scholarly journals A Differential Evolution with Two Mutation Strategies and a Selection Based on an Improved Constraint-Handling Technique for Bilevel Programming Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Hong Li ◽  
Li Zhang
Keyword(s):  
Differential Evolution ◽  
Bilevel Programming ◽  
Differential Evolution Algorithm ◽  
Constraint Handling ◽  
Mutation Operators ◽  
Bilevel Programming Problems ◽  
Evolution Algorithm ◽  
Handling Technique ◽  
Mutation Strategies ◽  
Selection Operator

Two mutation operators are used in the differential evolution algorithm to improve the diversity of population. An improved constraint-handling technique based on a comparison mechanism is presented, and then it is combined with the selection operator in the differential evolution algorithm to fulfill constraint handling and selection simultaneously. A differential evolution with two mutation strategies and a selection based on this improved constraint-handling technique is developed to solve bilevel programming problems. The simulation results on some linear and nonlinear bilevel programming problems show the effectiveness and efficiency of the proposed algorithm.

scholarly journals Sufficient Conditions for Global Convergence of Differential Evolution Algorithm

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Zhongbo Hu ◽  
Shengwu Xiong ◽  
Qinghua Su ◽  
Xiaowei Zhang
Keyword(s):  
Differential Evolution ◽  
Infinite Product ◽  
Differential Evolution Algorithm ◽  
Sufficient Conditions ◽  
Common Mutation ◽  
Convergence Conditions ◽  
De Algorithm ◽  
Mutation Operators ◽  
Evolution Algorithm ◽  
Algorithm Framework

The differential evolution algorithm (DE) is one of the most powerful stochastic real-parameter optimization algorithms. The theoretical studies on DE have gradually attracted the attention of more and more researchers. However, few theoretical researches have been done to deal with the convergence conditions for DE. In this paper, a sufficient condition and a corollary for the convergence of DE to the global optima are derived by using the infinite product. A DE algorithm framework satisfying the convergence conditions is then established. It is also proved that the two common mutation operators satisfy the algorithm framework. Numerical experiments are conducted on two parts. One aims to visualize the process that five convergent DE based on the classical DE algorithms escape from a local optimal set on two low dimensional functions. The other tests the performance of a modified DE algorithm inspired of the convergent algorithm framework on the benchmarks of the CEC2005.

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