Explainable Genetic Programming for Evolving Routing Policies of Uncertain Capacitated Arc Routing Problems
Authors:   , Wang Shaolin 
Published: September 2023

<p><strong>The Uncertain Capacitated Arc Routing Problem (UCARP) is a well-known combinatorial optimization problem that has many real-world applications. Genetic programming has successfully evolved routing policies that can make real-time routing decisions for uncertain arc routing problems. Although the evolved routing policies are highly effective, they are typically very complex thus hard for real users to understand and trust. Therefore, it is necessary to improve the interpretability of GP-evolved routing policies.</strong></p><p>The overall goal of this thesis is to develop both intrinsic and post-hoc methods to improve the interpretability of GP-evolved routing policies for UCARP.</p><p>First, this thesis proposes a novel intrinsic genetic programming approach that simplifies the routing policies during the evolutionary process using a niching technique. The simplified routing policies are stored in an external archive. This thesis also develops new elitism, parent selection, and breeding schemes for generating offspring from the original population and the archive. The experimental results show that the newly proposed approach can achieve significantly better test effectiveness than the current state-of-the-art genetic programming hyper heuristic methods for UCARP. The evolved routing policies are smaller, thus potentially more interpretable.</p><p>Second, this thesis develops several multi-objective genetic programming algorithms to evolve a Pareto front of routing policies with different interpretability and effectiveness, so that the end users can choose based on their preferences. This thesis handles two main challenges, i.e., objective selection bias issue and stochastic fitness evaluation issue, of designing Multi-Objective GP (MOGP) for UCARP. To handle the objective selection bias issue, an $\alpha$ dominance strategy is proposed. To further improve the $\alpha$ dominance strategy, this thesis develops a new $\alpha$ value adjustment scheme. To handle the stochastic fitness evaluation issue, this thesis proposes an archive strategy. The new archive strategy uses an external archive to store the potentially effective individuals that could have been lost during the traditional GP process. The individuals in the archive contribute back to the population in the breeding process. Finally, this thesis combines all the above strategies to develop a new MOGP algorithm. The experimental results show that the new MOGP algorithm outperforms state-of-the-art algorithms for UCARP in terms of HV and IGD. The evolved routing policies are much smaller, thus potentially more interpretable.</p><p>Lastly, this thesis proposes a new post-hoc explanation approach to explaining the effective but complex GP-evolved routing policies. This thesis proposes two metrics that can evaluate the quality of a local explanation for GP-evolved routing policies. Then, this thesis investigates the feasibility of using a linear model to construct a local explanation for a complex GP-evolved routing policy in a decision situation. After that, this thesis further improves the local explanation method using Particle Swarm Optimization (PSO) to learn an interpretable linear model that accurately explains the local behavior of the routing policy for each decision situation, and extends the local explanation method to a global explanation method. The experimental results and case studies show that the proposed method can obtain accurate and understandable explanations of GP-evolved routing policies for UCARP.</p><p>From the intrinsic aspect, both GP program simplification method and multi-objective GP methods are proposed. The GP program simplification approach addresses the case where only a single interpretable routing policy is required, i.e. where the user's preferences are known before the routing policy is generated. The multi-target approach is aimed at situations where several different interpretable routing policies are needed, because sometimes we cannot know the user's preferences in advance, and the user can choose their own routing policy according to their preferences. From the post-hoc aspect, this thesis proposes local and global explanation methods to further improve the interpretability of existing complex GP-evolved routing policies. Furthermore, the local and global explanation methods not only produce text explanations but also visual explanations.</p>