A Multi-Objective Genetic Programming Algorithm With α Dominance and Archive for Uncertain Capacitated Arc Routing Problem

Abstract

The uncertain capacitated arc routing problem is an important combinatorial optimization problem with many applications in the real world. Genetic programming hyper heuristic has been successfully used to automatically evolve routing policies, which can make real-time routing decisions for uncertain capacitated arc routing problems. It is desired to evolve routing policies that are both effective and small/simple to be easily understood. The effectiveness and size are two potentially conflicting objectives. A further challenge is the objective selection bias issue, i.e., it is much more likely to obtain small but ineffective routing policies than the effective ones that are typically large. In this paper, we propose a new multi-objective genetic programming algorithm to evolve effective and small routing policies. The new algorithm employs the α dominance strategy with a newly proposed α adaptation scheme to address the objective selection bias issue. In addition, it contains a new archive strategy to prevent the loss of promising individuals due to the rotation of training instances. The experimental results showed that the newly proposed algorithm can evolve significantly better routing policies than the current state-of-the-art algorithms for uncertain capacitated arc routing problem in terms of both effectiveness and size. We have also analysed the evolved routing policies to show better interpretability.