A Hybrid Algorithm for the Vehicle Routing Problem with Soft Time Windows and Hierarchical Objectives

Abstract This paper presents an algorithm for the vehicle routing problem with soft time windows (VRPSTW). It involves serving a set of customers, with earliest and latest time deadlines, which may be violated if a penalty is paid, and a constant service time at the customer site. Customer demands are served by capacitated vehicles. The purpose of this research is to develop a hybrid algorithm that includes an insertion heuristic, a local search algorithm and a meta-heuristic algorithm to solve VRPSTW problems with more than one objective. The first priority aims to find the minimum number of vehicles required and the second priority aims to search for the solution that minimizes the total travel time. Performance of the algorithmic approach is measured by two criteria: solution quality and run time. A set of well-known benchmark data and a genetic algorithm are used to compare the solution quality and running time of the algorithm. Results show a trade-off can be made between total cost and service when considering soft time windows. Running time results display that the hybrid algorithm has a higher performance than the genetic algorithm when the number of customers is less than 25.

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