Steady State models of Evolutionary Algorithms are widely used, yet surprisingly little attention has been paid to the effects arising from different replacement strategies. This paper explores the use of mathematical models to characterise the selection pressures arising in a selection-only environment. The first part brings together models for the behaviour of seven different replacement mechanisms and provides expressions for various proposed indicators of Evolutionary Algorithm behaviour. Some of these have been derived elsewhere, and are included for completeness, but the majority are new to this paper. These theoretical indicators are used to compare the behaviour of the different strategies. The second part of this paper examines the practical relevance of these indicators as predictors for algorithms' relative performance in terms of optimisation time and reliability. It is not the intention of this paper to come up with a “one size fits all” recommendation for choice of replacement strategy. Although some strategies may have little to recommend them, the relative ranking of others is shown to depend on the intended use of the algorithm to be implemented, as reflected in the choice of performance metrics.

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