Other Topics

Quadratic Convex Reformulations for MultiObjective Binary Quadratic Programming

  • Marianna De Santis
  • Lucas Létocart
  • Yue Zhang
    • Categories (Mixed) Integer Nonlinear Programming, 0-1 Programming, Multi-Criteria Optimization Tags , , ,

    Multiobjective binary quadratic programming refers to optimization problems involving multiple quadratic – potentially non-convex – objective functions and a feasible set that includes binary constraints on the variables. In this paper, we extend the well-established Quadratic Convex Reformulation technique, originally developed for single-objective binary quadratic programs, to the multiobjective setting. We propose a branch-and-bound algorithm … Read more

    On image space transformations in multiobjective optimization

  • Oliver Stein
  • Felix Neussel
    • Categories Multi-Criteria Optimization Tags , , , ,

    This paper considers monotone transformations of the objective space of multiobjective optimization problems which leave the set of efficient points invariant. Under mild assumptions, for the standard ordering cone we show that such transformations must be component-wise transformations. The same class of transformations also leaves the sets of weakly and of Geoffrion properly efficient points … Read more

    A Survey on the Applications of Stochastic Dual Dynamic Programming and its Variants

  • Bonn Kleiford Seranilla
  • Nils Löhndorf
    • Categories Dynamic Programming, Integer Programming, Stochastic Programming Tags , , ,

    Stochastic Dual Dynamic Programming (SDDP) is widely recognized as the predominant methodology for solving large-scale multistage stochastic linear programming (MSLP) problems. This paper aims to contribute to the extant literature by conducting a comprehensive survey of the literature on SDDP within the realm of practical applications. We systematically identify and analyze the various domains where … Read more

    Time Complexity and Optimality of Inventory and Production Policies for a Dynamic Lot Sizing Model with Remanufacturing and Separate Setup Costs

  • Chee-Khian Sim
    • Categories Dynamic Programming, Production and Logistics Tags , , ,

    We consider a dynamic lot sizing model in which end products to satisfy demands are obtained by remanufacturing m types of cores or manufacturing from raw materials. We consider separate setup costs for manufacturing and remanufacturing in our model. It is conjectured in [21], with reference to [24], that finding an optimal policy to the … Read more

    The improvement function reformulation for graphs of minimal point mappings

  • Stefan Schwarze
  • Oliver Stein
    • Categories Constrained Nonlinear Optimization, Game Theory, Global Optimization Theory Tags , , , , ,

    Graphs of minimal point mappings of parametric optimization problems appear in the definition of feasible sets of bilevel optimization problems and of semi-infinite optimization problems, and the intersection of multiple such graphs defines (generalized) Nash equilibria. This paper shows how minimal point graphs of nonconvex parametric optimization problems can be written with the help of … Read more

    An interactive optimization framework for incorporating a broader range of human feedback into stochastic multi-objective mixed integer linear programs

  • Damsara Jayarathne
  • Jennifer Pazour
  • John E. Mitchell
    • Categories (Mixed) Integer Linear Programming, Multi-Criteria Optimization, Stochastic Programming Tags , , , ,

    Interactive optimization leverages the strengths of optimization frameworks alongside the expertise of human users. Prior research in this area tends to either ask human users for the same type of information, or when varying information is requested, users must manually modify the optimization model directly. These limitations restrict the incorporation of wider human knowledge into … Read more

    Pareto Leap: An Algorithm for Biobjective Mixed-Integer Programming

  • Philip de Castro
  • Margaret Wiecek
    • Categories (Mixed) Integer Nonlinear Programming, Integer Programming, Multi-Criteria Optimization Tags , , ,

    Many real-life optimization problems need to make decisions with discrete variables and multiple, conflicting objectives. Due to this need, the ability to solve such problems is an important and active area of research. We present a new algorithm, called Pareto Leap, for identifying the (weak) Pareto slices of biobjective mixed-integer programs (BOMIPs), even when Pareto … Read more

    Rounding the Lovasz Theta Function with a Value Function Approximation

  • Rui Gong
  • Diego Cifuentes
  • Alejandro Toriello
    • Categories Dynamic Programming, Graphs and Matroids, Semi-definite Programming Tags , , , ,

    The Lovasz theta function is a semidefinite programming (SDP) relaxation for the maximum weighted stable set problem, which is tight for perfect graphs. However, even for perfect graphs, there is no known rounding method guaranteed to extract an optimal stable set from the SDP solution. In this paper, we develop a novel rounding scheme for … Read more

    Efficient search strategies for constrained multiobjective blackbox optimization

  • Sébastien Le Digabel
  • Antoine Lesage-Landry
  • Ludovic Salomon
  • Christophe Tribes
    • Categories Multi-Criteria Optimization, Nonlinear Optimization Tags ,

    Multiobjective blackbox optimization deals with problems where the objective and constraint functions are the outputs of a numerical simulation. In this context, no derivatives are available, nor can they be approximated by finite differences, which precludes the use of classical gradient-based techniques. The DMulti-MADS algorithm implements a state-of-the-art direct search procedure for multiobjective blackbox optimization … Read more

    Cost allocation in maintenance clustering

  • Andries van Beek
  • Loe Schlicher
    • Categories Applications - OR and Management Sciences, Game Theory Tags , , , ,

    Inspired by collaborative initiatives in the military domain, we analyze a setting in which multiple different players (e.g., Ministries of Defence) have to carry out preventive maintenance jobs. Each player is responsible for one job, with a job-specific minimal frequency and with maintenance costs, consisting of a job-specific variable component and a fixed component, which … Read more