One benefit of using probabilistic model-building genetic algorithms is the possibility of creating cheap and accurate surrogate models. Learning classifier systems—and genetics-based machine learning in general—can greatly benefit from such surrogates which can replace the costly matching procedure of a rule against large data sets. In this paper we investigate the accuracy of such surrogate fitness function when coupled with the probabilistic models evolved by the χ-ary extended compact classifier system (χeCCS). We present results showing how functional alignment between the probabilistic model of χeCCS and the surrogate fitness is required. We also present a transformation of populations of rules based on the dependency structure matrix genetic algorithm (DSMGA) that allows building accurate models of overlapping building blocks—a necessary condition to accurately estimate the fitness of the evolved rules. 1

Recent work has provided functions that can be used to prove a principled distinction between the capabilities of mutation-based and crossover-based algorithms. However, prior functions are isolated problem instances that do not provide much intuition about the space of possible functions that is relevant to this distinction or the characteristics of the problem class that affect the relative success of these operators. Modularity is a ubiquitous and intuitive concept in design, engineering and optimisation, and can be used to produce functions that discriminate the ability of crossover from mutation. In this paper, we present a new approach to representing modular problems, which parameterizes the amount of modular structure that is present in the epistatic dependencies of the problem. This adjustable level of modularity can be used to give rise to tuneable discrimination of the ability of genetic algorithms with crossover versus mutation-only algorithms.

The Building Block Hypothesis suggests that Genetic Algorithms (GAs) are well-suited for hierarchical problems, where efficient solving requires proper problem decomposition and assembly of solution from sub-solution with strong non-linear interdependencies. The paper proposes a hill-climber operating over the building block (BB) space that can efficiently address hierarchical problems. The new Building Block Hill-Climber (BBHC) uses past hill-climb experience to extract BB information and adapts its neighborhood structure accordingly. The perpetual adaptation of the neighborhood structure allows the method to climb the hierarchical structure solving successively the hierarchical levels. It is expected that for fully non deceptive hierarchical BB structures the BBHC can solve hierarchical problems in linearithmic time. Empirical results confirm that the proposed method scales almost linearly with the problem size thus clearly outperforms population based recombinative methods.

A byproduct benefit of using probabilistic model-building genetic algorithms is the creation of cheap and accurate surrogate models. Learning classifier systems—and geneticsbased machine learning in general—can greatly benefit from such surrogates which may replace the costly matching procedure of a rule against large data sets. In this paper we investigate the accuracy of such surrogate fitness functions when coupled with the probabilistic models evolved by the χ-ary extended compact classifier system (χeCCS). To achieve such a goal, we show the need that the probabilistic models should be able to represent all the accurate basis functions required for creating an accurate surrogate. We also introduce a procedure to transform populations of rules based into dependency structure matrices (DSMs) which allows building accurate models of overlapping building blocks—a necessary condition to accurately estimate the fitness of the evolved rules.

Genetic Algorithms are a class of metaheuristics with applications on several fields including biology, engineering and even arts. However, simple Genetic Algorithms may suffer from exponential scalability on hard problems. Estimation of Distribution Algorithms, a special class of Genetic Algorithms, can build complex models of the iterations among variables in the problem, solving several intractable problems in tractable polynomial time. However, the model building process can be computationally expensive and efficiency enhancements are oftentimes necessary to make tractable problems practical. This paper presents a new model building approach, called ClusterMI, inspired both on the Extended Compact Genetic Algorithm and the Dependency Structure Matrix Genetic Algorithm. The new approach has a more efficient model building process, resulting in speed ups of 10 times for moderate size problems and potentially thousands of times for large problems. Moreover, the new approach may be easily extended to perform incremental evolution, eliminating the burden of representing the population explicitly.