An Adaptive Cauchy Differential Evolution Algorithm for Global Numerical Optimization

Tae Jong Choi,Chang Wook Ahn,Jinung An

doi:10.1155/2013/969734

Abstract

Adaptation of control parameters, such as scaling factor (F), crossover rate (CR), and population size (NP), appropriately is one of the major problems of Differential Evolution (DE) literature. Well-designed adaptive or self-adaptive parameter control method can highly improve the performance of DE. Although there are many suggestions for adapting the control parameters, it is still a challenging task to properly adapt the control parameters for problem. In this paper, we present an adaptive parameter control DE algorithm. In the proposed algorithm, each individual has its own control parameters. The control parameters of each individual are adapted based on the average parameter value of successfully evolved individuals' parameter values by using the Cauchy distribution. Through this, the control parameters of each individual are assigned either near the average parameter value or far from that of the average parameter value which might be better parameter value for next generation. The experimental results show that the proposed algorithm is more robust than the standard DE algorithm and several state-of-the-art adaptive DE algorithms in solving various unimodal and multimodal problems.

Highlights

Differential Evolution (DE) is a powerful population based search technique for optimizing problems
We found out that the parameter adaptation should be performed in every generation and the control parameters of each individual should be adapted based on the average parameter value of successfully evolved individuals’ parameter values by using the Cauchy distribution
Finding suitable values demands a lot of computational resources

Summary

Introduction

Differential Evolution (DE) is a powerful population based search technique for optimizing problems. The adaptive and self-adaptive parameter controls are more applicable than the trial-and-error search method. We found out that the parameter adaptation should be performed in every generation and the control parameters of each individual should be adapted based on the average parameter value of successfully evolved individuals’ parameter values by using the Cauchy distribution. The proposed algorithm but in different manner, utilizes the Cauchy distribution for the parameter adaptation. The control parameters of each individual are adapted based on the average parameter value of successfully evolved individuals’ parameter values by using the Cauchy distribution. In view of the above considerations, the parameter adaptation of proposed algorithm utilizes the Cauchy distribution as a large step method.

Related Work

Analysis of the Cauchy Distribution

Adaptive Cauchy DE

Performance Evaluation

Conclusion