An Evolutionary Algorithm and a Variable Neighborhood Descent Algorithm for the Single Vehicle Problem with Deliveries and Selective Pickups

This paper presents two approaches for the Single Vehicle Routing Problem with Deliveries and Selective Pickups (SVRPDSP), where a vehicle departs loaded from the depot and must visit every delivery customer serving a certain demand, but may not visit all the pickup customers, only the ones that are profitable, since for every pickup made, there is an associated revenue. The objective is to find a minimal cost and feasible route, where the cost is defined as the total travel costs minus the total revenue earned with the pickups performed. Despite the many real applications, there are not many researchs on this problem. We propose an improved Evolutionary (EA) Algorithm whose crossover and mutation operators use data mining strategies to keep trac of good features of the individuals of the population. This EA has an intensification phase, which uses a local search procedure to improve the quality of the individuals and new solutions are introduced regularly to avoid premature convergence. The second approach is a Variable Neighborhood Descent Algorithm (VND) that uses constructive algorithms to generate good solutions to start from. The algorithms were tested with a benchmark of 68 instances from the literature, and the results compared to other papers. The results show that this version of the EA is better than the previous one and finds 7 optimal solutions and some new best values. The VND approach, although is less time costly is not able to find the same or better results than the EA in most cases.