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In this paper, we consider a fitness-level model of a non-elitistmutation-only evolutionary algorithm (EA) with tournament selection. The modelprovides upper and lower bounds for the expected proportion of the individualswith fitness above given thresholds. In the case of so-called monotonemutation, the obtained bounds imply that increasing the tournament sizeimproves the EA performance. As corollaries, we obtain an exponentiallyvanishing tail bound for the Randomized Local Search on unimodal functions andpolynomial upper bounds on the runtime of EAs on 2-SAT problem and on a familyof Set Cover problems proposed by E. Balas.

On Proportions of Fit Individuals in Population of Evolutionary Algorithm with Tournament Selection