Abstract
In this paper, the expected running time of two multiobjectiveevolutionary algorithms, SEMO and FEMO, is analyzed for a simpleinstance of the multiobjective 0/1 knapsack problem. The considered problem instance has two profit values per item andcannot be solved by one-bit mutations. In the analysis, we make use of two general upper bound techniques, thedecision space partition method and the graph search method. The paperdemonstrates how these methods, which have previously only beenapplied to algorithms with one-bit mutations, are equally applicablefor mutation operators where each bit is flipped independently with acertain probability.
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Bäck T, Fogel DB and Michalewicz Z (eds) (1997) Handbook of Evolutionary Computation. IOP Publishing and Oxford University Press, Bristol, UK
Beyer H-G, Schwefel H-P and Wegener I (2002) How to analyse evolutionary algorithms. Theoretical Computer Science 287: 101–130
Deb K (2001) Multi-Objective Optimization Using Evolutionary Algorithms. Wiley, Chichester
Giel O (2003) Expected runtimes of a simple multi-objective evolutionary algorithm. In: Congress on Evolutionary Computation (CEC 2003). Piscataway, NJ
Jaszkiewicz A (2002) On the performance of multiple objective genetic local search on the 0/1 knapsack problem. A comparative experiment. IEEE Transactions on Evolutionary Computation 6(4): 402–412
Laumanns M, Thiele L and Zitzler E (2004) Running time analysis of multiobjective evolutionary algorithms on pseudo-boolean functions. IEEE Transactions on Evolutionary Computation. Accepted for publication
Laumanns M, Thiele L, Zitzler E, Welzl E and Deb K (2002) Running time analysis of multiobjective evolutionary algorithms on a simple discrete optimization problem. In: Parallel Problem Solving From Nature (PPSN VII), pp. 44–53. Springer, Berlin
Schaffer JD (1985) Multiple objective optimization with vector evaluated genetic algorithms. In: Grefenstette JJ (ed) Proceedings of an International Conference on Genetic Algorithms and Their Applications, pp. 93–100
Scharnow J, Tinnefeld K and Wegener I (2002) Fitness landscapes based on sorting and shortest paths problems In: Guervas JJM et al. (eds) Parallel Problem Solving From Nature (PPSN VII), pp. 54–63. Springer, Berlin
Wegener I (2000) Methods for the analysis of evolutionary algorithms on pseudo-boolean functions. In: Sarker R, Yao X and Mohammadian M (eds) Evolutionary Optimization, pp. 349–369. Kluwer Academic Publishers, Dordrecht
Zitzler E and Thiele L (1999) Multiobjective evolutionary algorithms: A comparative case study and the strength Pareto approach. IEEE Transactions on Evolutionary Computation 3(4): 257–271
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Laumanns, M., Thiele, L. & Zitzler, E. Running time analysis of evolutionary algorithms on a simplified multiobjective knapsack problem. Natural Computing 3, 37–51 (2004). https://doi.org/10.1023/B:NACO.0000023415.22052.55
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DOI: https://doi.org/10.1023/B:NACO.0000023415.22052.55