A Time Dependent Pollution Routing Problem in Multi-graph

This paper considers a time dependent(the travel time is not constant throughout the day) pollution routing problem (TDPRP), which aids the decision makers in minimizing travel time, toll cost and emitted pollution cost. In complexity of urban areas most of the time one point is accessible from another with more than one edge. In contrast to previous TDPRP models, which are designed with only one edge between two nodes, the existence of more than one edge between two nodes is allowed in our modeling. Thus we develop a new model that is called time dependent pollution routing problem in multi-graph (TDPRPM). Since the problem is NP-hard, a tabu search (TS) algorithm is developed to solve it. Finally, computational results of tabu search procedure and its comparison to exact solution are presented.