An adapted version of the water wave optimization algorithm for the capacitated vehicle routing problem with time windows with application to a real case using probe data

Customers' habits, as far as shipping requests are concerned, have changed in the last decade, due to the fast spread of e-commerce and business to consumer (B2C) systems, thus generating more and more vehicles on the road, traffic congestion and, consequently, more pollution. Trying to partially solve this problem, the operational research field dedicates part of its research to possible ways to optimize transports in terms of costs, travel times, full loads etc., with the aim of reducing inefficiencies and impacts on profit, planet and people, i.e., the well-known triple bottom line approach to sustainability, also thanks to new technologies able to instantly provide probe data, which can detail information as far as the vehicle behavior. In line with this, an adapted version of the metaheuristic water wave optimization algorithm is here presented and applied to the context of the capacitated vehicle routing problem with time windows. This latter one is a particular case of the vehicle routing problem, whose aim is to define the best route in terms of travel time for visiting a set of customers, given the vehicles capacity and time constraints in which some customers need to be visited. The algorithm is then tested on a real case study of an express courier operating in the South of Italy. A nearest neighbor heuristic is applied, as well, to the same set of data, to test the effectiveness and accuracy of the algorithm. Results show a better performance of the proposed metaheuristic, which could improve the journeys by reducing the travel time by up to 23.64%.