A two-phase Pareto local search heuristic for the bi-objective pollution-routing problem

This article deals with the bi-objective pollution-routing problem (bPRP), a vehicle routing variant that arises in the context of green logistics. The two conflicting objectives considered are the minimization of the CO2 emissions and the costs related to driver's wages. A multi-objective approach based on the two-phase Pareto local search heuristic is employed to generate a good approximation of the Pareto front. During the first phase of the method, a first set of potentially efficient solutions is obtained by solving a series of weighted sum problems with an efficient heuristic originally developed to solve the single-objective PRP. A dichotomous scheme is used to generate the different weight sets in an automatic way. In the second phase, the set is improved with an efficient Pareto local search (PLS) procedure. The use of PLS allows to limit the number of computational demanding weighted sum problems solved in the first phase, while keeping high-quality results. Extensive computational experiments over existing benchmark instances show that the proposed approach leads to better results in less CPU time when compared to those obtained by state-of-the-art methods.