An electromagnetism metaheuristic for solving the Maximum Betweenness Problem

In this paper we present an electromagnetism (EM) metaheuristic for solving NP hard Maximum Betweenness Problem (MBP). A new encoding scheme with appropriate objective functions is implemented. Specific representation of the individuals enables the EM operators to explore the searching space in a way that achieves high quality solutions. An effective 1-swap based local search procedure improved by the specific caching technique is performed on each EM point. The algorithm is tested both on real and artificial instances from the literature. Experimental results show that the proposed EM approach achieves all previously known optimal solutions, except one, and achieves the best-known solutions or outperforms other approaches on all large-scale instances, except two. Provided statistical analysis indicates that the EM approach is significantly better than other approaches.

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► We presented an electromagnetism-like algorithm for solving the MBP.
► An effective 1-swap local search is successfully applied on each EM point.
► Overall running time is improved by a caching technique.
► Experiments are performed both on real and artificial instances known in literature.
► Statistical analysis indicates the superiority of EM approach.