Running Time Analysis of Evolutionary Algorithms on Vector-Valued Pseudo-Boolean Functions

Abstract

This paper presents a rigorous running time analysis of evolutionary algorithms on pseudo-Boolean multiobjective optimization problems. We propose and analyze di erent population-based algorithms, the simple evolutionary multiobjective optimizer SEMO and two improved versions, FEMO and GEMO. The analysis is carried out on two bi-objective model problems, LOTZ (Leading Ones Trailing Zeroes) and COCZ (Count Ones Count Zeroes) as well as on the scalable m-objective versions mLOTZ and mCOCZ. Results on the running time of the di erent population-based algorithms and for an alternative approach, a multistart (1+1)-EA based on the -constraint method, are derived The comparison reveals that for many problems, the simple algorithm SEMO is as eÆcient as the (1+1)-EA. For some problems, the improved variants FEMO and GEMO are provably better. For the analysis we propose and apply two general tools, an upper bound technique based on a decision space partition and a randomized graph search algorithm, which facilitate the analysis considerably.

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Cite this paper

@inproceedings{Laumanns2003RunningTA, title={Running Time Analysis of Evolutionary Algorithms on Vector-Valued Pseudo-Boolean Functions}, author={Marco Laumanns and Lothar Thiele and Eckart Zitzler}, year={2003} }