A Convergent Differential Evolution Algorithm with Hidden Adaptation Selection for Engineering Optimization

Zhongbo Hu,Zhixiang Fang,Shengwu Xiong,Qinghua Su

doi:10.1155/2014/135652

Abstract

Many improved differential Evolution (DE) algorithms have emerged as a very competitive class of evolutionary computation more than a decade ago. However, few improved DE algorithms guarantee global convergence in theory. This paper developed a convergent DE algorithm in theory, which employs a self-adaptation scheme for the parameters and two operators, that is, uniform mutation and hidden adaptation selection (haS) operators. The parameter self-adaptation and uniform mutation operator enhance the diversity of populations and guarantee ergodicity. The haS can automatically remove some inferior individuals in the process of the enhancing population diversity. The haS controls the proposed algorithm to break the loop of current generation with a small probability. The breaking probability is a hidden adaptation and proportional to the changes of the number of inferior individuals. The proposed algorithm is tested on ten engineering optimization problems taken from IEEE CEC2011.

Highlights

Differential evolution (DE) is a population-based stochastic real-parameter algorithm for continuous optimization problems firstly introduced by [1, 2]
From Theorem 2, it is needed to prove that SaCDEhaS satisfies the following two characteristics
According to the characteristic (2) of the “How to understand hidden adaptation selection (haS) operator” in Section 3, we can know that the haS selection operator can remain greedily the current best solution to the generation

Summary

Introduction

Differential evolution (DE) is a population-based stochastic real-parameter algorithm for continuous optimization problems firstly introduced by [1, 2]. The analysis is Mathematical Problems in Engineering based on the assumption that the objective function has the following two properties: (1) the objective function has the second-order continual derivative in the search space, and (2) it possesses a unique global optimum within the range of search. These researches show that the enhancement of population diversity is an efficient route to the development of globally convergent DE algorithms.

Basic Differential Evolution Algorithm

Convergent DE Algorithm with Hidden Adaptation Selection

Trial Vector Generation Strategies

Proof of Global Convergence for the Proposed Algorithm

Conclusion

Numerical Experiment