Solving optimization problems with multiple (often conflicting) objectives is, generally, a very difficult goal. Evolutionary algorithms (EAs) were initially extended and applied during the mid-eighties in an attempt to stochastically solve problems of this generic class. During the past decade, a variety of multiobjective EA (MOEA) techniques have been proposed and applied to many scientific and engineering applications. Our discussion's intent is to rigorously define multiobjective optimization problems and certain related concepts, present an MOEA classification scheme, and evaluate the variety of contemporary MOEAs. Current MOEA theoretical developments are evaluated; specific topics addressed include fitness functions, Pareto ranking, niching, fitness sharing, mating restriction, and secondary populations. Since the development and application of MOEAs is a dynamic and rapidly growing activity, we focus on key analytical insights based upon critical MOEA evaluation of c...

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.

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.

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.

This paper proposes an algorithm that uses an estimation of the joint distribution of promising solutions in order to generate new candidate solutions. The algorithm is settled into the context of genetic and evolutionary computation and the algorithms based on the estimation of distributions. The proposed algorithm is called the Bayesian Optimization Algorithm (BOA). To estimate the distribution of promising solutions, the techniques for modeling multivariate data by Bayesian networks are used. TheBOA identifies, reproduces, and mixes building blocks up to a specified order. It is independent of the ordering of the variables in strings representing the solutions. Moreover, prior information about the problem can be incorporated into the algorithm, but it is not essential. First experiments were done with additively decomposable problems with both nonoverlapping as well as overlapping building blocks. The proposed algorithm is able to solve all but one of the tested problems in linear or close to linear time with respect to the problem size. Except for the maximal order of interactions to be covered, the algorithm does not use any prior knowledge about the problem. The BOA represents a step toward alleviating the problem of identifying and mixing building blocks correctly to obtain good solutions for problems with very limited domain information.

To solve hierarchical problems, one must be able to learn the linkage, represent partial solutions efficiently, and assure effective niching. We propose the 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-

FDA - the Factorized Distribution Algorithm - is an evolutionary algorithm which combines mutation and recombination by using a distribution instead. The distribution is estimated from a set of selected points. In general a discrete distribution defined for n binary variables has 2 n parameters. Therefore it is too expensive to compute. For additively decomposed discrete functions (ADFs) there exist algorithms which factor the distribution into conditional and marginal distributions. This factorization is used by FDA. The scaling of FDA is investigated theoretically and numerically. The scaling depends on the ADF structure and the specific assignment of function values. Difficult functions on a chain or a tree structure are solved in about O(n p n) operations. More standard genetic algorithms are not able to optimize these functions. FDA is not restricted to exact factorizations. It also works for approximate factorizations as is shown for a circle and a grid structure. By using results from Bayes networks, FDA is extended to LFDA. LFDA computes an approximate factorization using only the data, not the ADF structure. The scaling of LFDA is compared to the scaling of FDA. Keywords Genetic algorithms, Boltzmann distribution, simulated annealing, Bayes network, learning of Bayes networks, convergence, factorization of distributions. 1

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.

This paper describes a probabilistic model building genetic programming (PMBGP) developed based on the extended compact genetic algorithm (eCGA). Unlike traditional genetic programming, which use fixed recombination operators, the proposed PMBGA adapts linkages. The proposed algorithms...