NSGA-II and TOPSIS for a Multi-objective Vehicle Routing Problem with Ecological Considerations

Reducing CO2 emissions in transport and logistics is currently a goal of utmost importance in vehicle routing. Environmental awareness has grown in recent years, and organizations are more willing to consider sustainability in their decision-making at all levels, from strategic to operational. This research is concerned with the vehicle routing problem (VRP) with simultaneous pickup and delivery (VRPSPD), which considers not only economic objectives but also environmental ones. Although environmental issues have been included in VRP models, traditionally multiple objectives have been combined in a single-objective function. In these approaches, a decision maker (e.g. the logistic manager) has to determine the importance of objectives a priori, which is often a difficult task. In our research, the VRPSPD is modeled as a multi-objective optimization problem where the objectives are minimization of travelled distance and fuel consumption, the latter being equivalent to CO2 emissions. The development of the model is informed by a real-word VRPSPD from our industrial collaborator. A method for multi-objective optimization based on NSGA-II is developed, with a novel constructive heuristic that uses a multi-criteria decision-making method TOPSIS to generate initial solutions. Statistical analysis proves that initial populations that combine different ratios of solutions generated by TOPSIS to randomly generated solutions produce significantly different final Pareto fronts. Our algorithm produces solutions in which the travelled distance is comparable or smaller than the distance in the solutions generated by the company, but in a majority of instances reduces the fuel consumption. In addition, the performance of the developed algorithm is evaluated on problem instances of larger size taken from the literature. The obtained Pareto fronts with multiple solutions give an opportunity to the logistics manager to express a posteriori preferences toward the importance of objectives and choose a solution correspondingly.