Two-stage heuristic algorithm with pseudo node-based model for electric vehicle routing problem

Abstract

Electric vehicle routing problem (EVRP) is a special vehicle routing problem, which owns several specific characteristics of EV technology including the limited charging stations and the limited cruising range of EVs. This paper proposes a two-stage heuristic algorithm for EVRP with a kind of pseudo node, termed EVRPPN-TSH, which not only contributes to the model innovation but also to the algorithm design. In model innovation, the pseudo node is introduced into the EVRP model, forming EVRPPN, to reduce the search space and time complexity for obtaining service orders of customers from O(n) to O(1). Moreover, different from other research works which only use total distance as the fitness function, an improved fitness function is proposed, which takes all the distance, the electricity and capacity constraints compliance into consideration. In algorithm design, we first adopt the two-stage idea, which divides EVRP into the capacitated vehicle routing problem (CVRP) and a fixed route vehicle charging problem (FRVCP). Then we design a two-stage heuristic algorithm, termed as TSH. Specifically, for CVRP, a route division heuristic algorithm and a depot move heuristic algorithm are designed to divide routes. Further, an adjustment strategy with three operators is designed for adjusting the customer order. For FRVCP, an existing heuristic algorithm is adopted and enhanced by a variable extent shaking algorithm to avoid local trapped. Experimental results show that EVRPPN-TSH generally outperforms other state-of-the-art algorithms. Moreover, EVRPPN-TSH can obtain the best-known solution in all the 7 test cases, and update the best-known solution in test case E101 from 834.84 to 834.22.