Average Convergence Rate of Evolutionary Algorithms
This work addresses the need for a simple and broadly applicable convergence measure in evolutionary optimization, though it is incremental as it builds on existing convergence analysis methods.
The paper tackles the problem of measuring convergence speed in evolutionary algorithms by proposing a new metric called the average convergence rate, which is a normalized geometric mean of fitness reduction per generation, and derives theoretical lower bounds and asymptotic properties for discrete optimization.
In evolutionary optimization, it is important to understand how fast evolutionary algorithms converge to the optimum per generation, or their convergence rate. This paper proposes a new measure of the convergence rate, called average convergence rate. It is a normalised geometric mean of the reduction ratio of the fitness difference per generation. The calculation of the average convergence rate is very simple and it is applicable for most evolutionary algorithms on both continuous and discrete optimization. A theoretical study of the average convergence rate is conducted for discrete optimization. Lower bounds on the average convergence rate are derived. The limit of the average convergence rate is analysed and then the asymptotic average convergence rate is proposed.