This paper considers a number of selection schemes commonly used in modern genetic algorithms. Specifically, proportionate reproduction, ranking selection, tournament selection, and Genitor (or «steady state") selection are compared on the basis of solutions to deterministic difference or differential equations, which are verified through computer simulations. The analysis provides convenient approximate or exact solutions as well as useful convergence time and growth ratio estimates. The paper recommends practical application of the analyses and suggests a number of paths for more detailed analytical investigation of selection techniques.

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This paper analyzes the effect of noise on different selection mechanisms for genetic algorithms (GAs). Models for several selection schemes are developed that successfully predict the convergence characteristics of GAs within noisy environments. The selection schemes modeled in this paper include proportionate selection, tournament selection, (μ, λ) selection, and linear ranking selection. An allele-wise model for convergence in the presence of noise is developed for the OneMax domain, and then extended to more complex domains where the building blocks are uniformly scaled. These models are shown to accurately predict the convergence rate of GAs for a wide range of noise levels.

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.

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