An Improved Multi-Objective Genetic Programming Hyper-Heuristic with Archive for Uncertain Capacitated Arc Routing Problem

Genetic Programming Hyper-heuristic (GPHH) is an effective technique to deal with the Uncertain Capacitated Arc Routing Problem (UCARP). The GPHH can evolve a routing policy that can respond to the uncertain environment in real time. Previous studies have shown that the GPHH can evolve effective routing policies. However, the size (number of nodes) in the GP-evolved routing policy is still not taken into account. Smaller routing policies, in general, may have greater generalisation and interpretability. As a result, we should optimise the effectiveness and the size simultaneously. Evolutionary Multi-Objective (EMO) techniques can be applied to optimise the size along with the effectiveness. EMO can evolve a Pareto front of routing policies. TSNSGPII-a is the state-of-the-art EMO approach for UCARP. It keeps an archive to store potential individuals lost during the evolutionary process and select them to breed new offspring. In this paper, we further improve TSNSGPII-a in the way to select between the current population and the archive as parents. In addition, we propose a validation stage to increase the reliability of the final routing policy. The experimental results showed that the newly proposed algorithm, named TSNSGPII-arv, can achieve better HV and I G D on a set of instances. The controlled experimental results indicated both schemes are effective. The routing policies evolved by TSNSGPII-arv are smaller than the baseline single-objective GPHH approach without losing effectiveness.