Multi-Criteria Optimization

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

    Decision space decomposition for multiobjective optimization

  • Emma Soriano
  • Margaret Wiecek
  • Mishko Mitkovski
    • Categories Multi-Criteria Optimization Tags , , , ,

    Being inspired by the parametric decomposition theorem for multiobjective optimization problems (MOPs) of Cuenca Mira and Miguel García (2017), and by the block-coordinate descent for single objective optimization problems, we present a decomposition theorem for computing the set of minimal elements of a partially ordered set. This set is decomposed into subsets whose minimal elements … Read more

    Pareto sensitivity, most-changing sub-fronts, and knee solutions

  • Tommaso Giovannelli
  • Marcos M. Raimundo
  • Luis Nunes Vicente
    • Categories Multi-Criteria Optimization Tags , , ,

    When dealing with a multi-objective optimization problem, obtaining a comprehensive representation of the Pareto front can be computationally expensive. Furthermore, identifying the most representative Pareto solutions can be difficult and sometimes ambiguous. A popular selection are the so-called Pareto knee solutions, where a small improvement in any objective leads to a large deterioration in at … Read more

    Local Upper Bounds Based on Polyhedral Ordering Cones

  • Gabriele Eichfelder
  • Firdevs Ulus
    • Categories Multi-Criteria Optimization Tags , , ,

    The concept of local upper bounds plays an important role for numerical algorithms in nonconvex, integer, and mixed-integer multiobjective optimization with respect to the componentwise partial ordering, that is, where the ordering cone is the nonnegative orthant. In this paper, we answer the question on whether and how this concept can be extended to arbitrary … Read more

    On Two Vectorization Schemes for Set-valued Optimization

  • Gabriele Eichfelder
  • Tobias Gerlach
  • Ernest Quintana
  • Stefan Rocktäschel
    • Categories Multi-Criteria Optimization Tags , , ,

    In this paper, we investigate two known solution approaches for set-valued optimization problems, both of which are based on so-called vectorization strategies. These strategies consist of deriving a parametric family of multi-objective optimization problems whose optimal solution sets approximate those of the original set-valued problem with arbitrary accuracy in a certain sense. Thus, these approaches … Read more

    SMOP: Stochastic trust region method for multi-objective problems

  • Nataša Krejić
  • Nataša Krklec Jerinkić
  • Luka Rutešić
    • Categories Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    The problem considered is a multi-objective optimization problem, in which the goal is to find an optimal value of a vector function representing various criteria. The aim of this work is to develop an algorithm which utilizes the trust region framework with probabilistic model functions, able to cope with noisy problems, using inaccurate functions and … Read more

    New Nonlinear Conjugate Gradient Methods with Guaranteed Descent for Multi-Objective Optimization

  • Manuel Berkemeier
  • sonntagk
    • Categories Multi-Criteria Optimization, Nonlinear Optimization, Unconstrained Optimization Tags , , , ,

    In this article, we present several examples of special nonlinear conjugate gradient directions for nonlinear (non-convex) multi-objective optimization. These directions provide a descent direction for the objectives, independent of the line-search. This way, we can provide an algorithm with simple, Armijo-like backtracking and prove convergence to first-order critical points. In contrast to other popular conjugate … Read more

    Universal nonmonotone line search method for nonconvex multiobjective optimization problems with convex constraints

  • Maria Eduarda Pinheiro
  • Geovani Nunes Grapiglia
    • Categories Multi-Criteria Optimization Tags

    In this work we propose a general nonmonotone line-search method for nonconvex multi-objective optimization problems with convex constraints. At the \(k\)th iteration, the degree of nonmonotonicity is controlled by a vector \(\nu_{k}\) with nonnegative components. Different choices for \(\nu_{k}\) lead to different nonmonotone step-size rules. Assuming that the sequence \(\left\{\nu_{k}\right\}_{k\geq 0}\) is summable, and that … Read more

    Scaled Proximal Gradient Methods for Multiobjective Optimization: Improved Linear Convergence and Nesterov’s Acceleration

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

    Over the past two decades, descent methods have received substantial attention within the multiobjective optimization field. Nonetheless, both theoretical analyses and empirical evidence reveal that existing first-order methods for multiobjective optimization converge slowly, even for well-conditioned problems, due to the objective imbalances. To address this limitation, we incorporate curvature information to scale each objective within … Read more

    Designing sustainable diet plans by solving triobjective integer programs

  • Marianna De Santis
  • Alberto De Santis
  • Daniele Patria
    • Categories Applications - OR and Management Sciences, Multi-Criteria Optimization Tags , ,

    We present an algorithm for triobjective nonlinear integer programs that combines the epsilon-constrained method with available oracles for biobjective integer programs. We prove that our method is able to detect the nondominated set within a finite number of iterations. Specific strategies to avoid the detection of weakly nondominated points are devised. The method is then … Read more