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A brain storm optimization approach for the cumulative capacitated vehicle routing problem

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Abstract

The cumulative capacitated vehicle routing problem (CCVRP) is a combinatorial optimization problem which aims to minimize the sum of arrival times at customers. This paper presents a brain storm optimization algorithm to solve the CCVRP. Based on the characteristics of the CCVRP, we design new convergent and divergent operations. The convergent operation picks up and perturbs the best-so-far solution. It decomposes the resulting solution into a set of independent partial solutions and then determines a set of subproblems which are smaller CCVRPs. Instead of directly generating solutions for the original problem, the divergent operation selects one of three operators to generate new solutions for subproblems and then assembles a solution to the original problem by using those new solutions to the subproblems. The proposed algorithm was tested on benchmark instances, some of which have more than 560 nodes. The results show that our algorithm is very effective in contrast to the existing algorithms. Most notably, the proposed algorithm can find new best solutions for 8 medium instances and 7 large instances within short time.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their insightful comments. This work was supported by National Natural Science Foundation of China (No. 61573277), the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. PolyU 15201414), the Fundamental Research Funds for the Central Universities, the Open Research Fund of the State Key Laboratory of Astronautic Dynamics under Grant 2016ADL-DW403, and the Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, Natural Science Basic Research Plan in Shaanxi Province of China (No. 2015JM6316). The authors also would like to thank The Hong Kong Polytechnic University Research Committee for financial and technical support.

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  1. The State Key Laboratory for Manufacturing Systems Engineering, Xian Jiaotong University, Xi’an, 710049, China

    Liangjun Ke

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  1. Liangjun Ke
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Correspondence to Liangjun Ke.

Appendix

Appendix

Table 4 reports the running time consumed by BSO, TPM, ALNS, and HAL for the small instances.

Table 4 The running time (in seconds) consumed for seven instances proposed by [4]
Full size table

Table 5 reports the running time consumed by BSO, TPM, ALNS, and HAL for the medium instances.

Table 5 The running time (in seconds) for the twenty instances proposed by Golden et al. [7]
Full size table

Table 6 reports the running time spent by BSO and HAL for the large instances.

Table 6 The running time (in seconds) for the twelve instances proposed by Li et al. [11]
Full size table

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Ke, L. A brain storm optimization approach for the cumulative capacitated vehicle routing problem. Memetic Comp. 10, 411–421 (2018). https://doi.org/10.1007/s12293-018-0250-0

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