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Analysis of multiobjective evolutionary algorithms on the biobjective traveling salesman problem (1,2)

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Abstract

Multiobjective evolutionary algorithms have been successfully used to deal with multiobjective combinatorial optimization problems for more than two decades. However, we know little about the performance of multiobjective evolutionary algorithms on multiobjective combinatorial optimization problems in theory so far, especially on NP-hard ones from real-world, since Pareto curves are often of exponential size, meanwhile, evolutionary algorithms rely heavily on the use of randomness and are hard to understand from a theoretical point of view. In this paper, we theoretically investigate the performance of two simple multiobjective evolutionary algorithms with different population diversity mechanisms on the biobjective traveling salesman problem (1,2). It is found that one of them can efficiently find a \(\frac {3}{2}\)-approximation Pareto curve for the problem, the best result so far. At the same time, these two multiobjective evolutionary algorithms are proved to be superior to a multiobjective local search algorithm, and the multiobjective local search algorithm is also proven to outperform these two multiobjective evolutionary algorithms as well. Finally, the population diversity is proved to be helpful in reducing the expected runtime of multiobjective evolutionary algorithm.

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Acknowledgments

The authors are very grateful to the anonymous referees and editors for their valuable suggestions and comments, which have helped to improve the paper greatly. The authors also thank Qing Yan, Xiaoyun Xia and Langping Tang for their help in revising this manuscript. This work was supported by National Natural Science Foundation of China (Nos. 61562071, 61773410).

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  1. School of Computer Science and Engineering, Shaoxing University, Shaoxing, 312000, Zhejiang, China

    Xinsheng Lai

  2. School of Data and Computer Science, Sun Yat-sen University, Guangzhou, 510006, China

    Yuren Zhou

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  1. Xinsheng Lai
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  2. Yuren Zhou
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Correspondence to Xinsheng Lai.

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Lai, X., Zhou, Y. Analysis of multiobjective evolutionary algorithms on the biobjective traveling salesman problem (1,2). Multimed Tools Appl 79, 30839–30860 (2020). https://doi.org/10.1007/s11042-020-09399-z

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  • DOI: https://doi.org/10.1007/s11042-020-09399-z

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