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  • 1.
    Ding, Xiaosong
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
    Bilinear optimization in computational decision analysis2005Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    In real-life decision analysis, significant recognition has been given to theunrealistic expectation of numerically precise information. Many modernapproaches attempting to handle imprecision have focused more on representationand less on evaluation. The DELTA method, as one of the fewleading approaches, challenges this issue by its evaluation framework thatcan accommodate both precision and imprecision. However, computationally,DELTA and similar approaches may incur time-consuming calculationsdue to the introduction of imprecise information concerning probability andutility. In general, those problems are bounded non-convex bilinear optimizationprograms with disjoint linear constraints, which cannot be solvedeffectively by any existing general-purpose global optimization technique.This thesis presents two enhanced cutting plane algorithms for solvingbounded disjoint bilinear programs arising in computational decision analysis.Each algorithm consists of a local phase designed to determine a localoptimizer from an approximate solution, and a global phase designed to systematicallyexplore the feasible region, subset by subset. These two phasesare switched automatically during the global search procedure. The basicframework builds upon previously developed efficient cutting plane methods.By embedding the lower bounding technique in a branch and bound procedure,the improvement of their performances seems encouraging in the lightof computational experience. Even though the motivation to develop thesealgorithms stems from computational decision analysis, the idea can also beextended to the development of optimization approaches for handling generalbounded disjoint bilinear programs, especially for larger sized ones.

  • 2.
    Ding, Xiaosong
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
    Al-Khayya, Faiz
    Cutting plane method in decision analysis2004In: Proceedings of the Ninth Meeting of the Nordic Section of the Mathematical Programming Society, October 22–23, 2004, Linköpings universitet, Norrköping, Sweden, 2004Conference paper (Other academic)
    Abstract [en]

    Several computational decision analysis approaches have been developed over a number of years for solving decision problems when vague and numerically imprecise information prevails. However, the evaluation phases in the DELTA method and similar methods often give rise to special bilinear programming problems, which are time-consuming to solve in an interactive environment with general nonlinear programming solvers. This paper proposes a linear programming based global optimization algorithm that combines the cutting plane method together with the lower bound information for solving this type of problems. The central theme is to identify the global optimum as early as possible in order to save additional computational efforts.

  • 3.
    Ding, Xiaosong
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
    Al-Khayyal, F.
    Georgia Institute of Technology, United States.
    Accelerating convergence of cutting plane algorithms for disjoint bilinear programming2007In: Journal of Global Optimization, ISSN 0925-5001, E-ISSN 1573-2916, Vol. 38, no 3, p. 421-436Article in journal (Refereed)
    Abstract [en]

    This paper presents two linear cutting plane algorithms that refine existing methods for solving disjoint bilinear programs. The main idea is to avoid constructing (expensive) disjunctive facial cuts and to accelerate convergence through a tighter bounding scheme. These linear programming based cutting plane methods search the extreme points and cut off each one found until an exhaustive process concludes that the global minimizer is in hand. In this paper, a lower bounding step is proposed that serves to effectively fathom the remaining feasible region as not containing a global solution, thereby accelerating convergence. This is accomplished by minimizing the convex envelope of the bilinear objective over the feasible region remaining after introduction of cuts. Computational experiments demonstrate that augmenting existing methods by this simple linear programming step is surprisingly effective at identifying global solutions early by recognizing that the remaining region cannot contain an optimal solution. Numerical results for test problems from both the literature and an application area are reported.

  • 4.
    Ding, Xiaosong
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
    Al-Khayyal, F
    Improved Cutting Plane Methods for Disjoint Bilinear ProgrammingManuscript (preprint) (Other academic)
  • 5.
    Ding, Xiaosong
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
    Al-Khayyal, F. A.
    Global Optimization in Decision AnalysisManuscript (preprint) (Other academic)
    Abstract [en]

    Computational decision analysis methods, such as the DELTA method, have been developed and implemented over a number of years for solving decision problems where vague and numerically imprecise information prevails. However, the evaluation phases in those methods often give rise to bilinear programming problems, which are time-consuming to solve in an interactive environment with general nonlinear programming solvers. This paper proposes a linear programming based algorithm that combines a cutting plane method with the lower bounding technique for solving this type of problem. The central theme is to identify the global optimum as early as possible in order to avoid generating unnecessary cuts in the convergent cutting plane procedure.

  • 6.
    Ding, Xiaosong
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
    Danielson, Mats
    Inst. för data- och systemvetenskap, Stockholms universitet.
    Ekenberg, Love
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
    Disjoint Programming in Computational Decision Analysis2010In: Journal of Uncertain Systems, ISSN 1752-8917, Vol. 4, no 1, p. 4-13Article in journal (Refereed)
  • 7.
    Ding, Xiaosong
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
    Danielson, Mats
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
    Ekenberg, Love
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
    Generalized Bilinear Decision AnalysisManuscript (preprint) (Other academic)
  • 8.
    Ding, Xiaosong
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
    Danielsson, Mats
    Ekenberg, Love
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
    Non-Linear Programming Solvers for Decision Analysis2004In: Operations Research Proceedings 2003: Selected Papers of the International Conference on Operations Research (OR 2003) Heidelberg, September 3-5, 2003, Springer , 2004, p. 475-Conference paper (Other academic)
    Abstract [en]

    Several methods have been developed over a number of years for solving decision problems when vague and numerically imprecise information prevails. However, the DELTA method and similar methods give rise to particular bilinear programming problems that are time consuming to solve in a real-time environment. This paper presents a set of benchmark tests for non-linear programming solvers for solving this special type of problems. With two existing linear programming based algorithms, it also investigates the performance of linear programming solvers for special decision situations in decision support systems.

  • 9.
    Ding, Xiaosong
    et al.
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
    Ekenberg, Love
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
    Danielsson, Mats
    A Fast Bilinear Optimization Algorithm2004In: Proceedings of the Third International Conference on Nonlinear Analysis and Convex Analysis 2003 (NACA 2003), Yokohama: Yokohama Publishers , 2004Conference paper (Refereed)
    Abstract [en]

    Computational decision analysis methods (such as DELTA) have been developed and implemented over a number of years for solving decision problems when vague and numerically imprecise information prevails. However, the evaluation phases in those methods often give rise to bilinear programming problems, which are time-consuming to solve in an interactive environment with general nonlinear programming solvers such as SNOPT. This paper proposes a linear programming based algorithm for solving this type of problems, thus enabling interactive use of such methods.

  • 10.
    Ding, Xiasong
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Information Technology and Media.
    Fast local optimization in decision analytic software2004Licentiate thesis, monograph (Other academic)
    Abstract [en]

    In decision analysis, significant recognition has been given to the fact that requiring numerically precise information seems unrealistic for real-life decision situations, Despite the emergence of many modern apporaches, which attempt to handle imprecise estimates, concentration has focused more on representation and less on evaluation. Methods such as the DELTA method  challenged this issue by its evaluation framework that can accommodate both precision an imprecision, and thus pushes forward the disign of advanced dicision analysis systems. However, computationally, DELTA may incur time-consuming calculations due to the introduction of imprecise information into the probability space as well as the value space. Although two fast linear programming based bilinear optimazation algorithms were suggested, which were supporsed to satisfy certain presumed conditions, they are found to be too restrictive.

    This thesis presents a fast potimization approach that can be viewed as a generalized version of the two fast algorithms. The motivation stems from the attempts to discard those presumed conditions. This approach combines ideas from both matrix computations and linear programming, and is, in fact, an iterative method. Since the DELTA method inteds to compute the difference of two expected utilities, this bilinear optimization issue is non-convex, and thus will certainly touch upon the global optimization area. As previously suggested, actually all methods for global optimization consist of two phases: a global phose to thoroughly explore subsets of the feasible region where it is known the blobal optimum will be found, an a local phase to improve the approximation to some local optima, Basically, this fast algorithm is devoted to the local optimization phase.

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