A comparison of Lagrangean and surrogate relaxations for the maximal covering location problem

We compare heuristics based on Lagrangean and surrogate relaxations of the Maximal Covering Location Problem (MCLP). The Lagrangean relaxation of MCLP used in this paper has the integrality property and the surrogate relaxed problem we solve is the LP relaxation of the original 0ÿ1 knapsack problem. The heuristics were compared using 331 test problems available in the literature, corresponding to networks ranging from 55 to 900 vertices. The gaps obtained with both heuristics were very low and did not di€er substantially among themselves for the several problem sets used, in accordance with theoretical results reviewed in the paper. When the initial set of multipliers was determined using a valid bound for MCLP the computing times did not di€er signi®cantly between the Lagrangean and surrogate heuristics. Ó 2000 Elsevier Science B.V. All rights reserved.