Abstract
It has been reported for multi-objective knapsack problems that the recombination of similar parents often improves the performance of evolutionary multi-objective optimization (EMO) algorithms. Recently performance improvement was also reported by exchanging only a small number of genes between two parents (i.e., crossover with a very small gene exchange probability) without choosing similar parents. In this paper, we examine these performance improvement schemes through computational experiments where NSGA-II is applied to 500-item knapsack problems with 2-10 objectives. We measure the parent-parent distance and the parent-offspring distance in computational experiments. Clear performance improvement is observed when the parent-offspring distance is small. To further examine this observation, we implement a distance-based crossover operator where the parent-offspring distance is specified as a user-defined parameter. Performance of NSGA-II is examined for various parameter values. Experimental results show that an appropriate parameter value (parent-offspring distance) is surprisingly small. It is also shown that a very small parameter value is beneficial for diversity maintenance.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Beume, N., Naujoks, B., Emmerich, M.: SMS-EMOA: Multiobjective Selection based on Dominated Hypervolume. European J. of Operational Research 181, 1653–1669 (2007)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II. IEEE Trans. on Evolutionary Computation 6, 182–197 (2002)
Ishibuchi, H., Akedo, N., Nojima, Y.: Recombination of Similar Parents in SMS-EMOA on Many-Objective 0/1 Knapsack Problems. In: Coello Coello, C.A., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds.) PPSN 2012, Part II. LNCS, vol. 7492, pp. 132–142. Springer, Heidelberg (2012)
Ishibuchi, H., Akedo, N., Nojima, Y.: Relation between Neighborhood Size and MOEA/D Performance on Many-Objective Problems. In: Purshouse, R.C., Fleming, P.J., Fonseca, C.M., Greco, S., Shaw, J. (eds.) EMO 2013. LNCS, vol. 7811, pp. 459–474. Springer, Heidelberg (2013)
Ishibuchi, H., Akedo, N., Nojima, Y.: Behavior of Multi-Objective Evolutionary Algorithms on Many-Objective Knapsack Problems. IEEE Trans. on Evolutionary Computation (in press)
Ishibuchi, H., Narukawa, K., Tsukamoto, N., Nojima, Y.: An Empirical Study on Similarity-Based Mating for Evolutionary Multiobjective Combinatorial Optimization. European J. of Operational Research 188, 57–75 (2008)
Ishibuchi, H., Tsukamoto, N., Nojima, Y.: Evolutionary Many-Objective Optimization: A Short Review. In: Proc. of IEEE CEC, pp. 2424–2431 (2008)
Ishibuchi, H., Tsukamoto, N., Nojima, Y.: Diversity Improvement by Non-Geometric Binary Crossover in Evolutionary Multiobjective Optimization. IEEE Trans. on Evolutionary Computation 14, 985–998 (2010)
Jaszkiewicz, A.: On the Computational Efficiency of Multiple Objective Metaheuristics: The Knapsack Problem Case Study. European J. of Operational Research 158, 418–433 (2004)
Moraglio, A., Poli, R.: Topological Interpretation of Crossover. In: Deb, K., Tari, Z. (eds.) GECCO 2004. LNCS, vol. 3102, pp. 1377–1388. Springer, Heidelberg (2004)
Moraglio, A., Poli, R.: Product Geometric Crossover. In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN IX. LNCS, vol. 4193, pp. 1018–1027. Springer, Heidelberg (2006)
Moraglio, A., Poli, R.: Inbreeding Properties of Geometric Crossover and Non-geometric Recombinations. In: Stephens, C.R., Toussaint, M., Whitley, L.D., Stadler, P.F. (eds.) FOGA 2007. LNCS, vol. 4436, pp. 1–14. Springer, Heidelberg (2007)
Sato, H., Aguirre, H.E., Tanaka, K.: Local Dominance and Local Recombination in MOEAs on 0/1 Multiobjective Knapsack Problems. European J. of Operational Research 181, 1708–1723 (2007)
Sato, H., Aguirre, H., Tanaka, K.: Variable Space Diversity, Crossover and Mutation in MOEA Solving Many-Objective Knapsack Problems. Annals of Mathematics and Artificial Intelligence 68, 197–224 (2013)
While, L., Bradstreet, L., Barone, L.: A Fast Way of Calculating Exact Hypervolumes. IEEE Trans. on Evolutionary Computation 16, 86–95 (2012)
Zhang, Q., Li, H.: MOEA/D: A Multiobjective Evolutionary Algorithm Based on Decomposition. IEEE Trans. on Evolutionary Computation 11, 712–731 (2007)
Zitzler, E., Thiele, L.: Multiobjective Evolutionary Algorithms: A Comparative Case Study and the Strength Pareto Approach. IEEE Trans. on Evolutionary Computation 3, 257–271 (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Ishibuchi, H., Tanigaki, Y., Masuda, H., Nojima, Y. (2014). Distance-Based Analysis of Crossover Operators for Many-Objective Knapsack Problems. In: Bartz-Beielstein, T., Branke, J., Filipič, B., Smith, J. (eds) Parallel Problem Solving from Nature – PPSN XIII. PPSN 2014. Lecture Notes in Computer Science, vol 8672. Springer, Cham. https://doi.org/10.1007/978-3-319-10762-2_59
Download citation
DOI: https://doi.org/10.1007/978-3-319-10762-2_59
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-10761-5
Online ISBN: 978-3-319-10762-2
eBook Packages: Computer ScienceComputer Science (R0)