Optimising the Vehicle Routing Problem with Time Windows under Standardised Metrics

Abstract

The Vehicle Routing Problem with Time Windows (VRPTW) is an established NP-hard Combinatorial Optimisation Problem (COP). While much research has been undertaken in developing solution mechanisms to the VRPTW, this work has been developed without comparative metrics. Previous work on the VRPTW has failed to provide both a comprehensive computational review comparing the performance of metaheuristics applied to finding solutions to the VRPTW under standardised experimental conditions, and the effects of the employed metric schemes. This work aims to introduce a means of comparison between leading metaheuristic methods found in the literature. Conducted experiments applied Genetic Algorithm (GA) and Particle Swarm Optimisation algorithm (PSO) under two standardised metrics on a well-known benchmark dataset. The results verify and resemble previously reported results, question the design of the applied metric schemes and record the CPU time taken to obtain solutions to the VRPTW. This computational comparative review critically analyses, compares and comments on the replicated applied techniques and employed metric schemes. Significant results include: obtaining competitive timings relative to those which have been reported if the GA is terminated when the best known solution is met; the quality of the solutions produced by the GA and the PSO algorithm; insight into the design of the metric schemes. The results obtained match the benchmark values, and the time within which the solutions are computed are competitive with the benchmark times. The solution technique and metric scheme combination which, in general, efficiently obtained solutions to the VRPTW are the PSO algorithm and Metric A.