Expected Running Time Analysis of a Multiobjective Evolutionary Algorithm on Pseudo-boolean Functions
In this paper we suggest a multiobjective evolutionary algorithm based on a restricted mating pool (REMO) with a separate archive for storing the remaining population. Such archive based algorithms have been used for solving real-world applications, however, no theoretical results are available. In this paper, we present a rigorous expected running time complexity analysis for the algorithm on two discrete pseudo boolean functions. We use the well known linear function LOTZ (Leading Zeros : Trailing Ones) and a continuous multiobjective quadratic function which is adapted to the discrete boolean space, for the analysis. The analysis shows that the algorithm runs with an expected time of O(n 2) on LOTZ. Moreover, we prove that the bound holds with an overwhelming probability. For an unary encoding of the multiobjective quadratic function ( (x–a)2,(x–b)2 ) in the boolean space, the expected running time of REMO is found to be O(nlogn). A simple strategy based on partitioning of the decision space into fitness layers is used for the analysis.
KeywordsDecision Space Multiobjective Evolutionary Algorithm Successful Mutation Overwhelming Probability Boolean Space
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- 2.Garnier, J., Kallel, L., Schoenauer, M.: Rigourous Hitting Times for Binary Mutations. Evolutionary Computation 7(2), 167–203 (2002)Google Scholar
- 4.Jagerskupper, J.: Analysis of Simple Evolutionary Algorithm for Minimization in Euclidean Spaces. In: Proceedings of the 30th International Colloquium on Automata, Languages and Programming. LNCS, vol. 2719, pp. 1068–1079 (2003)Google Scholar
- 5.Jansen, T., Wegener, I.: On the analysis of evolutionary algorithms – A proof that crossover really can help. In: Nešetřil, J. (ed.) ESA 1999. LNCS, vol. 1643, pp. 184–193. Springer, Heidelberg (1999)Google Scholar
- 6.Laumanns, M., Thiele, L., Zitzler, E., Welzl, E., Deb, K.: Running time analysis of multi-objective evolutionary algorithms on a simple discrete optimization problem. In: Guervós, J.J.M., Adamidis, P.A., Beyer, H.-G., Fernández-Villacañas, J.-L., Schwefel, H.-P. (eds.) PPSN 2002. LNCS, vol. 2439, pp. 44–53. Springer, Heidelberg (2002)CrossRefGoogle Scholar
- 7.Laumanns, M., Thiele, L., Zitzler, E.: Running Time Analysis of Evolutionary Algorithms on Vector-Valued Pseudo-Boolean Functions. IEEE Transactions on Evolutionary Computation (2004)Google Scholar