Finding the optimum location in a one-median network problem with correlated demands using simulated annealing

The one median location problem with stochastic demands can be solved as a deterministic problem by considering the mean of weights as demands. There are also some other approaches in consideration of this problem. However, it is better to find the probability for each node that shows the chance of the node being in the optimal location, especially when demands are correlated to each other. With this approach, alternative answers with their optimality probability can be found. In small networks with a few nodes, it is not so difficult to solve the problem, because a multivariate normal probability for each node should be calculated. But, when the number of nodes increases, not only do the number of probability calculations increase, but also, the computation time for each multivariate normal distribution grows exponentially. In this paper, a meta-heuristic algorithm, based on modified Simulated Annealing (SA), with consideration of a short term memory module is proposed to find the optimality probability more efficiently. The algorithm was performed on some sample networks with correlated demands.