A gamma heuristic for the p-median problem

Heuristic concentration (HC) is a two-stage metaheuristic that can be applied to a wide variety of combinatorial problems. It is particularly suited to location problems in which the number of facilities is given in advance. In such settings, the first stage of HC repeatedly applies some random-start interchange (or other) heuristic to produce a number of alternative facility configurations. A subset of the best of these alternatives is collected and the union of the facility sites in them is called a concentration set (CS). Among the component elements of the CS are likely to be included those sites which are members of the optimal solution. In earlier studies the second stage of HC has consisted of an exact procedure to extract the best possible solution from the CS. In this paper we demonstrate, for the p-median problem, the use of two sequentially active heuristics in the second stage of HC. That is, we offer two additional layers of heuristics to improve solutions which are found in the first stage of HC. Thus we are describing a variant of the HC metaheuristic consisting of three layers of heuristics which are utilized in sequence. We propose for this procedure the name of Gamma Heuristic.