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An improved fireworks algorithm for the capacitated vehicle routing problem

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Abstract

The capacitated vehicle routing problem (CVRP), which aims at minimizing travel costs, is a well-known NP-hard combinatorial optimization. Owing to its hardness, many heuristic search algorithms have been proposed to tackle this problem. This paper explores a recently proposed heuristic algorithm named the fireworks algorithm (FWA), which is a swarm intelligence algorithm. We adopt FWA for the combinatorial CVRP problem with several modifications of the original FWA: it employs a new method to generate “sparks” according to the selection rule, and it uses a new method to determine the explosion amplitude for each firework. The proposed algorithm is compared with several heuristic search methods on some classical benchmark CVRP instances. The experimental results show a promising performance of the proposed method. We also discuss the strengths and weaknesses of our algorithm in contrast to traditional algorithms.

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 61573277), the Fundamental Research Funds for the Central Universities, the Open Projects Program of National Laboratory of Pattern Recognition, the Open Research Fund of the State Key Laboratory of Astronautic Dynamics (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 (2015JM6316). We are also thankful to the anonymous referees.

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

    Weibo Yang & Liangjun Ke

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  1. Weibo Yang
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  2. Liangjun Ke
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Correspondence to Liangjun Ke.

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Weibo Yang received the BS degree in automation from Xi’an Jiaotong University (XJTU), China. He is currently working toward the PhD degree in control science and engineering at XJTU. His research interests include combinatorial optimization and evolutionary computation.

Liangjun Ke received the BS and MS degrees in mathematics from Wuhan University, China in 1998 and 2001, respectively, and the PhD degree in systems engineering from Xi’an Jiaotong University (XJTU), China in 2008.

He is currently an associate professor at XJTU. His current research interests include optimization theory and applications, especially multiobjective optimization, evolutionary computation, and robust optimization.

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Yang, W., Ke, L. An improved fireworks algorithm for the capacitated vehicle routing problem. Front. Comput. Sci. 13, 552–564 (2019). https://doi.org/10.1007/s11704-017-6418-9

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