The effects of selection on noisy fitness optimization

This paper examines how the choice of the selection mech-anism in an evolutionary algorithm impacts the objective function it optimizes, specifically when the fitness function is noisy. We provide formal results showing that, in an ab-stract infinite-population model, proportional selection opti-mizes expected fitness, truncation selection optimizes order statistics, and tournament selection can oscillate. The “win-ner ” in a population depends on the choice of selection rule, especially when fitness distributions differ between individ-uals resulting in variable risk. These findings are further developed through empirical results on a novel stochastic optimization problem called “Die4”, which, while simple, ex-tends existing benchmark problems by admitting a variety of interpretations of optimality