the system, which involves creating a schedule for both tasks and a communication network. While avionic systems are growing more and more complex, so is the challenge of scheduling them. The scheduling of the system has an important role in the development of new avionic systems, since functionality is typically added to the system over a period of several years and a scheduling tool is used both to detect if the platform can host the new functionality and, if this is possible, to create a new schedule. For this reason an exact solution strategy for avionics scheduling is preferred over a heuristic one. In this paper we present a mathematical model for an industrially relevant avionic system and present a constraint generation procedure for the scheduling of such systems. We apply our optimisation approach to instances provided by our industrial partner. These instances are of relevance for the development of future avionic systems and contain up to 20,000 tasks to be scheduled. The computational results show that our optimisation approach can be used to create schedules for such instances within a reasonable time.

    Keywords
    Avionic system Scheduling Discrete optimisation Integer programming Multiprocessor scheduling Constraint generation
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-148854 (URN)10.1007/s11081-018-9385-6 (DOI)000447870700007 ()
    Note

    Funding agencies: Swedish Armed Forces; Swedish Defence Materiel Administration; Swedish Governmental Agency for Innovation Systems [NFFP6-2014-00917]; Center for Industrial Information Technology (CENIIT); Research School in Interdisciplinary Mathematics at Linkoping Univ

    Available from: 2018-06-20 Created: 2018-06-20 Last updated: 2019-05-24
    2. Explicit modelling of multiple intervals in a constraint generation procedure for multiprocessor scheduling
    Open this publication in new window or tab >>Explicit modelling of multiple intervals in a constraint generation procedure for multiprocessor scheduling
    2017 (English)In: Operations Research Proceedings 2017 / [ed] N. Kliewer, J.F. Ehmke and R. Borndörfer, Springer, 2017, p. 567-572Conference paper, Published paper (Refereed)
    Abstract [en]

    Multiprocessor scheduling is a well studied NP-hard optimisation problem that occurs in variety of forms. The focus of this paper is explicit modelling of multiple task intervals. This work extends a constraint generation procedure previously developed for an avionics scheduling context. We here address a relaxation of the original problem and this relaxation can be considered as multiprocessor scheduling with precedence relations and multiple intervals.

    The explicit modelling of multiple intervals strengthens the formulation used in the constraint generation procedure and we illustrate the computational effects on an industrial relevant avionics scheduling problem.

    Place, publisher, year, edition, pages
    Springer, 2017
    Series
    Operations Research Proceedings, ISSN 0721-5924
    Keywords
    multiprocessor scheduling, multiple intervals, avionics scheduling and constraint generation
    National Category
    Computational Mathematics
    Identifiers
    urn:nbn:se:liu:diva-143021 (URN)10.1007/978-3-319-89920-6_75 (DOI)978-3-319-89919-0 (ISBN)978-3-319-89920-6 (ISBN)
    Conference
    Operations Research 2017, Freie Universität Berlin, Berlin, Germany, September 6-8, 2017
    Available from: 2017-11-16 Created: 2017-11-16 Last updated: 2019-05-24Bibliographically approved
    3. A matheuristic approach to large-scale avionic scheduling
    Open this publication in new window or tab >>A matheuristic approach to large-scale avionic scheduling
    2019 (English)Report (Other academic)
    Abstract [en]

    Pre-runtime scheduling of avionic systems is used to ensure that the systems provide the desired functionality at the correct time. This paper considers scheduling of an integrated modular avionic system which from a more general perspective can be seen as a multiprocessor scheduling problem that includes a communication network. The addressed system is practically relevant and the computational evaluations are made on large-scale instances developed together with the industrial partner Saab. A subset of the instances is made publicly available.

    Our contribution is a matheuristic for solving these large-scale instances and it is obtained by improving the model formulations used in a previously suggested constraint generation procedure and by including an adaptive large neighbourhood search to extend it into a matheuristic. Characteristics of our adaptive large neighbourhood search are that it is made over both discrete and continuous variables and that it needs to balance the search for feasibility and profitable objective value. The repair operation is to apply a mixed-integer programming solver on a model where most of the constraints are treated as soft and a violation of them is instead penalised in the objective function. The largest solved instance, with respect to the number of tasks, has 45 988 tasks and 2 011 communication messages.

    Place, publisher, year, edition, pages
    Linköping: Linköping University Electronic Press, 2019. p. 40
    Series
    LiTH-MAT-R, ISSN 0348-2960 ; 2019:2
    Keywords
    Multiprocessor scheduling; avionic system; matheuristic; adaptive large neighbourhood search; integer programming; scheduling
    National Category
    Mathematics
    Identifiers
    urn:nbn:se:liu:diva-157140 (URN)LiTH-MAT-R--2019/02--SE (ISRN)
    Available from: 2019-05-29 Created: 2019-05-29 Last updated: 2019-05-29
  • 6.
    Karlsson, Emil
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    The unweighted mean estimator in a Growth Curve model2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis
    Abstract [en]

    The field of statistics is becoming increasingly more important as the amount of data in the world grows. This thesis studies the Growth Curve model in multivariate statistics which is a model that is not widely used. One difference compared with the linear model is that the Maximum Likelihood Estimators are more complicated. That makes it more difficult to use and to interpret which may be a reason for its not so widespread use.

    From this perspective this thesis will compare the traditional mean estimator for the Growth Curve model with the unweighted mean estimator. The unweighted mean estimator is simpler than the regular MLE. It will be proven that the unweighted estimator is in fact the MLE under certain conditions and examples when this occurs will be discussed. In a more general setting this thesis will present conditions when the un-weighted estimator has a smaller covariance matrix than the MLEs and also present confidence intervals and hypothesis testing based on these inequalities.

  • 7.
    Karlsson, Emil
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering. Saab AB, Linköping, Sweden.
    Rönnberg, Elina
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering. Saab AB, Linköping, Sweden.
    Explicit modelling of multiple intervals in a constraint generation procedure for multiprocessor scheduling2017In: Operations Research Proceedings 2017 / [ed] N. Kliewer, J.F. Ehmke and R. Borndörfer, Springer, 2017, p. 567-572Conference paper (Refereed)
    Abstract [en]

    Multiprocessor scheduling is a well studied NP-hard optimisation problem that occurs in variety of forms. The focus of this paper is explicit modelling of multiple task intervals. This work extends a constraint generation procedure previously developed for an avionics scheduling context. We here address a relaxation of the original problem and this relaxation can be considered as multiprocessor scheduling with precedence relations and multiple intervals.

    The explicit modelling of multiple intervals strengthens the formulation used in the constraint generation procedure and we illustrate the computational effects on an industrial relevant avionics scheduling problem.

  • 8.
    Karlsson, Emil
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering. Saab AB, SE-581 88 Linköping.
    Rönnberg, Elina
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering. Saab AB, SE-581 88 Linköping.
    Stenberg, Andreas
    Saab AB, SE-581 88 Linköping.
    Uppman, Hannes
    Saab AB, SE-581 88 Linköping.
    A matheuristic approach to large-scale avionic scheduling2019Report (Other academic)
    Abstract [en]

    Pre-runtime scheduling of avionic systems is used to ensure that the systems provide the desired functionality at the correct time. This paper considers scheduling of an integrated modular avionic system which from a more general perspective can be seen as a multiprocessor scheduling problem that includes a communication network. The addressed system is practically relevant and the computational evaluations are made on large-scale instances developed together with the industrial partner Saab. A subset of the instances is made publicly available.

    Our contribution is a matheuristic for solving these large-scale instances and it is obtained by improving the model formulations used in a previously suggested constraint generation procedure and by including an adaptive large neighbourhood search to extend it into a matheuristic. Characteristics of our adaptive large neighbourhood search are that it is made over both discrete and continuous variables and that it needs to balance the search for feasibility and profitable objective value. The repair operation is to apply a mixed-integer programming solver on a model where most of the constraints are treated as soft and a violation of them is instead penalised in the objective function. The largest solved instance, with respect to the number of tasks, has 45 988 tasks and 2 011 communication messages.

  • 9.
    Karlsson, Emil
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Rönnberg, Elina
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Stenberg, Andreas
    Saab AB, Sweden.
    Uppman, Hannes
    Saab AB, Sweden.
    Heuristic enhancements of a constraint generation procedure for scheduling of avionic systems2018In: PATAT 2018: Proceedings of the 12th International Conference of the Practice and Theory of Automated Timetabling / [ed] E. K. Burke, L. Di Gaspero, B. McCollum, N. Musliu, E. Özcan, 2018, p. 417-419Conference paper (Refereed)
  • 10.
    Karlsson, Emil
    et al.
    Linköping University, Department of Mathematics, Optimization . Linköping University, Faculty of Science & Engineering.
    Singull, Martin
    Linköping University, Department of Mathematics, Mathematical Statistics . Linköping University, Faculty of Science & Engineering.
    More on explicit estimators for a banded covariance matrix2015In: Acta et Commentationes Universitatis Tartuensis de Mathematica, ISSN 1406-2283, E-ISSN 2228-4699, Vol. 19, no 1, p. 49-62Article in journal (Refereed)
    Abstract [en]

    The problem of estimating mean and covariances of a multivariate normally distributed random vector has been studied in many forms. This paper focuses on the estimators proposed by Ohlson et al. (2011) for a banded covariance structure with m-dependence. We rewrite the estimator when m = 1, which makes it easier to analyze. This leads to an adjustment, and an unbiased estimator can be proposed. A new and easier proof of consistency is then presented.

    This theory is also generalized to a general linear model where the corresponding theorems and propositions are stated to establish unbiasedness and consistency.

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