On the Runtime Analysis of the Clearing Diversity-Preserving Mechanism
This work addresses the need for theoretical foundations in evolutionary computation to explain why diversity-preserving mechanisms like Clearing are effective, offering insights for researchers in optimization and algorithm design.
The paper tackles the problem of understanding the effectiveness of the Clearing diversity-preserving mechanism in evolutionary algorithms by providing a rigorous runtime analysis. It proves that with phenotypic distance, the algorithm optimizes all functions of unitation in polynomial time for small niches, while genotypic distance requires exponential time, and it also finds optima for Twomax and bimodal functions in polynomial expected time.
Clearing is a niching method inspired by the principle of assigning the available resources among a niche to a single individual. The clearing procedure supplies these resources only to the best individual of each niche: the winner. So far, its analysis has been focused on experimental approaches that have shown that clearing is a powerful diversity-preserving mechanism. Using rigorous runtime analysis to explain how and why it is a powerful method, we prove that a mutation-based evolutionary algorithm with a large enough population size, and a phenotypic distance function always succeeds in optimising all functions of unitation for small niches in polynomial time, while a genotypic distance function requires exponential time. Finally, we prove that with phenotypic and genotypic distances clearing is able to find both optima for Twomax and several general classes of bimodal functions in polynomial expected time. We use empirical analysis to highlight some of the characteristics that makes it a useful mechanism and to support the theoretical results.