Abstract
This work proposes a method to control the dominance area of solutions in order to induce appropriate ranking of solutions for the problem at hand, enhance selection, and improve the performance of MOEAs on combinatorial optimization problems. The proposed method can control the degree of expansion or contraction of the dominance area of solutions using a user-defined parameter S. Modifying the dominance area of solutions changes their dominance relation inducing a ranking of solutions that is different to conventional dominance. In this work we use 0/1 multiobjective knapsack problems to analyze the effects on solutions ranking caused by contracting and expanding the dominance area of solutions and its impact on the search performance of a multi-objective optimizer when the number of objectives, the size of the search space, and the complexity of the problems vary. We show that either convergence or diversity can be emphasized by contracting or expanding the dominance area. Also, we show that the optimal value of the area of dominance depends strongly on all factors analyzed here: number of objectives, size of the search space, and complexity of the problems.
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References
Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons, Chichester (2001)
Coello, C.A.C., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer Academic Publishers, Dordrecht (2002)
Purshouse, R.C., Fleming, P.J.: Conflict, Harmony, and Independence: Relationships in Evolutionary Multi-criterion Optimisation. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 16–30. Springer, Heidelberg (2003)
Hughes, E.J.: Evolutionary Many-Objective Optimisation: Many Once or One Many? In: Proc. 2005 IEEE Congress on Evolutionary Computation, vol. 1, September, pp. 222–227. IEEE, Los Alamitos (2005)
Aguirre, H., Tanaka, K.: Working Principles, Behavior, and Performance of MOEAs on MNK-Landscapes. European Journal of Operational Research, Special Issue on Evolutionary Multi-Objective Optimization (in press) (Sep. 2006)
Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining Convergence and Diversity in Evolutionary Multi-objective Optimization. Evolutionary Computation 10(3), 263–282 (2002)
Ikeda, K., Kita, H., Kobayashi, S.: Failure of Pareto-based MOEAs: Does Non-dominated Really Mean Near to Optimal? In: Proc. 2001 IEEE Congress on Evolutionary Computation, vol. 2, pp. 957–962. IEEE, Los Alamitos (2001)
Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: NSGA-II. KanGAL report 200001 (2000)
Zitzler, E., Thiele, L.: Multiobjective optimization using evolutionary algorithms – a comparative case study. In: Proc. of 5th Intl. Conf. on Parallel Problem Solving from Nature (PPSN-V), pp. 292–301 (1998)
Zitzler, E.: Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications, PhD thesis, Swiss Federal Institute of Technology, Zurich (1999)
Knowles, J., Corne, D.: On Metrics for Comparing Non-dominated Sets. In: Proc. 2002 IEEE Congress on Evolutionary Computation, pp. 711–716. IEEE Computer Society Press, Los Alamitos (2002)
Sato, H., Aguirre, H., Tanaka, K.: Local Dominance Using Polar Coordinates to Enhance Multi-objective Evolutionary Algorithms. In: Proc. 2004 IEEE Congress on Evolutionary Computation, vol. 1, pp. 188–195. IEEE, Los Alamitos (2004)
Veldhuizen, D.A.V., Lamont, G.B.: On Measuring Multiobjective Evolutionary Algorithm Performance. In: Proc. IEEE 2000 Congress on Evolutionary Computation, vol. 1, pp. 204–211. IEEE, Los Alamitos (2000)
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Sato, H., Aguirre, H.E., Tanaka, K. (2007). Controlling Dominance Area of Solutions and Its Impact on the Performance of MOEAs. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds) Evolutionary Multi-Criterion Optimization. EMO 2007. Lecture Notes in Computer Science, vol 4403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70928-2_5
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DOI: https://doi.org/10.1007/978-3-540-70928-2_5
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