An Analytical Framework for Runtime of a Class of Continuous Evolutionary Algorithms

Abstract

Although there have been many studies on the runtime of evolutionary algorithms in discrete optimization, relatively few theoretical results have been proposed on continuous optimization, such as evolutionary programming (EP). This paper proposes an analysis of the runtime of two EP algorithms based on Gaussian and Cauchy mutations, using an absorbing Markov chain. Given a constant variation, we calculate the runtime upper bound of special Gaussian mutation EP and Cauchy mutation EP. Our analysis reveals that the upper bounds are impacted by individual number, problem dimension number n, searching range, and the Lebesgue measure of the optimal neighborhood. Furthermore, we provide conditions whereby the average runtime of the considered EP can be no more than a polynomial of n. The condition is that the Lebesgue measure of the optimal neighborhood is larger than a combinatorial calculation of an exponential and the given polynomial of n.

Electricity Substitution Potential Prediction Based on Tent-CSO-CG-SSA-Improved SVM—A Case Study of China

“…In the traditional sparrow search algorithm, when the sparrow individuals iterate to the late stage, it is easy to ensure the population assimilation is the local optimum. To overcome this drawback, the method of Cauchy-Gaussian mutation [29] is introduced to mutate the individual with the highest current fitness, compare the positions before and after the mutation, and select a better position for iteration. The relevant equation is as follows:…”