Abstract Let a graph G = (V, E) with vertex set V and edge set E be given. The classical graph version of the p-median problem asks for a subset $$X\\subseteq V$$ of cardinality p, so that the (weighted) sum of the minimum distances from X to all other vertices in V is minimized. We consider the semi-obnoxious case, where every vertex has either a positive or a negative weight. This gives rise to two different objective functions, namely the weighted sum of the minimum distances from X to the vertices in V\\X and, differently, the sum over the minimum weighted distances from X to V\\X. In this paper an Ant Colony algorithm with a tabu restriction is designed for both problems. Computational results show its superiority with respect to a previously investigated variable neighborhood search and a tabu search heuristic.

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