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.

The paper describes the hierarchical Bayesian optimization algorithm which combines the Bayesian optimization algorithm, local structures in Bayesian networks, and a powerful niching technique. The proposed algorithm is able to solve hierarchical traps and other difficult problems very efficiently.

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 goal of linkage learning, or building block identification, is the creation of a more effective genetic algorithm (GA). This paper explores the relationship between the linkage-learning problem and that of learning probability distributions over multi-variate spaces. Herein, it is argued that these problems are equivalent. Using a simple but effective approach to learning distributions, and by implication linkage, this paper reveals the existence of GA-like algorithms that are potentially orders of magnitude faster and more accurate than the simple GA. I. Introduction Linkage learning in genetic algorithms (GAs) is the identification of building blocks to be conserved under crossover. Theoretical studies have shown that if an effective linkage-learning GA were developed, it would hold significant advantages over the simple GA (2). Therefore, the task of developing such an algorithm has drawn significant attention. Past approaches to developing such an algorithm have focused on ev...

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-

Theoretical and empirical evidence exists that the hierarchical Bayesian optimization algorithm (hBOA) can solve challenging hierarchical problems and anything easier. This paper applies hBOA to two important classes of real-world problems: Ising spin-glass systems and maximum satis ability (MAXSAT). The paper shows how easy it is to apply hBOA to realworld optimization problems. The results indicate that hBOA is capable of solving enormously dicult problems that cannot be solved by other optimizers and still provide competitive or better performance than problem-speci c approaches on other problems. The results thus con- rm that hBOA is a practical, robust, and scalable technique for solving challenging real-world problems.

Abstract—Ant colony optimization is a metaheuristic approach belonging to the class of model-based search algorithms. In this paper, we propose a new framework for implementing ant colony optimization algorithms called the hyper-cube framework for ant colony optimization. In contrast to the usual way of implementing ant colony optimization algorithms, this framework limits the pheromone values to the interval [0,1]. This is obtained by introducing changes in the pheromone value update rule. These changes can in general be applied to any pheromone value update rule used in ant colony optimization. We discuss the benefits coming with this new framework. The benefits are twofold. On the theoretical side, the new framework allows us to prove that in Ant System, the ancestor of all ant colony optimization algorithms, the average quality of the solutions produced increases in expectation over time when applied to unconstrained problems. On the practical side, the new framework automatically handles the scaling of the objective function values. We experimentally show that this leads on average to a more robust behavior of ant colony optimization algorithms. Index Terms—Ant colony optimization (ACO), metaheuristics. I.