Abstract
The vehicle routing problem with time windows is a widely studied problem with many real-world applications. The problem considered here entails the construction of routes that a number of identical vehicles travel to service different nodes within a certain time window. New benchmark problems with multi-objective features were recently suggested in the literature and the multi-objective optimisation cross-entropy method is applied to these problems to investigate the feasibility of the method and to determine and propose reference solutions for the benchmark problems. The application of the cross-entropy method to the multi-objective vehicle routing problem with soft time windows is investigated. The objectives that are evaluated include the minimisation of the total distance travelled, the number of vehicles and/or routes, the total waiting time and delay time of the vehicles and the makespan of a route.
Highlights
The vehicle routing problem (VRP) remains one of the most studied problems in the field of operations research
The research aims were twofold: [1] to show that the multi-objective cross-entropy method (MOO CEM) can be applied to the vehicle routing problem with time windows (VRPTW) and [2] to provide reference solutions to a new set of benchmark problems recently developed by Castro-Gutierrez et al (2011)
The first aim of this paper was to assess the possible application of the CEM for multi-objective optimisation (MOO) to the multi-objective vehicle routing problem with soft time windows
Summary
The vehicle routing problem (VRP) remains one of the most studied problems in the field of operations research. The multi-objective optimisation (MOO) version of the vehicle routing problem with time windows (VRPTW) is considered, with a focus on the VRP with soft time windows variant (VRPSTW). In this problem type, a number of vehicles have to provide a service to customers at different locations while adhering to constraints with regard to the capacity of the vehicle and the time window. The problem has been considered as a multiobjective problem by a number of authors [3, 9, 12, 13, 16, 20, 21], the focus has primarily been on minimising the number of vehicles and the total travel distances This paper considers these and other pairs of conflicting objectives. Since the benchmark set is new, and reference solutions could not be found at the time of writing, the solution sets presented in this paper may serve as a first reference set for OR practitioners
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