A bi-objective transportation vehicle routing problem for a waste collection using NSGA-II

The problem considered in this paper investigates a transportation vehicle routing problem (TVRP), which can be seen as an extension for a two-stage vehicle routing problem (VRP) is associated with a VRP and a transportation problem, respectively. A waste collection problem is one of the most important applications of the problem considered in this paper. Additionally, we consider a bi-objective function including economic cost and societal risk of the transportation of hazardous wastes crossing from city area. A new mathematical model for the bi-objective transportation vehicle routing problem is presented, which is applicable in a waste collection problem. A straightforward representation for the given problem is proposed to help us in reducing the computational effort and managing the problem easily. Since, this type of the problem is NP-hard, the non-dominated sorting genetic algorithm (NSGA-II) is utilized for larger sizes of the given problem.