The unrelated parallel machines scheduling problem is an important and challenging problem with significant industrial relevance. This paper addresses a specific variant involving precedence constraints between jobs and the requirement of additional resources for job execution. The problem is NP-hard, and practical solution approaches are therefore predominantly heuristic. In dynamic scheduling environments, dispatching rules (DRs) represent one of the most effective and widely used heuristic approaches. A DR consists of a schedule generation scheme (SGS) and a priority function (PF). The manual design of high-quality DRs is difficult and time-consuming, making the problem well suited for hyper-heuristic and evolutionary approaches. In this work, genetic programming (GP) is employed to automatically evolve the PF component of DRs. Additionally, several problem-specific SGSs are proposed and evaluated. The evolved DRs are compared against adapted state-of-the-art DRs from the literature. The results show that the proposed GP-based approach enables the automated generation of high-quality DRs, outperforming manually designed heuristics for the considered problem.

Efficient container handling in maritime ports represents an important issue in transportation of various goods, since most is being carried out by the sea. As such, various optimisation methods have been utilised to determine the best possible sequence of handling containers in container yards, in order to increase the throughput. One type of methods used for solving such problems are relocation rules (RRs), simple constructive heuristics that determine how the containers need to be rearranged in the yard while they are being retrieved. However, such heuristics are hard to design manually, which prompted the application of various hyper-heuristic methods. Although hyper-heuristics can design new and well performing heuristics, they still suffer from certain issues. For example, a single heuristic can hardly perform well in all possible situations, which can result in poor solutions. To resolve this issue, it is possible to combine such individual heuristics in ensembles, in which RRs jointly perform their decisions. In that way, even if a single RR performs a poor decisions, the other RRs in the ensemble can compensate for that so that in the end the ensemble still achieves a good overall solution. The goal of this study is to investigate how combining RRs into competitive ensembles can increase their performance in comparison to individual RRs and other ensemble types. The results demonstrate that the ensembles used in this study result in a significantly higher performance compared to individual RRs.

The container relocation problem (CRP) in shipping terminals is becoming increasingly important due to the growing amount of transferred goods. Until now, the most commonly investigated problem variant has been the offline CRP, in which the order in which the containers need to be retrieved is known beforehand. However, in many real-world situations this is not the case, which is modelled using the online CRP variant. In this variant, not all information is available from the beginning, but rather, it becomes available as the problem is being solved. Unfortunately, many traditional metaheuristic solution methods can not be applied to such a problem variant, which prompts the application of problem-specific heuristics called relocation rules (RRs). However, RRs are challenging to design manually, which prompted the application of genetic programming (GP) to design them automatically. Since GP was used only to design RRs for the offline problem variant, we apply GP to design relocation rules for the online variant in this study. The performance of GP is investigated under different levels of information availability to measure its performance. The results demonstrate that GP can evolve RRs that perform better than existing manually designed ones. Furthermore, the results show that in certain cases, rules generated for one level of information availability perform well for other levels, demonstrating that the evolved rules exhibit a good generalisation capability.

Automated design of heuristics with genetic programming (G P) has, in recent years, become an intensively researched research area. One of the most recent applications of this methodology is to generate relocation rules (RRs) for the container relocation problem (CRP). CRP is an important combinatorial optimisation problem that is found in ship ter-minals and warehouses. RRs are simple constructive heuristic methods that provide a good solution quickly, thus representing an alternative to computationally expensive exact or metaheuris-tic methods. Even though the RRs designed by GP provide an improvement over existing manually designed rules, they have limited performance. An efficient way to improve the performance of RRs generated by GP is to use ensemble learning. In this study, we apply ensemble learning on RRs generated by GP for CRP to improve the performance of individual rules. We investigate how different ensemble sizes and combination methods affect the quality of the results, as well as which rules are selected to form ensembles. The experimental study shows that ensembles constructed out of automatically designed RRs significantly improve performance compared to the individual rules.