Two-stage multi-objective genetic programming with archive for uncertain capacitated arc routing problem

Abstract

Genetic Programming Hyper-Heuristic (GPHH) is a promising technique to automatically evolve effective routing policies to handle the uncertain environment in the Uncertain Capacitated Arc Routing Problem (UCARP). Previous studies mainly focus on the effectiveness of the evolved routing policies, but the size is ignored. This paper aims to develop new GPHH methods to optimise the effectiveness and the size simultaneously. There are two challenges. First, it is much easier for GP to generate small but ineffective individuals than effective ones, thus the search can be easily stuck with small but ineffective individuals. Second, the effectiveness evaluation in GPHH is stochastic, making it challenging to identify and retain effective individuals. To address these issues, we develop a Two-Stage Multi-Objective GP algorithm with Archive (TSNSGPII-a). The two-stage framework addresses the bias towards the size. The external archive stores potentially effective individuals that may be lost during the evolution, and reuses them to generate offspring. The experimental results show that TSNSGPII-a can obtain significantly better routing policies than the existing state-of-the-art approaches in terms of both effectiveness and size. If selecting the most effective routing policy from the Pareto front, TSNSGPII-a can obtain significantly smaller routing policies with statistically comparable or significantly better effectiveness.