余弦适应性骨架差分进化算法

针对传统差分进化算法在解决复杂优化问题时存在收敛速度慢的问题，提出了一种余弦适应性骨架差分进化算法(CABDE)，算法设计了一种新的变异策略适应性机制。该机制引入一个余弦适应性因子，实现高斯变异策略和DE/current-to-best/1变异策略的优势互补，以平衡算法的勘探能力和开采能力。其中，高斯变异策略具有较强的全局搜索能力，有利于维持种群多样性。DE/current-to-best/1变异策略具有较强的局部搜索能力，能够加快对较优区域的开采。同时，高斯变异策略和DE/current-to-best/1变异策略都利用当前最优个体来引导算法搜索方向，从而尽可能地加快收敛速度。余弦适应性因子在进化过程中随迭代次数的增加而波动性调整，为不同进化阶段适应性地选择变异策略。设计的变异策略适应性机制能够在维持种群多样性的同时加快收敛速度。为测试算法性能，采用18个不同特性的测试函数对算法进行数值实验。对CABDE算法的变异策略和参数动态变化进行了分析，实验结果验证了变异策略和参数动态变化的有效性。此外，CABDE算法分别与新近的骨架算法变体、差分进化算法变体、粒子群优化算法变体和人工蜂群算法变体进行了比较。实验结果表明CABDE算法获得了较高的求解精度，加快了收敛速度，整体上优于其他比较算法。

Adaptive Bare-bones Differential Evolution Based on Cosine

In order to accelerate the convergence speed of the traditional DE algorithms for some complex optimization problems, an adaptive bare-bones differential evolution based on cosine (CABDE) was proposed. In the proposed CABDE, a new adaptive mechanism for mutation strategy selection was presented. Moreover, a cosine adaptive factor was introduced to achieve the complementary advantages of the Gaussian mutation strategy and the DE/current-to-best/1 mutation strategy. The Gaussian mutation strategy has excellent global search ability, which is good for maintaining the population diversity; While the DE/current-to-best/1 mutation strategy exhibits good local search ability, which is helpful for accelerating the convergence speed. Therefore, the presented adaptive mechanism can maintain a balance between exploration and exploitation. In addition, the information of best individual in both Gaussian mutation strategy and DE/current-to-best/1 mutation strategy was utilized to guide the search directions. During the evolution process, the cosine adaptive factor was adjusted according to the increase of the iterations and it can adaptively choose suitable mutation strategies in the different evolutionary stages. As a result, the presented adaptive mechanism can maintain the population diversity as well as accelerate the convergence speed. To test the performance of CABDE, 18 test functions with different characteristics were used in the experiments. The effectiveness of the mutation strategies and the dynamic parameters were discussed. The experimental results showed that the mutation strategies and the dynamic parameters can improve the search performance. Moreover, CABDE was compared with several new variants of bare-bones algorithms, DE variants, PSO variants, and ABC variants. The comparisons indicated that CABDE can achieve better solutions and exhibit faster convergence speed.