One of the organizations’ fundamental issues is supply chain network design. Optimization of this network can lead to effective management of the whole supply chain. Network design specifies the position, capacity, number and type of network facilities, and transportation network of materials and products from the supplier to the customer and vice versa. This research proposes new solution procedure based on Multi-objective Genetic Algorithm (MOGA) and Non-dominated Sorting Genetic algorithm-II (NSGAII) to find the set of Pareto optimal solutions that empowers the decision-makers by alternative solutions. Considering that in this study the level of service is very important, so this modeling was based on satisfying all customer demands. Objectives for network optimization are minimization of total cost and maximization of capacity utilization balance for network facilities that lead to the reduction of customers’ service time (increase service levels). Nine problems were designed from small to large. In order to compare the quality of the obtained Pareto solutions of both algorithms, seven criteria (for multi-objective problems) were used in this study. The results indicated that the solutions produced by NSGAII algorithm have higher quality.