Multi-Criteria Optimization

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

    An approximation algorithm for multi-objective mixed-integer convex optimization

  • Ina Lammel
  • Karl-Heinz Küfer
  • Philipp Süss
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization Tags , ,

    In this article we introduce an algorithm that approximates Pareto fronts of multiobjective mixed-integer convex optimization problems. The algorithm constructs an inner and outer approximation of the front exploiting the convexity of the patches and is applicable to problems with an arbitrary number of criteria. In the algorithm, the problem is decomposed into patches, which … Read more

    On the Relationship Between the Value Function and the Efficient Frontier of a Mixed Integer Linear Optimization Problem

  • Ted K. Ralphs
    • Categories Multi-Criteria Optimization, Other Topics

    In this study, we investigate the connection between the efficient frontier (EF) of a general multiobjective mixed integer linear optimization problem (MILP) and the so-called restricted value function (RVF) of a closely related single-objective MILP. In the first part of the paper, we detail the mathematical structure of the RVF, including characterizing the set of … Read more

    A Column Generation Approach for the Lexicographic Optimization of Intra-Hospital Transports

  • Andreas Bärmann
  • Alexander Martin
  • Alexander Müller
  • Dieter Weninger
    • Categories Integer Programming, Multi-Criteria Optimization, Transportation Tags , , , , ,

    Over the last fewyears, the efficient design of processes in hospitals and medical facilities has received more and more attention, particularly when the improvement of the processes is aimed at relieving theworkload of medical staff. To this end,we have developed a method to determine optimal allocations of intra-hospital transports to hospital transport employees. When optimizing … Read more

    A Test Instance Generator for Multiobjective Mixed-integer Optimization

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

    Application problems can often not be solved adequately by numerical algorithms as several difficulties might arise at the same time. When developing and improving algorithms which hopefully allow to handle those difficulties in the future, good test instances are required. These can then be used to detect the strengths and weaknesses of different algorithmic approaches. … Read more