Distribution centers (DCs) play important role in maintaining the uninterrupted flow of goods and materials between the manufacturers and their customers.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 aid the decision maker choosing the best compromise solution from the Pareto front, the fuzzy-based mechanism is employed for this purpose. 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 algorithm. Results show that both NSACO and NSGA-II algorithms can yield an acceptable number of non-dominated solutions. In addition, the results show while the distribution of solutions in the trade-off surface of both NSACO and NSGA-II algorithms do not differ significantly, the computational CPU time of NSACO is considerably lower than that of NSGA-II. Moreover, it can be seen that the fast NSACO algorithm is more efficient than NSGA-II in the viewpoint of the optimality and convergence. Manuscript profile

Renewable energies are increasingly being considered for use in electricity networks. The high variability of consumption, and the instability of renewable energies, necessitate the use of energy storage systems. The problem of optimizing investment for an energy storage system is formulated here. The proposed model, in particular, determines the optimal size of the energy storage system based on maximizing social welfare. The problem is formulated as a mixed-integer linear programming (MILP), and an equivalent mixed complementary problem (MCP) to solve a quadratic system of nonlinear equations. Due to its high efficiency, the Benders decomposition technique is used to solve the proposed model. The results of solving a 300-node system that cannot be solved by CPLEX using the Benders decomposition technique are presented. The results demonstrate that the proposed method can efficiently find a solution while considering the network’s limitations, increasing social welfare. Finally, the performance of the MILP and MCP models for various numerical cases is compared. The findings of this paper indicate that by increasing the dimensions of the problem, the performance of the MCP model improves compared to the MILP model in terms of computational time and the value of the objective function. Manuscript profile