Confidence-Based Ant Colony Optimization for Capacitated Electric Vehicle Routing Problem With Comparison of Different Encoding Schemes

The blossoming of electric vehicles gives rise to a new vehicle routing problem (VRP) called capacitated electric VRP. Since charging is not as convenient as refueling, both the service of customers and the recharging of vehicles should be considered. In this article, we propose a confidence-based bilevel ant colony optimization (ACO) algorithm to solve the problem. It divides the whole problem into the upper level subproblem capacitated VRP and the lower level subproblem fixed routing vehicle charging problem. For the upper level subproblem, an ACO algorithm is used to generate customer service sequence. Both the direct encoding scheme and the order-first split-second encoding scheme are implemented to make a guideline of their applicable scenes. For the lower level subproblem, a new heuristic called simple enumeration is proposed to generate recharging schedules for vehicles. Between the two subproblems, a confidence-based selection method is proposed to select promising customer service sequence to conduct local search and lower level optimization. By setting adaptive confidence thresholds, the inferior service sequences that have little chance to become the iteration best are eliminated during the execution. The experiments show that the proposed algorithm has reached the state-of-the-art level and updated eight best known solutions of the benchmark.

I. Introduction

Vehicle routing problems (VRPs) have been widely studied since it was first proposed by Dantzig and Ramser in 1959 [1]. During the past few decades, many VRP variants were proposed to model different real-world applications [2]–[7]. Since fossil fuel is definitely the dominant energy source in the last century, most vehicles considered in VRPs are fossil-fueled vehicles. Benefited from the widespread gas stations and short refueling time, the refueling problem is usually not considered in VRPs [8]. New energy techniques have seen great development in the past few years, which has promoted the development of new energy vehicles, especially electric vehicles (EVs) [9]. Compared with fossil-fueled vehicles, EVs are more environmentally friendly [10]. To pursue the goal of carbon neutrality, logistics companies have already started to use EVs in their daily business [11].