Non-dominated sorting differential evolution algorithm for the minimization of route based fuel consumption multiobjective vehicle routing problems

In this paper, three parallel multi-start non-dominated sorting differential evolution algorithms (PMS-NSDEs) are proposed for the solution of four multiobjective route based fuel consumption vehicle routing problems (MRFCVRPs) and their results are compared with the results of a parallel multi-start NSGA II algorithm. All these algorithms use more than one initial population of solutions. In each algorithm a variable neighborhood search algorithm for the improvement of each solution separately is used. The problems that are formulated with two competitive objective functions are the multiobjective symmetric and asymmetric delivery route based fuel consumption vehicle routing problem (MSDRFCVRP and MADRFCVRP) and the multiobjective symmetric and asymmetric pick-up route based fuel consumption vehicle routing problem (MSPRFCVRP and MAPRFCVRP). The objective functions correspond to the optimization of the time needed for the vehicle to travel between two customers or between the customer and the depot and to the route based fuel consumption of the vehicle considering tlie traveled distance, the load of tlie vehicle, tlie slope of the road, tlie speed and the direction of the wind, and the driver's behavior when the decision maker plans delivery or pick-up routes. A number of modified Vehicle Routing Problem instances are used in order to measure the quality of the proposed algorithms.