Genetic Algorithms, Tournament Selection, and the Effects of Noise

Abstr act . Tournament select ion is a useful and rob ust select ion mechanism commonly used by genet ic algorithms (GAs). The selecti on pr essure of to urnament select ion direc tly varies wit h the tournam en t size-the more compe t it ors , t he higher the resulting select ion pr essur e. This pap er develops a model, based on order stat ist ics, that can be used to quantita tively predict th e resul ting select ion pr essure of a tournament of a given size. T his mo del is used to pr edict the convergence ra tes of GAs utili zing tournament selection. While to urnament selection is often used in conjunct ion wit h noisy (imperfect) fitness fun cti ons, lit tl e is understood abo ut how the noise affect s the resul ting select ion pr essur e. The model is extended to quantit atively pred ict t he select ion pressure for tournam ent select ion utili zing noisy fitn ess functions . Given the to urnament size and noise level of a noisy fitness fun ct ion , the exte nded mod el is used to pr ed ict t he resu lt ing select ion pr essure of to urnament select ion . T he accuracy of the mod el is verified using a simple test domain, t he onemax (bit-count ing) domain . T he model is shown to accurately predict t he convergence ra te of a GA using tournament select ion in the onemax domain for a wide range of t ournament sizes and noise levels. T he model develop ed in this paper has a number of immediat e pra cti cal uses as well as a number of longer term rami fica tions. Immediately, t he mod el may be used for determ ining appropria te ra nges of cont rol para meters , for est imat ing stopping times to achieve a spec ified level of solution qua lity , and for approximating convergence t imes in impor tant classes offunction evaluatio ns that utilize sampling . Longer term, the approach of this st udy may be applied to bet ter underst an d