Average Drift Analysis and Population Scalability

This paper aims to study how the population size affects the computation time of evolutionary algorithms in a rigorous way. The computation time of an evolutionary algorithm can be measured by either the expected number of generations (hitting time) or the expected number of fitness evaluations (running time) to find an optimal solution. Population scalability is the ratio of the expected hitting time between a benchmark algorithm and an algorithm using a larger population size. Average drift analysis is presented for comparing the expected hitting time of two algorithms and estimating lower and upper bounds on population scalability. Several intuitive beliefs are rigorously analysed. It is prove that (1) using a population sometimes increases rather than decreases the expected hitting time; (2) using a population cannot shorten the expected running time of any elitist evolutionary algorithm on unimodal functions in terms of the time-fitness landscape, but this is not true in terms of the distance-based fitness landscape; (3) using a population cannot always reduce the expected running time on fully-deceptive functions, which depends on the benchmark algorithm using elitist selection or random selection.