A predictive-reactive approach with genetic programming and cooperative coevolution for the uncertain capacitated arc routing problem

The uncertain capacitated arc routing problem is of great significance for its wide applications in the real world. In uncertain capacitated arc routing problem, variables such as task demands and travel costs are realised in real time. This may cause the predefined solution to become ineffective and/or infeasible. There are two main challenges in solving this problem. One is to obtain a high-quality and robust baseline task sequence, and the other is to design an effective recourse policy to adjust the baseline task sequence when it becomes infeasible and/or ineffective during the execution. Existing studies typically only tackle one challenge (the other being addressed using a naive strategy). No existing work optimises the baseline task sequence and recourse policy simultaneously. To fill this gap, we propose a novel proactive-reactive approach, which represents a solution as a baseline task sequence and a recourse policy. The two components are optimised under a cooperative co-evolution framework, in which the baseline task sequence is evolved by an estimation of distribution algorithm, and the recourse policy is evolved by genetic programming. The experimental results show that the proposed algorithm, called Solution-Policy Co-evolver, significantly outperforms the state-of-the-art algorithms to uncertain capacitated arc routing problem for the ugdb and uval benchmark instances. Through further analysis, we discovered that route failure is not always detrimental. Instead, in certain cases (e.g. when the vehicle is on the way back to the depot) allowing route failure can lead to better solutions.