Multi-Criteria Optimization

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

    Bi-objective autonomous vehicle repositioning problem with travel time uncertainty

  • Hadi Charkhgard
  • Zulqarnain Haider
  • Mahdi Takalloo
    • Categories Multi-Criteria Optimization, Stochastic Programming, Transportation Tags , ,

    We study the problem of repositioning autonomous vehicles in a shared mobility system in order to simultaneously minimize the unsatisfied demand and the total operating cost. We first present a mixed integer linear programming formulation for the deterministic version of the problem, and based on that we develop an extended formulation that is easier to … Read more

    New algorithms for discrete vector optimization based on the Graef-Younes method and cone-monotone sorting functions

  • Christian Günther
  • Nicolae Popovici
    • Categories Constrained Nonlinear Optimization, Multi-Criteria Optimization

    The well-known Jahn-Graef-Younes algorithm, proposed by Jahn in 2006, generates all minimal elements of a finite set with respect to an ordering cone. It consists of two Graef-Younes procedures, namely the forward iteration, which eliminates a part of the non-minimal elements, followed by the backward iteration, which is applied to the reduced set generated by … Read more

    Inexact scalarization proximal methods for multiobjective quasiconvex minimization on Hadamard manifold

  • Nancy Baygorrea
  • Nelson Maculan
  • Erik Alex Papa Quiroz
    • Categories Convex and Nonsmooth Optimization, Multi-Criteria Optimization, Nonsmooth Optimization Tags , , , ,

    In this paper we extend naturally the scalarization proximal point method to solve multiobjective unconstrained minimization problems, proposed by Apolinario et al.(2016), from Euclidean spaces to Hadamard manifolds for locally Lipschitz and quasiconvex vector objective functions. Moreover, we present a convergence analysis, under some mild assumptions on the multiobjective function, for two inexact variants of … Read more

    Best subset selection via bi-objective mixed integer linear programming

  • Hadi Charkhgard
  • Ali Eshragh
    • Categories Multi-Criteria Optimization, Statistics Tags , ,

    We study the problem of choosing the best subset of p features in linear regression given n observations. This problem naturally contains two objective functions including minimizing the amount of bias and minimizing the number of predictors. The existing approaches transform the problem into a single-objective optimization problem either by combining the two objectives using … Read more

    A Hausdorff-type distance, a directional derivative of a set-valued map and applications in set optimization

  • Xuan Duc Ha Truong
    • Categories Generalized Convexity/Monoticity, Multi-Criteria Optimization Tags , , , ,

    In this paper, we follow Kuroiwa’s set approach in set optimization, which proposes to compare values of a set-valued objective map $F$ respect to various set order relations. We introduce a Hausdorff-type distance relative to an ordering cone between two sets in a Banach space and use it to define a directional derivative for $F$. … Read more

    Bilevel optimization with a multiobjective problem in the lower level

  • Roberto Andreani
  • Sandra Augusta Santos
  • Viviana A. Ramirez
  • Leonardo D. Secchin
    • Categories Constrained Nonlinear Optimization, Multi-Criteria Optimization

    Bilevel problems model instances with a hierarchical structure. Aiming at an efficient solution of a constrained multiobjective problem according with some pre-defined criterion, we reformulate this optimization but non standard problem as a classic bilevel one. This reformulation intents to encompass all the objectives, so that the properly efficient solution set is recovered by means … Read more