彭虎, 吴志健, 周新宇, 邓长寿. 基于三角的骨架差分进化算法[J]. 计算机研究与发展, 2015, 52(12): 2776-2788.
 引用本文: 彭虎, 吴志健, 周新宇, 邓长寿. 基于三角的骨架差分进化算法[J]. 计算机研究与发展, 2015, 52(12): 2776-2788.
Peng Hu, Wu Zhijian, Zhou Xinyu, Deng Changshou. Bare-Bones Differential Evolution Algorithm Based on Trigonometry[J]. Journal of Computer Research and Development, 2015, 52(12): 2776-2788.
 Citation: Peng Hu, Wu Zhijian, Zhou Xinyu, Deng Changshou. Bare-Bones Differential Evolution Algorithm Based on Trigonometry[J]. Journal of Computer Research and Development, 2015, 52(12): 2776-2788.

## Bare-Bones Differential Evolution Algorithm Based on Trigonometry

• 摘要: 差分进化(differential evolution， DE)算法简单高效，但其控制参数和差分变异策略对待解的优化问题较为敏感，对问题的依赖性较强.为克服这一缺陷，提出了一种新的基于三角的骨架差分进化算法(bare-bones differential evolution algorithm based on trigonometry, tBBDE)，并使用随机泛函理论分析了算法的收敛性.算法采用了三角高斯变异策略以及三元交叉和交叉概率自适应策略对个体进行更新，并在收敛停滞时进行种群扰动，算法不仅继承了骨架算法无参数的优点，而且还很好地保留了DE算法基于随机个体差异进行的特性.通过对包括单峰函数、多峰函数、偏移函数和高维函数的26个基准测试函数的仿真实验和分析，验证了新算法的有效性和可靠性，经与多种同类的骨架算法以及知名的DE算法在统计学上的分析比较，证明了该算法是一种具有竞争力的新算法.

Abstract: DE algorithm is one of the most popular and powerful evolutionary algorithms for global optimization problems. However, the performance of DE is greatly influenced by the selected suitable mutation strategy and parameter settings, but this choosing task is a challenge work and time-consuming. In order to solve this defect, a novel bare-bones differential evolution algorithm based on trigonometry, called tBBDE, is proposed in this paper. The convergence performance of the algorithm is then analyzed in terms of the stochastic functional theory. In the paper the proposed algorithm adopts the triangle Gaussian mutation strategy as well as ternary crossover and adaptive crossover probability strategy for individual update. When the algorithm is trapped into premature convergence and stagnation, it will execute population disturbance. In this case, the proposed algorithm not only inherits the advantages of bare-bones algorithm but also retains the characteristics of DE evolution based on the differential information of randomly selected individuals. The experimental studies have been conducted on 26 benchmark functions including unimodal, multimodal, shifted and high-dimensional test functions, while the results have verified the effectiveness and reliability. Besides, comparied with the other bare-bones algorithms and the state-of-the-art, DE variants has proved that the algorithm is a type of new competitive algorithm.

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