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

Abstract

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.

A Review of Heuristics and Hybrid Methods for Green Vehicle Routing Problems considering Emissions

“…Kumar et al [60] presented a multi-objective model for multivehicle PPRP with a time windows (MMPPRP-TW), where the location and inventory decisions are taken into account and solved by a multi-objective self-learning PSO (MOSLPSO) and an NSGA-II. Costa et al [61] investigated the bi-objective PRP in the context of green logistics with a focus on reducing CO 2 emissions and driver salaries. +e authors developed a multi-objective approach based on the two-phase local search heuristic.…”

“…[62] Leng et al [32] • RLCLRPRCC, Leng et al [32] Masmoudi et al [99] • HF-VRPS, Masmoudi et al [99] Sousa Matos et al [90] • GVRSP-split, Sousa Matos et al [90] Fang et al [63] • PRPSPD, Fang et al [63] Guo and Liu [58] • TD-PRP, Guo and Liu [58] Jabir et al [35] • MD-GVRP, Jabir et al [35] Kaabachi et al [36] • GMDVRPTW, Kaabachi et al [36] Liao [89] • Online VRP considers real-time demands, Liao [89] Yavuz and Çapar [24] • • MGVRP, Yavuz and Çapar [24] Zhou et al [91] • Green real-life field scheduling problem, Zhou et al [91] Gang et al [87] • GVRSP of free picking up and delivering customers for airlines ticketing company, Gang et al • CIRP under a mixed fleet of electric and conventional vehicles, Soysal et al [74]; GVRP, Soysal et al [25]; CumVRP-TW, Fernández et al [105]; GLRP, Dukkanci et al [31]; Biobjective PRP, Costa et al [61]; GSTDCVRP, Çimen and Soysal [113]; TD-PRP, Franceschetti et al [57]; F-GVRPSPDTW, Majidi et al [80]; GSTDCVRP, Soysal and Çimen [113]; MMPPRP-TW, Kumar et al [60]; GVRSP, Xiao and Konak [86] • VRPTW using time-varying data, Maden et al [96] Bredstrom et al [137] • VRPTW-SPFC, Ettazi et al [111]; HF-VRPS, Masmoudi et al [99] Iori et al [138] • 2L-MDCVRPB, Zhao et al [84] Li and Lim [139] • Green-PDPTW, Lu and Huang…”

“…PRPLIB is one of the most commonly used benchmarks in the literature (e.g., TD-PRP in Franceschetti et al [57]; FSMPRP in Koç et al [54]; PRP in Kramer et al [53]) and has served as the basis for the creation of new sets of instances. For instance, Kramer et al [53] modified the PRPLIB to create two additional sets called tighter time windows (e.g., BiPRP in Costa et al [61]; TD-PRP in Franceschetti et al [57]). On the other hand, Goeke and Schneider [134] adjusted the PRPLIB for the E-VRPTW with a mixed fleet (see GMFVRPREC-PR in Yu et al [71]).…”

A matheuristic algorithm for the pollution and energy minimization traveling salesman problems

“…The ALNS algorithm proposed in Demir et al (2012) was used to solve this extension by integrating four multiobjective methods: the weighting method, weighting method with normalization, epsilon-constraint method, and a hybrid method. The biobjective PRP was also studied in Costa et al (2018). They obtained an approximation of the Pareto front by a two-phase local search heuristic algorithm: the first phase solves a set of weighted sum PRPs, while the second phase consists of applying a Pareto local search procedure.…”

“…The biobjective PRP was also studied in Costa et al. (2018). They obtained an approximation of the Pareto front by a two‐phase local search heuristic algorithm: the first phase solves a set of weighted sum PRPs, while the second phase consists of applying a Pareto local search procedure.…”