Constructing Ensembles of Automatically Designed Relocation Rules for the Container Relocation Problem

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.