On Averaging the Best Samples in Evolutionary Computation

Laurent Meunier, Yann Chevaleyre, Jérémy Rapin, Clément W. Royer, Olivier Teytaud

Abstract: Choosing the right selection rate is a long standing issue in evolutionary computation. In the continuous unconstrained case, we prove mathematically that a single parent $$\mu =1$$ leads to a sub-optimal simple regret in the case of the sphere function. We provide a theoretically-based selection rate $$\mu /\lambda $$ that leads to better progress rates. With our choice of selection rate, we get a provable regret of order $$O(\lambda ^{-1})$$ which has to be compared with $$O(\lambda ^{-2/d})$$ in the case where $$\mu =1$$ . We complete our study with experiments to confirm our theoretical claims.