Scatter search for an uncapacitated p-hub median problem

Scatter search is a population-based method that has been shown to yield high-quality outcomes for combinatorial optimization problems. It uses strategies for combining solution vectors that have proved effective in a variety of problem settings. In this paper, we present a scatter search implementation for an NP -hard variant of the classic p-hub median problem. Specifically, we tackle the uncapacitated r-allocation p-hub median problem, which consists of minimizing the cost of transporting the traffics between nodes of a network through special facilities that act as transshipment points. This problem has a significant number of applications in practice, such as the design of transportation and telecommunications networks.As it is customary in metaheuristic implementations, we design specific methods to create an efficient solving procedure based on the scatter search methodology. In particular, we propose mechanisms to generate, combine, and improve solutions for this problem. Special mention deserves the use of path-relinking as an extension of the classical combination method. Extensive computational experiments establish the effectiveness of our procedure in relation to approaches previously identified to be best.