A hybrid artificial bee colony algorithm for the p-median problem with positive/negative weights

In the classical p-median problem, the objective is to find a set Y of p vertices on an undirected graph $$G=(V,E)$$ in such a way that $$ Y \subseteq V$$ and the sum of distances from all the vertices to their respective closest vertices in Y is minimized. In this paper, we have considered the weighted case where every vertex in G has either a positive or a negative weight under two different objective functions, viz. the sum of the minimum weighted distances and the sum of the weighted minimum distances. In this paper, we have proposed a hybrid artificial bee colony (ABC) algorithm for the positive/negative weighted p-median problem where each solution generated by ABC algorithm is improved by an interchange based randomized local search. In addition, an interchange based exhaustive local search is applied on some of the best solutions obtained after the execution of ABC algorithm in a bid to further improve their quality. We have compared our approach with the state-of-the-art approaches available in the literature on the standard benchmark instances. Computational results demonstrate the effectiveness of our approach.