Abstract
The recent interest in multiobjective combinatorial optimization problems resulted in the development of several exact algorithms and metaheuristics for the a posteriori solution of these problems. However, there are as yet no commonly used, reliable methods to compare approximations generated by these algorithms. In this paper, we introduce a new measure for this purpose: Integrated Convex Preference (ICP). We compare the performance of ICP with that of the existing measures using approximations generated by two different genetic algoithms for an NP-hard, bi-criteria parallel machine scheduling problem. Our results show that our measure outperforms existing measures previously used in the literature, and that ICP can handle approximate solution sets with diverse geometric features effectively.
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References
Carlyle, W. M., Kim, B., Fowler, J. W., and Gel, E. S. (2000) A measure to compare sets of Pareto optimal solutions for multiobjective optimization problems. Technical Report ASU-IE-ORPS-2000-022, Department of Industrial Engineering, Arizona State University, Tempe, AZ.
Cieniawski, S. E., Eheart, J. W., and Ranjithan, S. (1995) Using Genetic Algorithms to Solve a Multiobjective Groundwater Monitoring Problem. Water Resources Research, 31(2):399–409.
Czyzak, P. and Jaszkiewicz, B. (1998) Pareto Simulated annealing — A Metahueristic Technique for Multiple-Objective Combinatorial Optimization. Journal of Multi-Criteria Decision Analyses, 7:34–47.
De, P., Ghosh, J. B., and Wells, C. E. (1992) Heuristic Estimation of the Efficient Frontier for a Bi-Criteria Scheduling Problem. Decision Sciences, 23:596–609.
Daniels, R. L., (1992). Analytical evaluation of multi-criteria heuristics. Management Science, 38(4):501–513.
Ehrgott, M. and Gandibleux, X. (2000) An Annotated Bibliography of Multiobjective Combinatorial Optimization Problems. To appear in OR Spektrum.
Fowler, J. W., Horng, S.-H., and Cochran, J. K. (1999) A Multi Population Genetic Algorithm to Solve Parallel Machine Scheduling Problem with Sequence Dependent Setups. Technical Report ASU-IE-ORPS-1999-007, Department of Industrial Engineering, Arizona State University, Tempe, AZ.
Hansen M. P. and Jaszkiewicz, A. (1998) Evaluating the quality of approximations to the non-dominated set. IMM Technical Report IMM-REP-1998-7, Technical University of Denmark, Denmark.
Hyun, C. J., Kim, Y., and Kim, Y. K. (1998) A Genetic Algorithm for Multiple Objective Sequencing Problems in Mixed Model Assembly Lines. Computers & Operations Research, 25(7/8):675–690.
Murata, T., Ishibuchi, H., and Tanaka, H. (1996) Multiobjective genetic algorithm and its application to flowshop scheduling. Computers Industrial Engineering, 30(4):957–968.
Pinedo, M. (1995). Scheduling: Theory, Algorithms, and Systems. Prentice Hall, New Jersey.
Sayin, S. (2000) Measuring the quality of discrete representaions of efficient sets in multiple objective mathematical programming. Mathematical Programming, 87(2):543–560
Schaffer, J. D. (1985) Multiple objective optimization with vector evaluated genetic algorithms. Proceedings of the first International Conference on Genetic Algorithms, 93–100.
Schenkerman, S. (1990) Relative Objective Functions in Multiobjective Decision Support Models. Decision Sciences, 21:727–737.
Viana, A. and Sousa, J. P. (2000) Using metaheuristics in multiobjective resource constrained project scheduling. European Journal of Operations Research, 120:359–374.
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© 2001 Springer-Verlag Berlin Heidelberg
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Kim, B., Gel, E.S., Carlyle, W.M., Fowler, J.W. (2001). A New Technique to Compare Algorithms for Bi-criteria Combinatorial Optimization Problems. In: Köksalan, M., Zionts, S. (eds) Multiple Criteria Decision Making in the New Millennium. Lecture Notes in Economics and Mathematical Systems, vol 507. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56680-6_10
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DOI: https://doi.org/10.1007/978-3-642-56680-6_10
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