Abstract
Population heuristics present native abilities for solving optimization problems with multiple objectives. The convergence to the efficient frontier is improved when the population contains à good genetic information’. In the context of combinatorial optimization problems with two objectives, the supported solutions are used to elaborate such information, defining a resolution principle in two phases. First the supported efficient solution set, or an approximation, is computed. Second this information is used to improve the performance of a population heuristic during the generation of the effiient frontier. This principle has been experimented on two classes of problems : the 1 | | (ΣCi ; Tmax) permutation scheduling problems, and the biobjective 0-1 knapsack problems. The motivations of this principle are developed. The numerical experiments are reported and discussed.
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References
J.E. Beasley Population heuristics, Working paper, March 1999, The Management School, Imperial College, London, England (1999).
Ch.-L. Chen and R. Bulfin, Complexity of single machine, multi-criteria scheduling problems, European Journal of Operational Research, 70, pp. 115–125 (1993).
M. Ehrgott. Multiple Criteria Optimization — Classification and Methodology. Shaker Verlag, Aachen (1997).
M. Ehrgott and X. Gandibleux, A survey and annotated bibliography of multi-objective combinatorial optimization, OR-Spectrum, Vol.22, No.4, pp.425–460 (2000).
M. Ehrgott and X. Gandibleux, Bounds and bound sets for biobjective combinato-rial optimization problems, Technical report (to appear in the proceedings of 15th MCDM International Conference), University of Auckland, New-Zealand (2000).
X. Gandibleux, H. Morita and N. Katoh, A genetic Algorithm for 0-1 MultiObjec-tive Knapsack Problem, Technical report (presented at NACA98, July 28-31 1998, Niigata, Japan), University of Valenciennes, France (1998).
A. M. Geoffrion, Proper efficiency and the theory of vector maximization. Journal of Mathematical Analysis and Applications, 22, pp. 618–630 (1968).
D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learn-ing, Addison-Wesley (1989).
A. Hertz and D. Kobler, A framework for the Description of Population Based Methods, EUROXVI, Tutorials and Research Reviews, 23 pages (1998).
S. Martello and P. Toth. Knapsack Problems-Algorithms and Computer Implemen-tations. John Wiley & Sons, Chichester (1990).
H. Morita and N. Katoh, A Genetic algorithm for a bicriteria flow-shop schedul-ing problem (in Japanese), Transactions of the Institute of Systems, Control and Information Engineers, Vol.10, No.3, pp.127–136 (1997).
H. Morita, X. Gandibleux and N. Katoh, Experimental feedback on biobjective permutation scheduling problems solved with a population heuristic, Technical report(submitted to Foundations of Computing and Decision Sciences Journal), University of Valenciennes, France (2000).
A. Nagar, J. Haddock and S. Heragu, Multiple and bicriterion scheduling: A liter-ature survey, European Journal of Operational Research, Vol.81, pp.88–104 (1995).
E.L. Ulungu, J. Teghem and P. Fortemps, Heuristics for multi-objective combinato-rial optimization problem by simulated annealing, MCDM: Theory and applications (J. Gu, G. Chen, Q. Wei and S. Wang Edts.), SCI-TECH Information services, pp. 228–238 (1995).
L. N. Van Wassenhove and L. F. Gelders, Solving a bicriterion scheduling problem, European Journal of Operational Research, Vol.4, pp.42–48 (1980).
M. Visée, J. Teghem, M. Pirlot, and E.L. Ulungu. Two-phases method and branch and bound procedures to solve the bi-objective knapsack problem. Journal of Global Optimization, 12, pp. 139–155 (1998).
MCDM Numerical Instances Library, MultiObjective Combinatorial Optimization Problems, http://www.univ-valenciennes.fr/ROAD/MCDM/.
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Gandibleux, X., Morita, H., Katoh, N. (2001). The Supported Solutions Used as a Genetic Information in a Population Heuristic. In: Zitzler, E., Thiele, L., Deb, K., Coello Coello, C.A., Corne, D. (eds) Evolutionary Multi-Criterion Optimization. EMO 2001. Lecture Notes in Computer Science, vol 1993. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44719-9_30
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DOI: https://doi.org/10.1007/3-540-44719-9_30
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