This paper introduces the compact genetic algorithm (cGA) which represents the population as a probability distribution over the set of solutions and is operationally equivalent to the order-one behavior of the simple GA with uniform crossover. It processes each gene independently and requires less memory than the simple GA. The development of the compact GA is guided by a proper understanding of the role of the GA's parameters and operators. The paper clearly illustrates the mapping of the simple GA's parameters into those of an equivalent compact GA. Computer simulations compare both algorithms in terms of solution quality and speed.Finally, this work raises important questions about the use of information in a genetic algorithm, and its ramifications show us a direction that can lead to the design of more efficient GA's.Index Terms-Bit wise simulated crossover, genetic algorithms, population based incremental learning, probabilistic modeling, univariate marginal distribution algorithm.

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.

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