Multi-Criteria Optimization

A novel elitist multiobjective optimization algorithm: multiobjective extremal optimization

  • Min-Rong Chen
  • Yong-Zai Lu
    • Categories Approximation Algorithms, Meta Heuristics, Multi-Criteria Optimization

    Recently, a general-purpose local-search heuristic method called Extremal Optimization (EO) has been successfully applied to some NP-hard combinatorial optimization problems. This paper presents an investigation on EO with its application in multiobjective optimization and proposes a new novel elitist multiobjective algorithm, called Multiobjective Extremal Optimization (MOEO). In order to extend EO to solve the multiobjective … Read more

    Multi-objective branch-and-bound. Application to the bi-objective spanning tree problem.

  • Francis Sourd
  • Olivier Spanjaard
    • Categories Multi-Criteria Optimization

    This paper focuses on a multi-objective derivation of branch-and-bound procedures. Such a procedure aims to provide the set of Pareto optimal solutions of a multi-objective combinatorial optimization problem. Unlike previous works on this issue, the bounding is performed here via a set of points rather than a single ideal point. The main idea is that … Read more

    A new adaptive algorithm for linear multiobjective programming problems

  • M.O. Bibi
  • M.S Radjef
  • Sonia Radjef
    • Categories Linear, Cone and Semidefinite Programming, Multi-Criteria Optimization Tags , , , , , ,

    In this paper, we present a new adaptive algorithm for defining the solution set of a multiobjective linear programming problem, where the decision variables are upper and lower bounded, using the direct support method. The principle particularitie of this method is the fact that it handles the bounds of variables such are they are initially … Read more

    An Adaptive Primal-Dual Warm-Start Technique for Quadratic Multiobjective Optimization

  • Jörg Fliege
    • Categories Control Applications, Multi-Criteria Optimization, Quadratic Programming Tags , , ,

    We present a new primal-dual algorithm for convex quadratic multicriteria optimization. The algorithm is able to adaptively refine the approximation to the set of efficient points by way of a warm-start interior-point scalarization approach. Results of this algorithm when applied on a three-criteria real-world power plant optimization problem are reported, thereby illustrating the feasibility of … Read more

    The Effects of Adding Objectives to an Optimization Problem on the Solution Set

  • Jörg Fliege
    • Categories Multi-Criteria Optimization Tags , , , ,

    Suppose that for a given optimisation problem (which might be multicriteria problem or a single-criteron problem), an additional objective function is introduced. How does the the set of solutions, i.~e.\ the set of efficient points change when instead of the old problem the new multicriteria problem is considered? How does the set of properly efficient … Read more

    The Efficient Outcome Set of a Bi-criteria Linear Programming and Application

  • Phan Vu Dao
  • Bach Kim Nguyen Thi
  • Minh Hue Nguyen Thi
    • Categories Multi-Criteria Optimization

    We study the efficient outcome set $Y_E$ of a bi-criteria linear programming problem $(BP)$ and present a quite simple algorithm for generating all extreme points of $Y_E$. Application to optimization a scalar function $h(x)$ over the efficient set of $(BP)$ in case of $h$ which is a convex and dependent on the criteria is considered. … Read more

    A Note on Multiobjective Optimization and Complementarity Constraints

  • Sven Leyffer
    • Categories Complementarity and Variational Inequalities, Constrained Nonlinear Optimization, Multi-Criteria Optimization Tags , , ,

    We propose a new approach to convex nonlinear multiobjective optimization that captures the geometry of the Pareto set by generating a discrete set of Pareto points optimally. We show that the problem of finding an optimal representation of the Pareto surface can be formulated as a mathematical program with complementarity constraints. The complementarity constraints arise … Read more

    Transposition theorems and qualification-free optimality conditions

  • Arnold Neumaier
  • Hermann Schichl
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory, Multi-Criteria Optimization Tags , , , , , , , , , , , ,

    New theorems of the alternative for polynomial constraints (based on the Positivstellensatz from real algebraic geometry) and for linear constraints (generalizing the transposition theorems of Motzkin and Tucker) are proved. Based on these, two Karush-John optimality conditions — holding without any constraint qualification — are proved for single- or multi-objective constrained optimization problems. The first … Read more

    An Improved Algorithm for Biobjective Integer Programs

  • Ted K. Ralphs
  • Matthew Saltzman
  • Margaret Wiecek
    • Categories Branch and Cut Algorithms, Multi-Criteria Optimization, Problem Solving Environments Tags , , , , , , , ,

    A parametric algorithm for identifying the Pareto set of a biobjective integer program is proposed. The algorithm is based on the weighted Chebyshev (Tchebycheff) scalarization, and its running time is asymptotically optimal. A number of extensions are described, including: a technique for handling weakly dominated outcomes, a Pareto set approximation scheme, and an interactive version … Read more

    An Efficient Interior-Point Method for Convex Multicriteria Optimization Problems

  • Jörg Fliege
    • Categories Convex Optimization, Multi-Criteria Optimization Tags , , , ,

    In multicriteria optimization, several objective functions, conflicting with each other, have to be minimized simultaneously. We propose a new efficient method for approximating the solution set of a multiobjective programming problem, where the objective functions involved are arbitary convex functions and the set of feasible points is convex. The method is based on generating warm-start … Read more