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Performance Analysis of the (1+1) Evolutionary Algorithm for the Multiprocessor Scheduling Problem

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Abstract

In recent years, there has been considerable progress in the theoretical study of evolutionary algorithms (EAs) for discrete optimization problems. However, results on the performance analysis of EAs for NP-hard problems are rare. This paper contributes a theoretical understanding of EAs on the NP-hard multiprocessor scheduling problem. The worst-case bound on the (1+1)EA for the multiprocessor scheduling problem and a worst-case example are presented. It is proved that the (1+1)EA on \(Q2\mid \mid C_\mathrm{max}\) problem achieves an approximation ratio of \(\frac{1+\sqrt{5}}{2}\) in expected time \(O(n^2)\). Finally, the theoretical analysis on three selected instances of the multiprocessor scheduling problem shows that EAs outperform local search algorithms on these instances.

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Acknowledgments

Y. Zhou supported by National Natural Science Foundation of China under the Grant 61170081. J. Zhang supported by National Natural Science Foundation of China under the Grants 61125205 and 61332002. Y. Wang supported by National Natural Science Foundation of China under the Grant 61273314.

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Authors and Affiliations

  1. School of Computer Science and Engineering, South China University of Technology, Guangzhou, 510006, China

    Yuren Zhou

  2. Department of Computer Science, Sun Yat-Sen University, Guangzhou, 510275, China

    Jun Zhang

  3. College of Information Science and Engineering, Central South University, Changsha, Hunan, China

    Yong Wang

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  1. Yuren Zhou
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  2. Jun Zhang
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  3. Yong Wang
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Correspondence to Yuren Zhou.

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Zhou, Y., Zhang, J. & Wang, Y. Performance Analysis of the (1+1) Evolutionary Algorithm for the Multiprocessor Scheduling Problem. Algorithmica 73, 21–41 (2015). https://doi.org/10.1007/s00453-014-9898-0

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  • DOI: https://doi.org/10.1007/s00453-014-9898-0

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