A bi-objective two-stage stochastic programming model for the resilient and consistent vehicle routing problem: a hybrid learning-based metaheuristic algorithm

The vehicle routing problem is fundamental to the fields of transportation and logistics management, where maintaining consistent service is crucial for customer satisfaction. However, improving service consistency can lead to higher routing costs. To address this, a bi-objective two-stage stochastic programming model called the consistent vehicle routing problem is proposed, aiming to minimize total costs and service inconsistency. In the first stage, <i>a priori</i> routing decisions are made, while in the second stage, revealed values of uncertain parameters such as demand and transport capacity are used to adjust the prior routing solution. One critical aspect of the model is ensuring service consistency through resilience, which involves the ability to absorb and withstand disruptions. Given that the optimization problem is NP hard, a hybrid algorithm is developed that combines multi-objective particle swarm optimization with a learning-based local search. Computational experiments confirm the validity and effectiveness of the model and hybrid algorithm.