The container relocation problem is a critical combinatorial optimisation problem in warehouses and container ports. The goal is to retrieve all containers while minimising unnecessary relocations. As this problem is NP-hard, various heuristics have been proposed, including relocation rules (RRs), simple constructive heuristics that iteratively build solutions by determining how containers should be relocated within the yard for efficient retrieval. However, manually designing effective RRs is challenging, leading to the use of genetic programming to generate them automatically. A key limitation of both manually and automatically designed RRs is their restricted problem view and limited decision-making scope. This often results in suboptimal relocations, negatively impacting future operations and overall efficiency. A crucial aspect of RR design is defining effective relocation schemes that enhance decision-making by considering the long-term impact of relocations. This study investigates several relocation schemes that provide RRs with lookahead capabilities, enabling them to anticipate future consequences and make more informed moves. In addition to two standard schemes, four novel relocation schemes are introduced and evaluated using an established problem set. The results demonstrate that properly adapting relocation schemes can significantly enhance the performance of automatically designed RRs, leading to significantly better results.

Fuzzy Pattern Trees (FPTs) are symbolic tree-based structures whose internal nodes are fuzzy operators, and the leaves are fuzzy features, which enhance interpretability by representing data with meaningful fuzzy terms. However, conventional FPT approaches typically employ uniformly distributed membership functions, which often fail to accurately represent features in real-world datasets. In this work, we propose an automatic method to adapt the bounds of fuzzy features based on their data distributions, with a focus on a simple triangular membership scheme. We evaluate our approach across 11 benchmark classification problems, incorporating six parsimony pressure methods to promote more compact solutions. Our results demonstrate that the adapted fuzzification scheme, beyond improving interpretability, consistently yields models that better balance accuracy and size when compared to uniform representations, appearing on the Pareto front 20 times, while the second-best scheme appeared only 15 times.

When considering those optimization problems where the solution is a combination of two parts, as, e.g., the concurrent optimization of the body and the brain of a robotic agent, one might want to solve them “in a quality-diversity (QD) way”, i.e., obtaining not just one very good solution, but a set of good and diverse solutions. We call them QD composite problems, and we propose a general formulation for them, as well as a set of indexes useful for comprehensively assessing solutions by measuring both quality and diversity. We experimentally compare a few QD evolutionary algorithms (EAs) on a case study of body–brain optimization of simulated robots, including several variants of MAP-elites (ME), a popular and effective EA for QD. We also propose a novel ME variant, called coevolutionary MAP-elites (CoME), that internally employs two populations, one for each part of the solution, and enforces diversity on them through user-provided descriptors, as the underlying ME does. CoME, instead of blindly combining all the respective parts to obtain full solutions, adopts a specific mapping strategy that is based on the location of each solution part in the respective descriptors space. The results of our comparative analysis show that ME works well in QD composite problems, but only if two archives, instead of just one, are employed, one for each part of the solution. Moreover, we show that the use of multi-archive variants of ME, e.g., CoME, can provide insights on the interplay between the two parts of the solution for the problem at hand, shedding light on key dynamics in co-evolution.

A key ingredient in any successful genetic programming is robust initialisation. Many successful initialisation methods used in genetic programming have been adapted to use with grammatical evolution,...

The representation of individuals in Genetic Programming (GP) has a large impact on the evolutionary process. In previous work, we investigated the evolutionary process of three Grammar-Guided GP (GGG...

Genetic Programming and Evolvable Machines -