A Multi-Objective Genetic Programming Approach with Self-Adaptive α Dominance to Uncertain Capacitated Arc Routing Problem

The Uncertain Capacitated Arc Routing Problem (UCARP) has a variety of real-world applications. Genetic Programming Hyper-heuristic (GPHH) is considered a promising technique to handle UCARP. Many scholars have shown the power of GPHH of evolving effective routing policies. However, the size of the evolved routing policies is ignored. Typically, smaller routing policies can have better interpretability and generalisation. Thus, it is necessary to optimise the size along with the effectiveness. The objective selection bias issue arises as the size is much easier to be optimised than effectiveness. The Pareto front is biased to the size gradually during the evolutionary process. To address this issue, we develop an α dominance criteria based Multi-Objective GP with a self-adaptive α scheme (αMOGP-sa). The basic idea of the α dominance criteria is to set tradeoff rates between objectives. For different instances, the search space can be very different. In this case, the self-adaptive α scheme is employed to automatically tuning the α value during the evolutionary process so that we can identify a valid α value for different instances. This paper examines the proposed algorithm in eight different problem instances. The experimental results showed that αMOGP-sa could effectively handle the objective selection bias issue, and evolve much better Pareto front on Hyper-Volume and Inverted Generational Distance than the current state-of-the-art MOGP approach for UCARP in terms of effectiveness and size on all instances. Also, αMOGP-sa can evolve much smaller routing policies than the state-of-art single-objective GPHH without sacrificing effectiveness.