Evolve ensemble rules automatically for the block spatial scheduling under dynamic environments via surrogate-assisted cooperative evolution genetic programming

The spatial scheduling problem is a crucial investigated problem in operations research and is widely used in shipbuilding, assembly line production and engineering projects. In this paper, we introduce a new block spatial scheduling problem (BSSP) by considering regular resources (manpower and equipment) and dynamic environments. Then, a surrogate-assisted cooperative evolution genetic programming (SCE-GP) is designed to address the BSSP. For the developed algorithm, we firstly propose a new surrogate model by considering the problem surrogate and fitness function surrogate simultaneously, and compare it with the existing models that consider only the fitness function surrogate or problem surrogate under different uncertain environments. Secondly, the cooperative evolution mechanism and random forest technique are embedded in the algorithm to improve its performance. More importantly, we compare different methods for selecting promising individuals. In addition, the design-of-experiment (DOE) approach is utilised to explore the effect of parameter settings. Finally, the performance of SCE-GP with different surrogate models is investigated on our configured data sets based on the benchmark instances of the PSPLIB library. At the same time, we verify the effectiveness of the SCE-GP under different surrogate models and uncertain environments, the performance of the cooperative evolution mechanism, random forest technique and selected method for promising individuals through extensive numerical experiments is also investigated. The results show that the SCE-GP is more excellent than traditional heuristic priority rules (PRs), but different surrogate models yield different results in different uncertain environments.