Automated design of relocation rules for minimising energy consumption in the container relocation problem

The container relocation problem (CRP) is a combinatorial optimisation problem in which the sequence of container relocations must be determined to retrieve all containers from the yard while optimising a given objective. Prior to now, the primary objective of CRP was to minimise the number of container relocations; however, due to environmental concerns, optimising energy consumption is gaining importance. This criterion was not considered extensively in the literature about CRP; therefore, there is a lack of suitable methods to tackle this problem variant. Primarily, there is a lack of relocation rules (RRs), simple heuristics that efficiently solve large problems in negligible time. Unfortunately, RRs are challenging to design manually since this process requires significant domain knowledge and is time-consuming. Using hyperheuristics to evolve new RRs automatically is one way to circumvent this problem. In this study, we evolved new RRs that aim to minimise energy consumption using genetic programming. We consider both the scenario in which only energy consumption is optimised and a multi-objective scenario where energy consumption is optimised together with the number of container relocations. The proposed approach is compared with an existing approach from the literature that uses a genetic algorithm to design RRs. The results show that RRs designed using genetic programming perform significantly better than the existing method, especially in multi-objective scenarios.