This study proposes a new, robust multi-objective model for capacitated multivehicle allocation of customers to potential Distribution Centers (DCs) under uncertain environment. Uncertainty is dened by discrete scenarios on demands where occurrence probability of each scenario is known. The optimization objectives are to minimize transit time and total cost, including opening cost, assumed for opening potential DCs and shipping cost from DCs to the customers, where considering dierent types of vehicles leads to a more realistic model and causes more con ict in these two objectives. A swarm intelligencebased algorithm named Non-dominated Sorting Ant Colony Optimization (NSACO) is used as the optimization tool. The proposed methodology is based on a new variant of Ant Colony Optimization (ACO) customized in multi-objective optimization problem of this research. For ensuring the authenticity of the proposed method, the computational results are compared with those obtained by NSGA-II. Results show the advantages and the eectiveness of the used method in reporting the optimal Pareto front of the proposed model. Moreover, the optimal solutions of the robust optimization model are insensitive to the disturbance of parameters under dierent scenarios, thus the risk of decision can be effectively reduced.