This paper consider a reverse logistics network problem (rLNP) with two objectives i.e. minimizing total cost of transportation as well as purchase and, simultaneously, minimizing cost of inventory that is must be reduced which is concerned with relationship between the demands of products and the quantity of provided products from processing center. For applying an evolutionary approach for this rLNP, priority-based encoding method and adaptive weight approach (AWA) are proposed. The effectiveness of proposed approach is evaluated through numerical experiments.