Finding representative systems for discrete bicriterion optimization problems

Given a discrete bicriterion optimization problem, we propose two box algorithms to compute a finite representative system for the non-dominated set satisfying a number of quality features. Its cardinality N and the accuracy @D satisfy the relation O(A/@D), where A is the area of a starting box defined by the ideal and the nadir point.

[1]  Matthias Ehrgott,et al.  Multiple criteria decision analysis: state of the art surveys , 2005 .

[2]  Serpil Sayin,et al.  Algorithm robust for the bicriteria discrete optimization problem , 2006, Ann. Oper. Res..

[3]  Arthur Warburton,et al.  Approximation of Pareto Optima in Multiple-Objective, Shortest-Path Problems , 1987, Oper. Res..

[4]  Pierre Hansen,et al.  Bicriterion Path Problems , 1980 .

[5]  M. Hansen,et al.  Evaluating the quality of approximations to the non-dominated set , 1998 .

[6]  Serpil Sayin,et al.  Measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming , 2000, Math. Program..

[7]  Margaret M. Wiecek,et al.  A Survey of Approximation Methods in Multiobjective Programming , 2003 .

[8]  Kathrin Klamroth,et al.  Unbiased approximation in multicriteria optimization , 2003, Math. Methods Oper. Res..

[9]  Ralph E. Steuer,et al.  Intra-set point generation and filtering in decision and criterion space , 1980, Comput. Oper. Res..

[10]  Horst W. Hamacher,et al.  Multiple objective minimum cost flow problems: A review , 2007, Eur. J. Oper. Res..

[11]  Matthias Ehrgott,et al.  Multicriteria Optimization , 2005 .

[12]  Simon French,et al.  Multiple Criteria Decision Making: Theory and Application , 1981 .

[13]  C. Goh,et al.  A method for convex curve approximation , 1997 .

[14]  A. Payne,et al.  An interactive rectangle elimination method for biobjective decision making , 1980 .

[15]  S. Ruzika,et al.  Approximation Methods in Multiobjective Programming , 2005 .

[16]  Jin-Kao Hao,et al.  A Population and Interval Constraint Propagation Algorithm for Multi-objective Optimization , 2003 .

[17]  Serpil Sayin,et al.  The Multiobjective Discrete Optimization Problem: A Weighted Min-Max Two-Stage Optimization Approach and a Bicriteria Algorithm , 2005, Manag. Sci..

[18]  G. Rote,et al.  Approximation of convex curves with application to the bicriterial minimum cost flow problem , 1989 .

[19]  G. Rote,et al.  Sandwich approximation of univariate convex functions with an application to separable convex programming , 1991 .

[20]  Günther F. Rühe Algorithmic Aspects of Flows in Networks , 1991 .

[21]  Marco Laumanns,et al.  An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method , 2006, Eur. J. Oper. Res..

[22]  Yacov Y. Haimes,et al.  Multiobjective Decision Making: Theory and Methodology , 1983 .

[23]  A. Payne,et al.  Efficient approximate representation of bi-objective tradeoff sets , 1993 .

[24]  Kim Allan Andersen,et al.  The bicriterion semi-obnoxious location (BSL) problem solved by an epsilon-approximation , 2003, Eur. J. Oper. Res..