multiobjective optimization

A Subspace Minimization Barzilai-Borwein Method for Multiobjective Optimization Problems

  • Jian Chen
    • Categories Multi-Criteria Optimization Tags , , ,

    Nonlinear conjugate gradient methods have recently garnered significant attention within the multiobjective optimization community. These methods aim to maintain consistency in conjugate parameters with their single-objective optimization counterparts. However, the preservation of the attractive conjugate property of search directions remains uncertain, even for quadratic cases, in multiobjective conjugate gradient methods. This loss of interpretability of … Read more

    Preconditioned Barzilai-Borwein Methods for Multiobjective Optimization Problems

  • Jian Chen
    • Categories Multi-Criteria Optimization Tags , , ,

    Preconditioning is a powerful approach for solving ill-conditioned problems in optimization, where a preconditioning matrix is used to reduce the condition number and speed up the convergence of first-order method. Unfortunately, it is impossible to capture the curvature of all objective functions with a single preconditioning matrix in multiobjective optimization. Instead, second-order methods for multiobjective … Read more

    An Inexact Restoration Direct Multisearch Filter Approach to Multiobjective Constrained Derivative-free Optimization

  • Everton Silva
  • Ana Luisa Custódio
    • Categories Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , , , ,

    Direct Multisearch (DMS) is a well-established class of methods for multiobjective derivative-free optimization, where constraints are addressed by an extreme barrier approach, only evaluating feasible points. In this work, we propose a filter approach, combined with an inexact feasibility restoration step, to address constraints in the DMS framework. The filter approach treats feasibility as an … Read more

    The convergence rate of the Sandwiching algorithm for convex bounded multiobjective optimization

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

    Sandwiching algorithms, also known as Benson-type algorithms, approximate the nondominated set of convex bounded multiobjective optimization problems by constructing and iteratively improving polyhedral inner and outer approximations. Using a set-valued metric, an estimate of the approximation quality is determined as the distance between the inner and outer approximation. The convergence of the algorithm is evaluated … 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

    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

    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

    Relaxations and Duality for Multiobjective Integer Programming

  • Alex Dunbar
  • Saumya Sinha
  • Andrew J. Schaefer
    • Categories Integer Programming, Multi-Criteria Optimization Tags , , , ,

    Multiobjective integer programs (MOIPs) simultaneously optimize multiple objective func- tions over a set of linear constraints and integer variables. In this paper, we present continuous, convex hull and Lagrangian relaxations for MOIPs and examine the relationship among them. The convex hull relaxation is tight at supported solutions, i.e., those that can be derived via a … Read more

    Computing Tchebychev weight space decomposition for multiobjective discrete optimization problems

  • Tyler Perini
    • Categories Integer Programming, Multi-Criteria Optimization, Optimization in Data Science Tags , , ,

    Multiobjective discrete optimization (MODO) techniques, including weight space decomposition, have received increasing attention in the last decade. The primary weight space decomposition technique in the literature is defined for the weighted sum utility function, through which sets of weights are assigned to a subset of the nondominated set. Recent work has begun to study the … Read more