A statistical analysis of simulated annealing applied to the p-median problem

We present a statistical analysis of simulated annealing applied to the p-median problem. The algorithm we use combines elements of the vertex substitution method of Teitz and Bart with the general methodology of simulated annealing. The cooling schedule adopted incorporates the notion of temperature adjustments rather than just temperature reductions. Computational results are given for test problems ranging from 100 to 900 vertices, retrieved from Beasley's OR-Library for combinatorial problems. Each problem was run for a maximum of 100 different streams of random numbers. Optimal solutions were found for 26 of the 40 problems tested, although high optimum hitting rates were obtained for only 20 of them. The worst gap in relation to the optimal solution was 1.62%, after all runs for each of the test problems were computed.