عنوان مقاله [English]
In this paper, we introduce the sustainable routing problem in a network with forward and reverse flows, in which different economic, environmental and social factors are considered in a bi-objective mixed integer linear programming mathematical model. The purpose of the problem is to design the service routes and determine the optimal speed of vehicles in such a way that, on the one hand, the amount of fuel consumed and, consequently, pollution caused by the transportation process are minimized, and on the other hand, in order to create satisfaction among drivers, the workload of different vehicles in terms of the duration of tour is balanced. A comprehensive function is used to estimate the amount of fuel consumed, in which the amount of fuel consumed is a function of the distance traveled as well as the speed, load, and technical characteristics of the vehicle. In order to solve the problem optimally, the augmented epsilon constraint method is used. Also, for solving large-scale instances, two multi-objective meta-heuristic algorithms based on genetic algorithm and fireworks algorithm have been developed. In order to increase the efficiency of these algorithms, a local search method is also used in their structure. The results of solving various examples represent a better performance of the fireworks algorithm. Also analysis of the pareto-front shows that with a one percent increase in fuel cost, the longest tour can be reduced by more than 20% and the difference between the running times of different machines is reduced by 15%. This difference can also be reduced by up to 25% by increasing fuel consumption by 3%.