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An improved shuffled frog-leaping algorithm for the minmax multiple traveling salesman problem

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Abstract

The multiple traveling salesman problem (mTSP), as an extended version of the well-known traveling salesman problem, aims to search for a group of circuits when multiple salesmen are sent to travel a set of cities and each city should be visited exactly once. Although some research efforts have been devoted for this problem, most of them concentrate on how to minimize the sum of traveling distances of all salesmen, and only very few aim to specifically minimize the maximum distance traveled by all the salesmen (minmax mTSP). The minmax mTSP is of large practical importance as it is able to model various real-life applications where workload among salesmen should be balanced or where the travel time is adopted rather than the travel distance. This paper proposes a novel improved shuffled frog-leaping algorithm (ISFLA) to address this problem. In ISFLA, a novel population partition method and a heterogeneous evolution mechanism are introduced to improve cooperative evolution and yield a high-quality solution. Guided and unguided leaping mechanisms are devised to evolve frog individuals. Computational experiments on some benchmark problems are conducted, and the results reveal the superiority of ISFLA over some state-of-the-art approaches for this problem.

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Acknowledgements

This work is supported in part by the National Natural Science Foundation of China under Grant 62072060 and Technology Innovation and Application Development Foundation of Chongqing under Grant cstc2020jscx-gksbX0010. The authors would like to thank the editors and anonymous reviewers for their valuable comments and suggestions to improve this paper.

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  1. College of Computer Science, Chongqing University, Chongqing, China

    Yafei Dong, Quanwang Wu & Junhao Wen

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  1. Yafei Dong
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  2. Quanwang Wu
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  3. Junhao Wen
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Correspondence to Quanwang Wu.

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Dong, Y., Wu, Q. & Wen, J. An improved shuffled frog-leaping algorithm for the minmax multiple traveling salesman problem. Neural Comput & Applic 33, 17057–17069 (2021). https://doi.org/10.1007/s00521-021-06298-8

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