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Hybrid Max–Min ant system with four vertices and three lines inequality for traveling salesman problem

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Abstract

The objective of traveling salesman problem (TSP) is to find the optimal Hamiltonian circuit (OHC). It has been proven to be NP complete in most cases. The hybrid Max–Min ant system (MMA) integrated with a four vertices and three lines inequality is introduced to search the OHC. The four vertices and three lines inequality is taken as the constraints of the local optimal Hamiltonian paths (LOHP), including four vertices and three lines and all the LOHPs in the OHC conform to the inequality. At first, the MMA is used to search the approximate OHCs. Then, the local paths of adjacent four vertices in the approximate OHCs are converted into the LOHPs with the four vertices and three lines inequality to get the better approximation. The hybrid Max–Min ant system (HMMA) is tested with tens of TSP instances. The results show that the better approximations are computed with the HMMA than those with the MMA under the same preconditions.

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Acknowledgments

The authors acknowledge the project supported by NSFC (Grant No. 51205129) and the fund supported by the Fundamental Research Funds for the Central Universities (Grant No. 12MS48). The work benefits from the facilities of National Key Laboratory of New Energy Power System and the Beijing Key Laboratory of New and Renewable Energy, North China Electric Power University, Beijing, China.

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Authors and Affiliations

  1. School of Renewable Energy, North China Electric Power University, Beijing , 102206, China

    Wang Yong

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  1. Wang Yong
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Correspondence to Wang Yong.

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Communicated by M. J. Watts.

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Yong, W. Hybrid Max–Min ant system with four vertices and three lines inequality for traveling salesman problem. Soft Comput 19, 585–596 (2015). https://doi.org/10.1007/s00500-014-1279-8

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