Application of improved multi-objective particle swarm optimization algorithm to solve disruption for the two-stage vehicle routing problem with time windows

Nowadays, the complexity of the global supply chain is increasing. Thus, the vehicle routing problem (VRP) has become a very important problem because of its practicality in real-world applications. In addition, most cus-tomers prefer to have their goods delivered in a specific time interval, and sustainability has become a very important issue for most companies. Therefore, this study proposes a mathematical model for a multi-objective VRP with time windows (VRPTW) as well as an algorithm to solve it. The model consists of two objectives: minimizing the total supply chain cost, and carbon emission. Besides the objectives, the proposed model and algorithm also consider the disruption that commonly happens in the supply chain. This study designs a two-stage VRPTW to solve the disruption. The first stage is the supply chain in ideal condition, while the second one is the supply chain in disrupted condition since the increase in the supply chain complexity also leads to more vulnerability to disruptions. This study improves a multi-objective particle swarm optimization algorithm (MOPSO) to solve the problem. As fitness cannot decide which algorithm is better, this study uses quality in-dicators to compare all of the algorithms. Based on the computational result, the improved MOPSO has the highest hypervolume and lowest spacing. Thus, it can be concluded that the improved MOPSO is the best al-gorithm to solve disruption in the two-stage VRPTW.