Less is more: adjusting convergence of Cooper’s algorithm in the continuous location-allocation problem

This paper proposes a variant of the well-known heuristic by Cooper for continuous location-allocation problems in general, and in particular, the continuous p-median problem. This algorithm alternates between a location phase where the allocations are fixed and an allocation phase where the locations of the p new facilities are fixed. The main idea of the proposed variant is to partially solve the p independent one-median problems in the location phase (instead of solving optimally) in order to induce a larger number of cycles of location-allocation. In effect, we are trying to alter the descent path of the algorithm by slowing the convergence rate using smaller descent steps in the location phase. Computational experiments show that this approach is highly effective in finding alternate descent paths that lead to “deeper” local minima. The best improvements are obtained with random starting locations of the p facilities, and the larger values of p that were tested.