a meta heuristic algorithms based on ant colony system for solving multi depots location-routing problem with multiple using of vehicle

in a logistic system, decisions on location of depot, vehicle routing and assignment of routes to vehicles should be considered simultaneously. the location-routing problems are defined to find the optimal number and locations of depots, and at the same time with the distribution routes for the vehicles. because of the complexity and the time consuming computation, this problem belongs to a class of combinatorial optimization and np-hard problems. finding an optimal solution for this type of complex, huge problem in reasonable computational time by using traditional and exact approaches and optimization tools is very difficult. so a meta heuristic algorithm based on ant colony system is proposed to solve this problem. according to the experiments, this proposed algorithm reports near-optimal and promising solutions in reasonable time. also in this paper the assumption of assigning several routes to a vehicle during its available time is considered. finally, the computational results obtained by this algorithm are compared with the results reported by lingo software.