Finding representative systems for discrete bicriterion optimization problems

Operations Research Letters - Tập 35 - Trang 336-344 - 2007
Horst W. Hamacher1, Christian Roed Pedersen2, Stefan Ruzika1
1Fachbereich Mathematik, Universität Kaiserslautern, Postfach 3049, Kaiserslautern, Germany
2Department of Operations Research, University of Aarhus, Aarhus, Denmark

Tài liệu tham khảo

V. Barichard, J.-K. Hao, A population and interval constraint propagation algorithm for multi-objective optimization, in: Proceedings of The Fifth Metaheuristics International Conference, Japan, 2003, pp. 006-1–006-6. Burkard, 1991, Sandwich approximation of univariate convex functions with an application to separable convex programming, Naval Res. Logist. Quart., 38, 911, 10.1002/nav.3800380609 Burkard, 1989, Algorithmische Untersuchungen zu bikriteriellen kostenminimalen Flüssen in Netzwerken, Wiss. Z. Tech. Hochsch. Leipzig, 13, 333 Chankong, 1983 Ehrgott, 2005 Ehrgott, 2002 2005 Fruhwirth, 1989, Approximation of convex curves with application to the bicriterial minimum cost flow problem, European J. Oper. Res., 42, 326, 10.1016/0377-2217(89)90443-8 H.W. Hamacher, C.R. Pedersen, S. Ruzika, Multiple objective minimum cost flow problems: A review. European J. Oper. Res. (2005), in press. M.P. Hansen, A. Jaszkiewicz, Evaluating the quality of approximations to the non-dominated set. Working Paper IMM-REP-1998-7, Institute of Mathematical Modelling, Technical University of Denmark, 1998. Hansen, 1980, Bicriterion path problems, vol. 177, 109 Klamroth, 2002, Unbiased approximation in multicriteria optimization, Math. Methods Oper. Res., 56, 413, 10.1007/s001860200217 P. Kouvelis, S. Sayin, Algorithm robust for the bicriteria discrete optimization problem, Ann. Oper. Res., Revised (2004), to appear. Laumanns, 2006, An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method, European J. Oper. Res., 169, 924, 10.1016/j.ejor.2004.08.029 Payne, 1993, Efficient approximate representation of bi-objective tradeoff sets, J. Franklin Inst., 330, 1219, 10.1016/0016-0032(93)90073-4 Payne, 1980, An interactive rectangle elimination method for biobjective decision making, IEEE Trans. Automat. Control, 25, 421, 10.1109/TAC.1980.1102344 Ruhe, 1991 Ruzika, 2005, A survey of approximation methods in multiobjective programming, J. Optim. Theory Appl., 126, 10.1007/s10957-005-5494-4 Sayin, 2000, Measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming, Math. Programming, 87, 543, 10.1007/s101070050128 Sayin, 2005, The multiobjective discrete optimization problem: a weighted min–max two stage optimization approach and a bicriteria algorithm, Management Sci., 51, 1572, 10.1287/mnsc.1050.0413 Skriver, 2003, The bicriterion semi-obnoxious location (BSL) problem solved by an ɛ-approximation, European J. Oper. Res., 146, 517, 10.1016/S0377-2217(02)00271-0 Steuer, 1980, Intra-set point generation and filtering in decision and criterion space, Comput. Oper. Res., 7, 41, 10.1016/0305-0548(80)90013-1 Warburton, 1987, Approximation of Pareto optima in multiple-objective, shortest-path problems, Oper. Res., 35, 70, 10.1287/opre.35.1.70 Yang, 1997, A method for convex curve approximation, European J. Oper. Res., 97, 205, 10.1016/0377-2217(95)00368-1