Multi-Criteria Optimization

Numerical Results for the Multi-objective Trust Region Algorithm MHT

  • Gabriele Eichfelder
  • Jana Thomann
    • Categories Multi-Criteria Optimization Tags , , , ,

    A set of 78 test examples is presented for the trust region method MHT described in J. Thomann, G. Eichfelder, A trust region algorithm for heterogeneous multi-objective optimization, 2018 (available as preprint: http://optimization-online.org/DB_HTML/2018/03/6495.html) . It is designed for multi-objective heterogeneous optimization problems where one of the objective functions is an expensive black-box function, for example … Read more

    Multi-objective Ranking and Selection: Optimal Sampling Laws and Tractable Approximations via SCORE

  • Eric A. Applegate
  • Guy Feldman
  • Susan R. Hunter
  • Raghu Pasupathy
    • Categories Multi-Criteria Optimization, Optimization of Simulated Systems

    Consider the multi-objective ranking and selection (MORS) problem in which we select the Pareto-optimal set from a finite set of systems evaluated on three or more stochastic objectives. Solving this problem is difficult because we must determine how to allocate a simulation budget among the systems to minimize the probability that any systems are misclassified. … Read more

    A Wolfe line search algorithm for vector optimization

  • L. R. Lucambio Pérez
  • Leandro Fonseca Prudente
    • Categories Multi-Criteria Optimization

    In a recent paper, Lucambio Pérez and Prudente extended the Wolfe conditions for the vector-valued optimization. Here, we propose a line search algorithm for finding a step-size satisfying the strong Wolfe conditions in the vector optimization setting. Well definiteness and finite termination results are provided. We discuss practical aspects related to the algorithm and present … Read more

    Branching with Hyperplanes in the Criterion Space: the Frontier Partitioner Algorithm for Biobjective Integer Programming

  • Marianna De Santis
  • Giorgio Grani
  • Laura Palagi
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Multi-Criteria Optimization

    We present an algorithm for finding the complete Pareto frontier of biobjective integer programming problems. The method is based on the solution of a finite number of integer programs. The feasible sets of the integer programs are built from the original feasible set, by adding cuts that separate efficient solutions. Providing the existence of an … Read more

    A new concept of slope for set-valued maps and applications in set optimization studied with Kuroiwa’s set approach

  • Xuan Duc Ha Truong
    • Categories Multi-Criteria Optimization

    In this paper, scalarizing functions defined with the help of the Hiriart-Urruty signed distance are used to characterize set order relations and weak optimal solutions in set optimization studied with Kuroiwa’s set approach and to introduce a new concept of slope for a set-valued map. It turns out that this slope possesses most properties of … Read more

    Bi-objective Simulation Optimization on Integer Lattices using the Epsilon-Constraint Method in a Retrospective Approximation Framework

  • Kyle Cooper
  • Susan R. Hunter
  • Kalyani Nagaraj
    • Categories Integer Programming, Multi-Criteria Optimization, Optimization of Simulated Systems Tags , ,

    We consider multi-objective simulation optimization (MOSO) problems on integer lattices, that is, nonlinear optimization problems in which multiple simultaneous objective functions can only be observed with stochastic error, e.g., as output from a Monte Carlo simulation model. The solution to a MOSO problem is the efficient set, which is the set of all feasible decision … Read more

    MSEA.jl: A Multi-Stage Exact Algorithm for Bi-objective Pure Integer Linear Programming in Julia

  • Hadi Charkhgard
  • Aritra Pal
    • Categories Integer Programming, Multi-Criteria Optimization Tags , , ,

    We present a new exact method for bi-objective pure integer linear programming, the so-called Multi-Stage Exact Algorithm (MSEA). The method combines several existing exact and approximate algorithms in the literature to compute the entire nondominated frontier of any bi-objective pure integer linear program. Each algorithm available in MSEA has multiple versions in the literature. Hence, … Read more

    A barrier-type method for multiobjective optimization

  • Ellen H. Fukuda
  • L. M. Graña Drummond
  • Fernanda M. P. Raupp
    • Categories Multi-Criteria Optimization Tags , , ,

    For solving constrained multicriteria problems, we introduce the multiobjective barrier method (MBM), which extends the scalar-valued internal penalty method. This multiobjective version of the classical method also requires a penalty barrier for the feasible set and a sequence of nonnegative penalty parameters. Differently from the single-valued procedure, MBM is implemented by means of an auxiliary … Read more

    A Trust Region Algorithm for Heterogeneous Multiobjective Optimization

  • Gabriele Eichfelder
  • Jana Thomann
    • Categories Multi-Criteria Optimization Tags , , , ,

    This paper presents a new trust region method for multiobjective heterogeneous optimization problems. One of the objective functions is an expensive black-box function, for example given by a time-consuming simulation. For this function derivative information cannot be used and the computation of function values involves high computational effort. The other objective functions are given analytically … Read more

    A Branch-and-Bound based Algorithm for Nonconvex Multiobjective Optimization

  • Gabriele Eichfelder
  • Julia Niebling
    • Categories Global Optimization, Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    A new branch-and-bound based algorithm for smooth nonconvex multiobjective optimization problems with convex constraints is presented. The algorithm computes an $(\varepsilon,\delta)$-approximation of all globally optimal solutions. We introduce the algorithm which uses selection rules, discarding and termination tests. The discarding tests are the most important aspect, as they examine in different ways whether a box … Read more