Multi-Criteria Decision Making With Machine Learning for Vehicle Routing Problem

Introduction

In the era that we have been witnessing, the rapid developments in digital technologies enable us to collect real-time data from so many sources, store and process them to create value by applying advanced analytical techniques. Among these methods, machine learning methods have attracted great interest in the literature, especially in recent times. In previous studies, though researchers frequently apply machine learning methods in speech recognition, error prediction, fault detection, and predictive maintenance, they have started developing machine learning-based approaches to solving combinatorial optimization problems recently (Khalil et al., 2017; Lu et al., 2019).

VRPTW, one of the variants of the classical VRP, is one of the most well-known combinatorial optimization problems with many real-world applications in the transportation sector. This variant includes hard and/or soft time window constraints in addition to the constraints of the classical VRP. In VRPTW, a number of limited capacity vehicles are routed to start and finish their travels at a central depot to customer points without violating the customers' specific time intervals and capacity constraints of the vehicles (Ghoseiri and Ghannadpour, 2010). The appropriate routes are determined in accordance with the problem's objectives by satisfying the capacity and time interval constraints. Time windows represent the lower and upper time limits at which customers can be served. Hard-time windows seem to be more appropriate to maintain customer satisfaction, but for the companies that distribute the orders to their customers, complying with these windows can cause more vehicle use, more distance to travel, not being able to load vehicles fully, and more air pollution. Soft-time windows provide advantages in terms of flexibility and cost for the companies (Xia and Fu, 2019).

Time dependent VRP, which is set forth from the point that the travel times between nodes can be time-varying depending on many factors such as congestion, vehicle breakdowns, road works, road accident, has been studied by many researchers in the literature to deal with the problem more realistically, with or without time windows (e.g., Malandraki and Daskin, 1992; Figliozzi, 2012; Wen and Eglese, 2015; Liu et al., 2020).

The VRPTW has received a great deal of attention in the literature. Usually, the models in the literature for the VRPTW are concerned with the objective of minimization of the travel distance or related cost with it as the objective function. But most of the real-life applications of VRPTW have both consistent and contradictory objectives or criteria that need to be taken into consideration. From this perspective, addressing the VRPTW as a multi-objective and multi-criteria problem has become more attractive in recent years (e.g., Guo et al., 2017; Sawik et al., 2017; Zhang et al., 2019).