Multi-Criteria Optimization

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

    Network Models for Multiobjective Discrete Optimization

  • David Bergman
  • Merve Bodur
  • Carlos Cardonha
  • Andre Augusto Cire
    • Categories 0-1 Programming, Dynamic Programming, Multi-Criteria Optimization

    This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework formulates these problems as network models, in that enumerating the Pareto frontier amounts to solving a multicriteria shortest path problem in an auxiliary network. We design tools and techniques for exploiting the network model in … Read more

    An exact algorithm to find non-dominated facets of Tri-Objective MILPs

  • Ali Fattahi
  • Metin Turkay
  • Seyyed Amir Babak Rasmi
    • Categories (Mixed) Integer Linear Programming, Multi-Criteria Optimization Tags , ,

    Many problems in real life have more than one decision criterion, referred to as multi-objective optimization (MOO) problems, and the objective functions of these problems are conflicting in most cases. Hence, finding non-dominated solutions is very critical for decision making process. Tri-objective mixed-integer linear programs (TOMILP) are an important subclass of MOOs that are applicable … Read more

    On classes of set optimization problems which are reducible to vector optimization problems and its impact on numerical test instances

  • Gabriele Eichfelder
  • Tobias Gerlach
    • Categories Multi-Criteria Optimization, Nonlinear Optimization Tags , , , ,

    Set optimization with the set approach has recently gained increasing interest due to its practical relevance. In this problem class one studies optimization problems with a set-valued objective map and defines optimality based on a direct comparison of the images of the objective function, which are sets here. Meanwhile, in the literature a wide range … Read more

    Pareto efficient solutions in multi-objective optimization involving forbidden regions

  • Christian Günther
    • Categories Facility Planning and Design, Generalized Convexity/Monoticity, Multi-Criteria Optimization

    In this paper, the aim is to compute Pareto efficient solutions of multi-objective optimization problems involving forbidden regions. More precisely, we assume that the vector-valued objective function is componentwise generalized-convex and acts between a real topological linear pre-image space and a finite-dimensional image space, while the feasible set is given by the whole pre-image space … Read more

    A New Exact Algorithm to Optimize a Linear Function Over the Set of Efficient Solutions for Bi-objective Mixed Integer Linear Programs

  • Hadi Charkhgard
  • Alvaro Sierra-Altamiranda
    • Categories (Mixed) Integer Linear Programming, Multi-Criteria Optimization Tags , , ,

    We present the first (criterion space search) algorithm for optimizing a linear function over the set of efficient solutions of bi-objective mixed integer linear programs. The proposed algorithm is developed based on the Triangle Splitting Method (Boland et al. 2015b) which can find a full representation of the nondominated frontier of any bi-objective mixed integer … Read more

    FPBH.jl: A Feasibility Pump Based Heuristic for Multi-objective Mixed Integer Linear Programming in Julia

  • Hadi Charkhgard
  • Aritra Pal
    • Categories (Mixed) Integer Linear Programming, Multi-Criteria Optimization, Optimization Software and Modeling Systems Tags , , , ,

    Feasibility pump is one of the successful heuristic solution approaches developed almost a decade ago for computing high-quality feasible solutions of single-objective integer linear programs, and it is implemented in exact commercial solvers such as CPLEX and Gurobi. In this study, we present the first Feasibility Pump Based Heuristic (FPBH) approach for approximately generating nondominated … Read more