This paper presents a model to solve the multi-objective location-routing problem with capacitated vehicles. The main purposes of the model are to find the optimal number and location of depots, the optimal number of vehicles, and the best allocation of customers to distribution centers and to the vehicles. In addition, the model seeks to optimize vehicle routes and sequence to serve the customers. The proposed model considers vehicles’ traveled distances, service time and waiting time while guaranteeing that the sum of these parameters is lower than a predetermined value. Two objective functions are investigated. First objective function minimizes the total cost of the system and the second one minimizes the gap between the vehicles’ traveled distances. To solve the problem, a Multi-Objective Imperialist Competitive Algorithm (MOICA) is developed. The efficiency of the MOICA is demonstrated via comparing with a famous meta-heuristics, named Non-Dominated Sorting Genetic Algorithm-II (NSGA-II). Based on response surface methodology, for each algorithm, several crossover and mutation strategies are adjusted. The results, in terms of two well-known comparison metrics, indicate that the proposed MOICA outperforms NSGA-II especially in large sized problems.