A bi-objective vehicle-routing problem for optimization of a bioenergy supply chain by using NSGA- II algorithm

In this paper, we present a multi period model involving an economic and environmental consideration. A vehiclerouting problem is considered as an essential matter due to importance of decreasing the routing cost especially, in the concerned bioenergy supply chain. A few of the optimization model considered the vehicle routing for designing the bioenergy supply chain network. In this study, a bi-objective mixed-integer linear programming (MILLP) model is presented. The economic objective function minimizes the transportation, capacity expanding, fixed and variable cost as well as minimizes the locating routing cost in this problem. The proposed bi-objective model is solved using a nondominated genetic algorithm (NSGA- II). Utilizing a numerical examples, we have shown that, NSGA-II algorithm overcomes the augmented -constraint method in terms of CPU time. Also, this algorithm is validated through an augmented -constraint method.

Keywords:

bi-objective optimization , mixed-integr linear programming , bioenegy supply chain , Non-dominated genetic algorithm (NSGA- II)