Multi-Criteria Optimization

An Adaptive Patch Approximation Algorithm for Bicriteria Convex Mixed Integer problems

  • Erik Diessel
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization Tags , , ,

    Pareto frontiers of bicriteria continuous convex problems can be efficiently computed and optimal theoretical performance bounds have been established. In the case of bicriteria mixed-integer problems, the approximation of the Pareto frontier becomes, however, significantly harder. In this paper, we propose a new algorithm for approximating the Pareto frontier of bicriteria mixed-integer programs with convex … Read more

    A general branch-and-bound framework for continuous global multiobjective optimization

  • Gabriele Eichfelder
  • Peter Kirst
  • Oliver Stein
  • Laura Meng
    • Categories Global Optimization, Multi-Criteria Optimization, Nonlinear Optimization

    Current generalizations of the central ideas of single-objective branch-and-bound to the multiobjective setting do not seem to follow their train of thought all the way. The present paper complements the various suggestions for generalizations of partial lower bounds and of overall upper bounds by general constructions for overall lower bounds from partial lower bounds, and … Read more

    A Decision Space Algorithm for Multiobjective Convex Quadratic Integer Optimization

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

    We present a branch-and-bound algorithm for minimizing multiple convex quadratic objective functions over integer variables. Our method looks for efficient points by fixing subsets of variables to integer values and by using lower bounds in the form of hyperplanes in the image space derived from the continuous relaxations of the restricted objective functions. We show … Read more

    The use of multi-criteria decision-making methods in project portfolio selection: a literature review and future research directions

  • Sarah Ben Amor
  • Makbule Kandakoglu
  • Grit Walther
    • Categories Multi-Criteria Optimization Tags , , , ,

    In most project portfolio selection (PPS) situations, the presence of multiple attributes and decision-maker preference is inevitable. As Multi-criteria Decision Analysis (MCDA) methods provide a framework well-suited to deal with these challenges in PPS problems, the use of MCDA methods in real-life PPS problems has increased in recent years. This paper provides a comprehensive literature … Read more

    DMulti-MADS: Mesh adaptive direct multisearch for blackbox multiobjective optimization

  • Jean Bigeon
  • Sébastien Le Digabel
  • Ludovic Salomon
    • Categories Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    The context of this research is multiobjective optimization where conflicting objectives are present. In this work, these objectives are only available as the outputs of a blackbox for which no derivative information is available. This work proposes a new extension of the mesh adaptive direct search (MADS) algorithm to constrained multiobjective derivative-free optimization. This method … Read more

    Conditional gradient method for multiobjective optimization

  • Pedro Bonfim Assunção
  • Orizon Pereira Ferreira
  • Leandro Fonseca Prudente
    • Categories Constrained Nonlinear Optimization, Multi-Criteria Optimization

    We analyze the conditional gradient method, also known as Frank-Wolfe method, for constrained multiobjective optimization. The constraint set is assumed to be convex and compact, and the objectives functions are assumed to be continuously differentiable. The method is considered with different strategies for obtaining the step sizes. Asymptotic convergence properties and iteration-complexity bounds with and … Read more

    An inexact scalarized proximal algorithm with quasi- distance for convex and quasiconvex multi-objective minimization

  • Rogério Azevedo Rocha
  • Ronaldo Malheiros Gregório
  • Paulo Roberto Oliveira
  • Erik Alex Papa Quiroz
    • Categories Multi-Criteria Optimization, Nonlinear Optimization Tags

    In the paper of Rocha et al., J Optim Theory Appl (2016) 171:964979, the authors introduced a proximal point algorithm with quasi-distances to solve unconstrained convex multi-objective minimization problems. They proved that all accumulation points are ecient solutions of the problem. In this pa- per we analyze an inexact proximal point algorithm to solve convex … Read more

    The Magic of Nash Social Welfare in Optimization: Do Not Sum, Just Multiply!

  • Hadi Charkhgard
  • Parisa Charkhgard
  • Rasul Esmaeilbeigi
  • Kimia Keshanian
    • Categories Game Theory, Global Optimization, Multi-Criteria Optimization Tags , , , ,

    In this paper, we explain some key challenges when dealing with a single/multi-objective optimization problem in practice. To overcome these challenges, we present a mathematical program that optimizes a Nash Social Welfare function. We refer to this mathematical program as the Nash Social Welfare Program (NSWP). An interesting property of the NSWP is that it … Read more

    Nonconvex Constrained Optimization by a Filtering Branch and Bound

  • Gabriele Eichfelder
  • Kathrin Klamroth
  • Julia Niebling
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory, Multi-Criteria Optimization

    A major difficulty in optimization with nonconvex constraints is to find feasible solutions. As simple examples show, the alphaBB-algorithm for single-objective optimization may fail to compute feasible solutions even though this algorithm is a popular method in global optimization. In this work, we introduce a filtering approach motivated by a multiobjective reformulation of the constrained … Read more

    The Fermat Rule for Set Optimization Problems with Lipschitzian Set-Valued Mappings

  • Gemayqzel Bouza
  • Christiane Tammer
  • Ernest Quintana
  • Vu Anh Tuan
    • Categories Multi-Criteria Optimization, Nonsmooth Optimization, Robust Optimization Tags , , , ,

    n this paper, we consider set optimization problems with respect to the set approach. Specifically, we deal with the lower less and the upper less set relations. First, we derive properties of convexity and Lipschitzianity of suitable scalarizing functionals, under the same assumption on the set-valued objective mapping. We then obtain upper estimates of the … Read more