Multi-Criteria Optimization

An enhanced mathematical model for optimal simultaneous preventive maintenance scheduling and workshop planning

  • Gabrijela Obradović
  • Ann-Brith Strömberg
    • Categories (Mixed) Integer Linear Programming, Multi-Criteria Optimization, Scheduling

    For a system to stay operational, maintenance of its components is required and to maximize the operational readiness of a system, preventive maintenance planning is essential. There are two stakeholders—a system operator and a maintenance workshop—and a contract regulating their joint activities. Each contract leads to a bi-objective optimization problem. Components that require maintenance are … Read more

    Efficient Computation of the Approximation Quality in Sandwiching Algorithms

  • Ina Lammel
  • Karl-Heinz Küfer
  • Philipp Süss
    • Categories Convex Optimization, Multi-Criteria Optimization Tags , , ,

    Computing the approximation quality is a crucial step in every iteration of Sandwiching algorithms (also called Benson-type algorithms) used for the approximation of convex Pareto fronts, sets or functions. Two quality indicators often used in these algorithms are polyhedral gauge and epsilon indicator. In this article, we develop an algorithm to compute the polyhedral gauge … Read more

    K-Shortest Simple Paths Using Biobjective Path Search

  • Pedro Maristany de las Casas
  • Antonio Sedeño-Noda
  • Ralf Borndœrfer
    • Categories Dynamic Programming, Multi-Criteria Optimization, Network Optimization Tags , , ,

    In this paper we introduce a new algorithm for the k-Shortest Simple Paths (k-SSP) problem with an asymptotic running time matching the state of the art from the literature. It is based on a black-box algorithm due to Roddity and Zwick that solves at most 2k instances of the Second Shortest Simple Path (2-SSP) problem … Read more

    A Criterion Space Search Feasibility Pump Heuristic for Solving Maximum Multiplicative Programs

  • Ashim Khanal
  • Hadi Charkhgard
    • Categories Game Theory, Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    We study a class of nonlinear optimization problems with diverse practical applications, particularly in cooperative game theory. These problems are referred to as Maximum Multiplicative Programs (MMPs), and can be conceived as instances of “Optimization Over the Frontier” in multiobjective optimization. To solve MMPs, we introduce a feasibility pump-based heuristic that is specifically designed to … Read more

    Global convergence of a BFGS-type algorithm for nonconvex multiobjective optimization problems

  • Leandro Fonseca Prudente
  • D. R. Souza
    • Categories Multi-Criteria Optimization Tags , , , , , ,

    We propose a modified BFGS algorithm for multiobjective optimization problems with global convergence, even in the absence of convexity assumptions on the objective functions. Furthermore, we establish the superlinear convergence of the method under usual conditions. Our approach employs Wolfe step sizes and ensures that the Hessian approximations are updated and corrected at each iteration … Read more

    A novel UCB-based batch strategy for Bayesian optimization

  • Carmen-Ana Domínguez-Bravo
    • Categories Global Optimization, Multi-Criteria Optimization Tags , , ,

    The optimization of expensive black-box functions appears in many situations. Bayesian optimization methods have been successfully applied to solve these prob- lems using well-known single-point acquisition functions. Nowadays, the develop- ments in technology allow us to perform evaluations of some of these expensive function in parallel. Therefore, there is a need for batch infill criteria … Read more

    Using dual relaxations in multiobjective mixed-integer quadratic programming

  • Marianna De Santis
  • Gabriele Eichfelder
  • Daniele Patria
  • Leo Warnow
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization Tags , , ,

    We present a branch-and-bound method for multiobjective mixed-integer convex quadratic programs that computes a superset of efficient integer assignments and a coverage of the nondominated set. The method relies on outer approximations of the upper image set of continuous relaxations. These outer approximations are obtained addressing the dual formulations of specific subproblems where the values … Read more

    Test Instances for Multiobjective Mixed-Integer Nonlinear Optimization

  • Leo Warnow
  • Gabriele Eichfelder
  • Tobias Gerlach
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization, Nonlinear Optimization Tags , , ,

    A suitable set of test instances, also known as benchmark problems, is a key ingredient to systematically evaluate numerical solution algorithms for a given class of optimization problems. While in recent years several solution algorithms for the class of multiobjective mixed-integer nonlinear optimization problems have been proposed, there is a lack of a well-established set … Read more

    (ε-)Efficiency in Fractional Vector Optimization

  • Mounir El Maghri
    • Categories Convex and Nonsmooth Optimization, Global Optimization, Multi-Criteria Optimization Tags , , , ,

    The issue of characterizing completely efficient (Pareto) solutions to a fractional vector (multiobjective or multicriteria) minimization problem, where the involved functions are convex, has not been addressed previously. Thanks to an earlier characterization of weak efficiency in difference vector optimization by El Maghri, we get a vectorial necessary and sufficient condition given in terms of … Read more

    An Explicit Three-Term Polak-Ribière-Polyak Conjugate Gradient Method for Bicriteria Optimization

  • Mounir El Maghri
  • Youssef Elboulqe
    • Categories Multi-Criteria Optimization, Unconstrained Optimization Tags , , , , ,

    We propose in this paper a Polak-Ribière-Polyak conjugate gradient type method for solving bicriteria optimization problems by avoiding scalarization techniques. Two particular advantages in this contribution are to be noted. First, the suggested descent direction common to both criteria may be directly computed by a given formula without solving any intermediate subproblem. Second, the descent … Read more