A light-robust-optimization model and an effective memetic algorithm for an open vehicle routing problem under uncertain travel times

Abstract

This paper addresses an open vehicle routing problem with predetermined time windows under uncertain travel times (OVRP-UT). A novel light-robust-optimization model is proposed by integrating the goal programming formulations with set-based descriptions of the problem data, which can enable as many customers as possible to meet their demands within a group of predetermined time windows. An effective memetic algorithm (MA) is presented for solving the OVRP-UT model. We design a heuristic-based initialization mechanism to generate an initial population with a high level of quality and diversity. We design a timely-vertices based crossover operator and mutation operator to give birth to the offspring with high quality and good structure built in the search process. We provide a hybrid selection mechanism and a population updating strategy to remain the diversity of the population. We develop a self-adapted crossover and mutation rate to help the MA suit the different phases during the search process. A comprehensive simulation experiment based on the 320 benchmark instances demonstrates the effectiveness of the proposed algorithm.