A Hybrid Multiobjective Evolutionary Algorithm for Solving Vehicle Routing Problem with Time Windows

Abstract

Vehicle routing problem with time windows (VRPTW) involves the routing of a set of vehicles with limited capacity from a central depot to a set of geographically dispersed customers with known demands and predefined time windows. The problem is solved by optimizing routes for the vehicles so as to meet all given constraints as well as to minimize the objectives of traveling distance and number of vehicles. This paper proposes a hybrid multiobjective evolutionary algorithm (HMOEA) that incorporates various heuristics for local exploitation in the evolutionary search and the concept of Pareto's optimality for solving multiobjective optimization in VRPTW. The proposed HMOEA is featured with specialized genetic operators and variablelength chromosome representation to accommodate the sequence-oriented optimization in VRPTW. Unlike existing VRPTW approaches that often aggregate multiple criteria and constraints into a compromise function, the proposed HMOEA optimizes all routing constraints and objectives simultaneously, which improves the routing solutions in many aspects, such as lower routing cost, wider scattering area and better convergence trace. The HMOEA is applied to solve the benchmark Solomon's 56 VRPTW 100-customer instances, which yields 20 routing solutions better than or competitive as compared to the best solutions published in literature.

An improved multi-objective evolutionary algorithm for the vehicle routing problem with time windows

“…Most recently, Tan et al [31] and Ombuki et al [32] considered the VRPTW as a bi-objective optimization problem, minimizing the number of vehicles and the total travel distance, and used a GA for solving it. The former used the dominance rank scheme to assign fitness to individuals, designed a problem-specific crossover operator called route-exchange crossover, and used a multi-mode mutation which considered swapping, splitting and merging of routes.…”

“…These benchmark instances have been previously studied in detail, and a recent analysis by Tan et al [31] suggests that categories C1 and C2 have positively correlating objectives, which means that the travel cost of a solution increases with the number of vehicles, whereas many of the instances in categories R1, R2, RC1 and RC2 were found to have conflicting objectives.…”

Optimizing Delivery Time in Multi-Objective Vehicle Routing Problems with Time Windows

“…The lowest number of routes for the other categories, as well as the accumulated, was obtained by our BiEA [9], but MOEA found solutions with lower travel distances for categories R2, RC1 and RC2, and accumulated. Solutions from Tan et al [7] have the lowest travel distance for category R1, where results from MOEA are 0.33% higher, and Ombuki et al [8] obtained the shortest distances for categories R2 and RC2, and accumulated, where results from MOEA are 2.61%, 3.46%, and 0.16% higher, but have smaller numbers of routes. Finally, travel distances from MOEA for category RC1 are the shortest.…”

“…To carry out controlled experiments, we used the standard benchmark set of Solomon [13] that includes 56 instances of size N = 100 categorized as clustered (C1, C2), random (R1, R2), and mixed (RC1, RC2). Tan et al [7] found that categories C1 and C2 have positively correlating objectives, but the majority of the instances in categories R1, R2, RC1 and RC2 have conflicting objectives.…”

“…Tan et al [7] used the dominance rank scheme to assign fitness to individuals, and designed a problem-specific crossover operator and multi-mode mutation operator. They also considered three local search heuristics.…”