The location–allocation problems are a class of complicated optimization problems that requires finding sites for m facilities and to simultaneously allocate n customers to those facilities to minimize the total transportation costs. Indeed, these problems, belonging to the class NP-hard, have a lot of local optima solutions. In this chapter, three hybrid meta-heuristics: genetic algorithm, variable neighborhood search and particle swarm optimization, and a hybrid local search approaches are studied. These are investigated to solve the uncapacitated continuous location-allocation problem (multi-source Weber problem). In this regard, alternate location allocation and exchange heuristics are used to find the local optima of the problem within the framework of hybrid algorithms. In addition, some large-scale problems are employed to measure the effectiveness and efficiency of hybrid algorithms. Obtained results from these heuristics are compared with local search methods and with each other. The experimental results show that the hybrid meta-heuristics produce much better solutions to solve large-scale problems. Moreover, the results of two non-parametric statistical tests detected a significant difference in hybrid algorithms such that the hybrid variable neighborhood search and particle swarm optimization algorithm outperform the others.
