The center location-dependent relocation problem with a probabilistic line barrier

► This paper presents a new MINLP model for a probabilistic restricted center location-dependent relocation problem. ► Two meta-heuristics based on the genetic algorithm (GA) and imperialist competitive algorithm (ICA) are applied. ► With a specified number of function evaluations as termination criteria, the simulation of ICA and GA takes almost equal time. ► The average gap of the ICA is generally less than that of GA. ► ICA with the most powerful empire termination criterion performs faster than the ICA with predetermined function evaluations termination criterion.