Fast simulated annealing for single-row equidistant facility layout

Given n facilities and a flow matrix, the single-row equidistant facility layout problem (SREFLP) is to find a one-to-one assignment of n facilities to n locations equally spaced along a straight line so as to minimize the sum of the products of the flows and distances between facilities. We develop a simulated annealing (SA) algorithm for solving this problem. The algorithm provides a possibility to employ either merely pairwise interchanges of facilities or merely insertion moves or both of them. It incorporates an innovative method for computing gains of both types of moves. Experimental analysis shows that this method is significantly faster than traditional approaches. To further speed up SA, we propose a two-mode technique when for high temperatures, at each iteration, only the required gain is calculated and, for lower temperatures, the gains of all possible moves are maintained from iteration to iteration. We experimentally compare SA against the iterated tabu search (ITS) algorithm from the literature. Computational results are reported for SREFLP instances with up to 300 facilities. The results show that the performance of our SA implementation is dramatically better than that of the ITS heuristic.