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. The BOA 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.

This paper examines the scalability of several types of parallel genetic algorithms (GAs). The objective is to determine the optimal number of processors that can be used by each type to minimize the execution time. The first part of the paper considers algorithms with a single population. The investigation focuses on an implementation where the population is distributed to several processors, but the results are applicable to more common masterslave implementations, where the population is entirely stored in a master processor and multiple slaves are used to evaluate the fitness. The second part of the paper deals with parallel GAs with multiple populations. It first considers a bounding case where the connectivity, the migration rate, and the frequency of migrations are set to their maximal values. Then, arbitrary regular topologies with lower migration rates are considered and the frequency of migrations is set to its lowest value. The investigationis mainly theoretical, but experimental evidence with an additively-decomposable function is included to illustrate the accuracy of the theory. In all cases, the calculations show that the optimal number of processors that minimizes the execution time is directly proportional to the square root of the population size and the fitness evaluation time. Since these two factors usually increase as the domain becomes more difficult, the results of the paper suggest that parallel GAs can integrate large numbers of processors and significantly reduce the execution time of many practical applications.

This paper presents a model to predict the convergence quality of genetic algorithms based on the size of the population. The model is based on an analogy between selection in GAs and one-dimensional random walks. Using the solution to a classic random walk problem—the gambler's ruin—the model naturally incorporates previous knowledge about the initial supply of building blocks (BBs) and correct selection of the best BB over its competitors. The result is an equation that relates the size of the population with the desired quality of the solution, as well as the problem size and difficulty. The accuracy of the model is verified with experiments using additively decomposable functions of varying difficulty. The paper demonstrates how to adjust the model to account for noise present in the fitness evaluation and for different tournament sizes.