This paper summarizes the research on population-based probabilistic search algorithms based on modeling promising solutions by estimating their probability distribution and using the constructed model to guide the further exploration of the search space. It settles the algorithms in the field of genetic and evolutionary computation where they have been originated. All methods are classified into a few classes according to the complexity of the class of models they use. Algorithms from each of these classes are briefly described and their strengths and weaknesses are discussed.

The field of metaheuristics for the application to combinatorial optimization problems is a rapidly growing field of research. This is due to the importance of combinatorial optimization problems for the scientific as well as the industrial world. We give a survey of the nowadays most important metaheuristics from a conceptual point of view. We outline the different components and concepts that are used in the different metaheuristics in order to analyze their similarities and differences. Two very important concepts in metaheuristics are intensification and diversification. These are the two forces that largely determine the behaviour of a metaheuristic. They are in some way contrary but also complementary to each other. We introduce a framework, that we call the I&D frame, in order to put different intensification and diversification components into relation with each other. Outlining the advantages and disadvantages of different metaheuristic approaches we conclude by pointing out the importance of hybridization of metaheuristics as well as the integration of metaheuristics and other methods for optimization.

Parallel implementations of genetic algorithms (GAs) are common, and, in most cases, they succeed to reduce the time required to find acceptable solutions. However, the effect of the parameters of parallel GAs on the quality of their search and on their efficiency are not well understood. This insufficient knowledge limits our ability to design fast and accurate parallel GAs that reach the desired solutions in the shortest time possible. The goal of this dissertation is to advance the understanding of parallel GAs and to provide rational guidelines for their design. The research reported here considered three major types of parallel GAs: simple master-slave algorithms with one population, more sophisticated algorithms with multiple populations, and a hierarchical combination of the first two types. The investigation formulated simple models that predict accurately the quality of the solutions with different parameter settings. The quality predictors were transformed into population-sizing equations, which in turn were used to estimate the execution time of the algorithms.

There are four primary goals of this dissertation. First, design a competent optimization algorithm capable of learning and exploiting appropriate problem decomposition by sampling and evaluating candidate solutions. Second, extend the proposed algorithm to enable the use of hierarchical decomposition as opposed to decomposition on only a single level. Third, design a class of difficult hierarchical problems that can be used to test the algorithms that attempt to exploit hierarchical decomposition. Fourth, test the developed algorithms on the designed class of problems and several real-world applications. The dissertation proposes the Bayesian optimization algorithm (BOA), which uses Bayesian networks to model the promising solutions found so far and sample new candidate solutions. BOA is theoretically and empirically shown to be capable of both learning a proper decomposition of the problem and exploiting the learned decomposition to ensure robust and scalable search for the optimum across a wide range of problems. The dissertation then identifies important features that must be incorporated into the basic BOA to solve problems that are not decomposable on a single level, but that can still be solved by decomposition over multiple levels of difficulty. Hierarchical

Genetic and evolutionary algorithms have been increasingly applied to solve complex, large scale search problems with mixed success. Competent genetic algorithms have been proposed to solve hard problems quickly, reliably and accurately. They have rendered problems that were difficult to solve by the earlier GAs to be solvable, requiring only a subquadratic number of function evaluations. To facilitate solving large-scale complex problems, and to further enhance the performance of competent GAs, various efficiency-enhancement techniques have been developed. This study investigates one such class of efficiency-enhancement technique called evaluation relaxation. Evaluation-relaxation schemes replace a high-cost, low-error fitness function with a low-cost, high-error fitness function. The error in fitness functions comes in two flavors: Bias and variance. The presence of bias and variance in fitness functions is considered in isolation and strategies for increasing efficiency in both cases are developed. Specifically, approaches for choosing between two fitness functions with either differing variance or differing bias values have been developed. This thesis also investigates fitness inheritance as an evaluation-

Abstract In this paper we introduce model-based search as a unifying framework accommodating some recently proposed heuristics for combinatorial optimization such as ant colony optimization, stochastic gradient ascent, cross-entropy and estimation of distribution methods. We discuss similarities as well as distinctive features of each method, propose some extensions and present a comparative experimental study of these algorithms. 1

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

In this paper we perform a comparison among FSS-EBNA, a randomized, populationbased and evolutionary algorithm, and two genetic and other two sequential search approaches in the well known Feature Subset Selection (FSS) problem. In FSS-EBNA, the FSS problem, stated as a search problem, uses the EBNA (Estimation of Bayesian Network Algorithm) search engine, an algorithm within the EDA (Estimation of Distribution Algorithm) approach. The EDA paradigm is born from the roots of the GA community in order to explicitly discover the relationships among the features of the problem and not disrupt them by genetic recombination operators. The EDA paradigm avoids the use of recombination operators and it guarantees the evolution of the population of solutions and the discovery of these relationships by the factorization of the probability distribution of best individuals in each generation of the search. In EBNA, this factorization is carried out by a Bayesian network induced by a chea...

In this paper, we formalize the notion of performing optimization by iterated density estimation evolutionary algorithms as the IDEA framework. These algorithms build probabilistic models and estimate probability densities based upon a selection of available points. We show how these probabilistic models can be built and used for dierent probability density functions within the IDEA framework. We put the emphasis on techniques for vectors of continuous random variables and thereby introduce new continuous evolutionary optimization algorithms.

Scalable evolutionary computation has become an intensively studied research topic in recent years. The issue of scalability is predominant in any field of algorithmic design, but it became particularly relevant for the design of competent genetic algorithms once the scalability problems of simple genetic algorithms were understood. Here we present some of the work that has aided in getting a clear insight in the scalability problems of simple genetic algorithms. Particularly, we discuss the important issue of building block mixing. We show how the need for mixing places a boundary in the GA parameter space that, together with the boundary from the schema theorem, delimits the region where the GA converges reliably to the optimum in problems of bounded difficulty. This region shrinks rapidly with increasing problem size unless the building blocks are tightly linked in the problem coding structure. In addition, we look at how straightforward extensions of the simple genetic a...