Empirical Evaluation of Evolutionary Algorithms with Power-Law Ranking Selection

Abstract

It has been proven that non-elitist evolutionary algorithms (EAs) with proper selection mechanisms, including the recently proposed power-law ranking selection, can efficiently escape local optima on a broad class of problems called SparseLocalOpt $_{\alpha ,\varepsilon }$, where elitist EAs fail. However, those theoretical upper bounds on the runtime are not tight as they require large populations and a tight balance between mutation rates and selection pressure to keep the algorithms operating near the so-called “error threshold”. This paper empirically clarifies the significance of these theoretical requirements and makes a series of performance comparisons between the non-elitist EA using power-law ranking selection and other EAs on various benchmark problems.

Our experimental results show that non-elitist EAs optimise the Funnel problem with deceptive local optimum significantly faster with power-law ranking selection than with tournament selection. Furthermore, power-law selection outperforms UMDA and the (1+1) EA in our experiments on the NK-Landscape and Max k-Sat problems, but yields to the $(\mu ,\lambda )$-selection, tournament selection, and the self-adaptive MOSA-EA. On the unicost set cover problems, the EA with power-law selection shows competitive results.