When the plus strategy performs better than the comma strategy - and when not

Abstract

Occasionally there have been long debates on whether to use elitist selection or not. In the present paper the simple (1,lambd) EA and (1+lambda) EA operating on {0,1}^n are compared by means of a rigorous runtime analysis. It turns out that only values for lambda that are logarithmic in n are interesting. An illustrative function is presented for which newly developed proof methods show that the (1,lambda) EA - where lambda is logarithmic in n - outperforms the (1+lambda) EA for any lambda. For smaller offspring populations the (1,lambda) EA is inefficient on every function with a unique optimum, whereas for larger lambda the two randomized search heuristics behave almost equivalently.