Population size vs. runtime of a simple EA

Abstract

Evolutionary algorithms (EA) finds numerous applications, and practical knowledge on EAs is immense. In practice, sophisticated population-based EAs employing selection, mutation and crossover are applied. In contrast, theoretical analysis of EAs often concentrates on very simple algorithms like the (1+1) EA, where population size equals 1. In this paper, the question is addressed whether the use of a population by itself can be advantageous. A population-based EA does neither make use of crossover nor any diversity-maintaining operator is investigated on an example function. It is shown that an increase of the population size by polynomial factor decreases the expected runtime exponential to polynomial. Thereby, the so far best known gap is improved from superpolynomial to exponential. Moreover, it is proved that the stated runtime bounds occur with a probability exponentially close to one. Finally, a second example function is presented, where opposite results hold.