An electromagnetism-like metaheuristic for the uncapacitated multiple allocation p-hub median problem

• An efficient EM approach for solving the UMApHMP is presented.
• EM approach is combined with scaling technique.
• Local search is implemented very efficiently.
• Experimental comparison with other methods indicates superiority of EM approach.

This paper deals with the uncapacitated multiple allocation p-hub median problem (UMApHMP). An electromagnetism-like (EM) method is proposed for solving this NP-hard problem. Our new scaling technique, combined with the movement based on the attraction–repulsion mechanism, directs the EM towards promising search regions. Numerical results on a battery of benchmark instances known from the literature are reported. They show that the EM reaches all previously known optimal solutions, and gives excellent results on large-scale instances. The present approach is also extended to solve the capacitated version of the problem. As it was the case in the uncapacitated version, EM also reached all previously known optimal solutions.