A novel hyper-heuristic based on surrogate genetic programming for the three-dimensional spatial resource-constrained project scheduling problem under uncertain environments

For a class of large and complex engineering projects with limited construction sites, three-dimensional (3D) spatial resources usually become a bottleneck that hinders their smooth implementation. A project schedule is easily disturbed by space conflicts and uncertain environments if these factors are not considered in advance. Firstly, we extend the traditional resource-constrained project scheduling problem (RCPSP) by considering 3D spatial resource constraints under uncertain environments, and propose a new three-dimensional spatial resource-constrained project scheduling problem with stochastic activity durations (3D-sRCPSPSAD). The activity schedule and the space allocation need to be decided simultaneously, so we design the first-fit and the best-fit strategies, and integrate them into the traditional resource-based policy to schedule activities and allocate 3D space. Secondly, a novel hyper-heuristic based on surrogate genetic programming (HH-SGP) is designed to evolve rules automatically for the 3D-sRCPSPSAD. The main goal of the surrogate model in HH-SGP is to construct an approximate model of the fitness function based on the random forest technique. Therefore, it can be used as an efficient alternative to the more expensive fitness function in the evolutionary process. More importantly, the weak elitism mechanism and other modified techniques are designed to improve the performance of HH-SGP. Thirdly, we configure the parameters of 3D spatial resources and generate numerical instances. Finally, from the aspects of solution quality and stability, we verify the efficiency, quality and convergence rate of HH-SGP under different uncertain environments. The effectiveness of the surrogate model, and the performance of the first-fit and the best-fit strategies are also analyzed through extensive numerical experiments. The results indicate that our designed HH-SGP algorithm performs better than traditional heuristics for the 3D-sRCPSPSAD, and the performance of the fitness function surrogate model in HH-SGP is generally better than without it. This study can also help project practitioners schedule activities and allocate spatial resources more effectively under various uncertain scenarios.