ADVANCED GRASP FOR THE OBNOXIOUS p-MEDIAN PROBLEM J. MANUEL COLMENAR, PETER GREISTORFER, RAFAEL MART ´ I, AND ABRAHAM DUARTE Abstract. The Obnoxious p-Median problem consists in selecting a subset of p facilities from a given set of possible locations, in such a way that the sum of the distances between each customer and its nearest facility is maximized. The problem is NP-hard and can be formulated as an integer linear program. It was introduced in the 1990s, and a branch and cut method coupled with a tabu search has been recently proposed. In this paper, we propose a heuristic method – based on the GRASP methodology – for finding approximate so- lutions to this optimization problem. In particular, we consider an advanced GRASP design in which a filtering mechanism avoids applying the local search method to low quality constructed solutions. Empirical results indicate that the proposed implementation compares favorably to previous methods. This fact is confirmed with non-parametric statistical tests. 1. Introduction Facility location has been of practical and theoretical interest for more than the half of a century (Cohen, 1973; Klose and Drexl, 2005). First linear program- ming (LP) formulations origin in the late fifties and were soon followed by solution techniques, which later on became well-known as Branch and Bound (B&B) or Mixed Integer Programing (MIP). The classical so-called warehouse location prob- lem (WLP), also well-known as (simple) facility or plant location problem, is an uncapacitated optimization problem, which can be modeled as an LP (Balinski, 1965) or network problem (Drezner and Hamacher, 2004; Melkote and Daskin, 2001). It is a site-selecting location-allocation model with a min-sum objective, where from a number of potential facility or warehouse sites the set of costumers has to be serviced, while minimizing the total fixed site-costs (location) plus the to- tal variable customer assignment costs (allocation). The WLP is NP -hard (Garey and Johnson, 1979; Papadimitriou and Yannakakis, 1991) and, as such, has been in the focus of researchers interested in developing specialized LP-approaches (K¨orkel, 1999) or approximative constructive and local search or improvement algorithms, including standard add- or drop-heuristics, and Lagrangian approaches (Kuehn and Hamburger, 1963; Beasley, 1993), which then were followed by more advanced metaheuristics like genetic algorithms or tabu search and its derivatives (Kratica et al., 2001; Michel and Hentenryck, 2004; Greistorfer and Rego, 2006). Comparing the WLP with the p-median problem, pMP (Hakimi, 1964; 1965), one identifies two differences: (1) there are no fixed site-costs involved and (2) the number of finally opened sites, p, is no longer a decision variable, but becomes included in Key words and phrases. Obnoxious location, Diversity problem, Metaheuristics, GRASP, Filter solutions. 1 Manuscript (including abstract) Click here to view linked References