Explaining heuristic performance differences for vehicle routing problems with time windows

Abstract

Heuristic algorithms are most commonly applied in a competitive context in which the algorithm is tested on well-known benchmarks of some problem application with the objective of obtaining better performance results than the state-of-the-art. Focusing on characterising heuristic algorithm behaviour to acquire insight and knowledge of how these solution procedures operate given a certain problem application, is a rarely applied research context. In this paper we strive to obtain a better understanding of heuristic performance. Based on an exploratory analysis of a large neighbourhood search algorithm applied on instances of the vehicle routing problem with time windows, we perform a detailed study on one of the detected patterns and seek to explain it. We learn that a regret operator functions best when it can take into account many and good alternatives, which is not the case when removing geographical clusters of customers. In the latter case some customers become isolated and have no feasible insertion option in one of the existing routes at the start of the repair phase. Their insertion is therefore postponed, but we show that it is beneficial for performance to assign them a higher priority through the creation of individual routes.