A Multi-Objective Genetic Programming Hyper-Heuristic Approach to Uncertain Capacitated Arc Routing Problems

Abstract

The Uncertain Capacitated Arc Routing Problem (UCARP) is a very important problem which has many real world applications. Genetic Programming Hyper-heuristic (GPHH), which can automatically evolve effective routing policies, is considered as a promising technique that can handle UCARP effectively. However, GP-evolved routing policies are often very complex and hard to be understood and trusted by human users. In this paper, we aim to improve the interpretability of the GP-evolved routing policies by reducing the size of the GP-evolved routing policies since smaller routing policies tend to be easier to understand. We propose a new Multi-Objective GP (MOGP) to optimise the performance (total cost) and size simultaneously. One main challenge is that the size is much easier to be optimised than the performance. Thus, the population tends to be biased to the small but poor routing policies and quickly lose the ability of exploration. To address this issue, we propose a MOGP approach with $\alpha$ dominance strategy ($\alpha$-MOGP) which can balance the tradeoff between performance and individual size. The experimental results showed that $\alpha$-MOGP could obtain much smaller routing policies than the state-of-the-art single-objective GPHH, without deteriorating the performance. Compared with traditional MOGP, $\alpha$-MOGP can obtain a much better and more widespread Pareto front.