A Non-dominated Sorting Ant Colony Optimization Algorithm Approach to the Bi-objective Multi-vehicle Allocation of Customers to Distribution Centers

This paper proposes a mathematical model as the bi-objective capacitated multi-vehicle allocation of customers to distribution centers. an evolutionary algorithm named non-dominated sorting ant colony optimization (nsaco) is used as the optimization tool for solving this problem. the proposed methodology is based on a new variant of ant colony optimization (aco) specialized in multi-objective optimization problem. to help the decision maker to choose the best compromise solution from the pareto front, the fuzzy-based mechanism is employed. for ensuring the robustness of the proposed method and giving a practical sense of this study, the computational results are compared with those obtained by nsga-ii. results show that both nsaco and nsga-ii algorithms can yield an acceptable number of non-dominated solutions. in addition, the results show that while the distribution of solutions in the trade-off surface of both nsaco and nsga-ii algorithms do not differ significantly, nsaco algorithm is more efficient than nsga-ii with regard to optimality, convergence and the cpu time. also, the results in some small cases are compared with those obtained by lp-metric method. the error percentages of objective functions in comparison to the lp-metric method are less than 2%. furthermore, it can be seen that with increasing size of the problems, while the time of problem solving increases exponentially by using the lp-metric method, the running time of nsaco and nsga-ii are more stable.