Rule-based evolutionary online learning systems, often referred to as Michigan-style learning classifier systems (LCSs), were proposed nearly thirty years ago (Holland, 1976; Holland, 1977) originally calling them cognitive systems. LCSs combine the strength of reinforcement learning with the generalization capabilities of genetic algorithms promising a flexible, online generalizing, solely reinforcement dependent learning system. However, despite several initial successful applications of LCSs and their interesting relations with animal learning and cognition, understanding of the systems remained somewhat obscured. Questions concerning learning complexity or convergence remained unanswered. Performance in different problem types, problem structures, concept spaces, and hypothesis spaces stayed nearly unpredictable. This thesis has the following three major objectives: (1) to establish a facetwise theory approach for LCSs that promotes system analysis, understanding, and design; (2) to analyze, evaluate, and enhance the XCS classifier system (Wilson, 1995) by the means of the facetwise approach establishing a fundamental XCS learning theory; (3) to identify both the major advantages of an LCS-based learning approach as well as the most promising potential application areas. Achieving these three objectives leads to a rigorous understanding

This paper presents a competent selectomutative genetic algorithm (GA), that adapts linkage and solves hard problems quickly, reliably, and accurately. A probabilistic model building process is used to automatically identify key building blocks (BBs) of the search problem. The mutation operator uses the probabilistic model of linkage groups to find the best among competing building blocks. The competent selectomutative GA successfully solves additively separable problems of bounded difficulty, requiring only subquadratic number of function evaluations. The results show that for additively separable problems the probabilistic model building BBwise mutation scales as O(2 k m 1.5), and requires O ( √ k log m) less function evaluations than its selectorecombinative counterpart, confirming theoretical results reported elsewhere (Sastry & Goldberg, 2004). 1

This paper discusses the use of various scoring metrics in the Bayesian optimization algorithm (BOA) which uses Bayesian networks to model promising solutions and generate the new ones. The use of decision graphs in Bayesian networks to improve the performance of the BOA is proposed. To favor simple models, a complexity measure is incorporated into the Bayesian-Dirichlet metric for Bayesian networks with decision graphs. The presented modi cations are compared on a number of interesting problems.

This paper describes how fitness inheritance can be used to estimate fitness for a proportion of newly sampled candidate solutions in the Bayesian optimization algorithm (BOA). The goal of estimating fitness for some candidate solutions is to reduce the number of fitness evaluations for problems where fitness evaluation is expensive. Bayesian networks used in BOA to model promising solutions and generate the new ones are extended to allow not only for modeling and sampling candidate solutions, but also for estimating their fitness. The results indicate that fitness inheritance is a promising concept in BOA, because population-sizing requirements for building appropriate models of promising solutions lead to good fitness estimates even if only a small proportion of candidate solutions is evaluated using the actual fitness function. This can lead to a reduction of the number of actual fitness evaluations by a factor of 30 or more.

The paper discusses three major issues. First, it discusses why it makes sense to approach problems in a hierarchical fashion. It defines the class of hierarchically decomposable functions that can be used to test the algorithms that approach problems in this fashion. Finally, the Bayesian optimization algorithm (BOA) is extended in order to solve the proposed class of problems.

The evolutionary learning mechanism in XCS strongly depends on its accuracy-based fitness approach. The approach is meant to result in an evolutionary drive from classifiers of low accuracy to those of high accuracy. Since, given inaccuracy, lower specificity often corresponds to lower accuracy fitness pressure most often also results in a pressure towards higher specificity. Moreover

. The direct application of statistics to stochastic optimization based on iterated density estimation has become more important and present in evolutionary computation over the last few years. The estimation of densities over selected samples and the sampling from the resulting distributions, is a combination of the recombination and mutation steps used in evolutionary algorithms. We introduce the framework named IDEA to formalize this notion. By combining continuous probability theory with techniques from existing algorithms, this framework allows us to dene new continuous evolutionary optimization algorithms. 1 Introduction Algorithms in evolutionary optimization guide their search through statistics based on a vector of samples, often called a population. By using this stochastic information, non{deterministic induction is performed in order to attempt to use the structure of the search space and thereby aid the search for the optimal solution. In order to perform induct...

This paper shows how the Gaussian network paradigm can be used to solve optimization problems in continuous domains. Some methods of structure learning from data and simulation of Gaussian networks are applied in the Estimation of Distribution Algorithm (EDA) as well as new methods based on information theory are proposed. Experimental results are also presented. 1 Estimation of Distribution Algorithms approaches in continuous domains Figure 1 shows a schematic of the EDA approach for continuous domains. We will use x = (x 1 ; : : : ; xn ) to denote individuals, and D l to denote the population of N individuals in the l-th generation. Similarly, D Se l will represent the population of the selected Se individuals from D l . In the EDA [9] our interest will be to estimate f(x j D Se ), that is, the joint probability density function over one individual x being among the selected individuals. We denote as f l (x) = f l (x j D Se l 1 ) the joint density of the l-th genera...

The direct application of statistics to stochastic optimization in evolutionary computation has become more important and present over the last few years. With the introduction of the notion of the Estimation of Distribution Algorithm (EDA), a new line of research has been named. The application area so far has mostly been the same as for the classic genetic algorithms, being the binary vector encoded problems. The most important aspect in the new algorithms is the part where probability densities are estimated. In probability theory, a distinction is made between discrete and continuous distributions and methods. Using the rationale for density estimation based evolutionary algorithms, we present an algorithmic framework for them, named IDEA. This allows us to define such algorithms for vectors of both continuous and discrete random variables, combining techniques from existing EDAs as well as density estimation theory. The emphasis is on techniques for vectors of continuous random variables, for which we present new algorithms in the field of density estimation based evolutionary algorithms, using two different density estimation models.

This paper studies fitness inheritance as an efficiency enhancement technique for a class of competent genetic algorithms called estimation distribution algorithms. Probabilistic models of important sub-solutions are developed to estimate the fitness of a proportion of individuals in the population, thereby avoiding computationally expensive function evaluations. The effect of fitness inheritance on the convergence time and population sizing are modeled and the speed-up obtained through inheritance is predicted. The results show that a fitness-inheritance mechanism which utilizes information on building-block fitnesses provides significant efficiency enhancement. For additively separable problems, fitness inheritance reduces the number of function evaluations to about half and yields a speed-up of about 1.75–2.25.