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 deterministicproblem by considering the mean of weights as demands. there are also some other approaches inconsideration of this problem. however, it is better to find the probability for each node that shows thechance 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 networkswith a few nodes, it is not so difficult to solve the problem, because a multivariate normal probabilityfor each node should be calculated. but, when the number of nodes increases, not only do the number ofprobability calculations increase, but also, the computation time for each multivariate normal distributiongrows 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 probabilitymore efficiently. the algorithm was performed on some sample networks with correlated demands.