Nowadays, the supply chain management (SCM) is an interesting problem that has attracted the attention of many researchers. Transportation network design is one of the most important fields of SCM. In this paper, a multi-product logistic network design is considered to optimize total cost and time. First, a(the) mixed integer nonlinear programming model (MINLP) is formulated to minimize transportation time and transportation products cost. Then, a hybrid priority-based Non-dominated Sorting Genetic Algorithms (NSGA-II) and Sub-population Genetic Algorithm (SPGA- II) is provided in two phases to find the optimal solutions. The solutions are represented with a priority matrix and a Allocated vector. To compare the efficiency of two algorithms several criteria are used such as NPS, CS and HV. Several Sample problems are generated and solved that show the Sub-population Genetic Algorithm (SPGA- II) can find good solutions in reasonable time limit.
