基于共轭梯度法的反馈差分进化混合算法及其在弹簧设计中的应用

分析了差分进化算法多种变异方式的特点以及每种变异方式所适应的搜索状态，建立了一条能够让种群根据自身的搜索环境来动态选择变异方式的反馈回路，使个体能够自学习、自调节地高效搜索。在每一代的最优个体邻域内，采用共轭梯度法确定最佳的共轭搜索方向，向量能够在最优解邻域内进行细致的局部搜索。根据混合算法的子代更新形式，从理论上证明了种群能够以概率1的方式收敛到全局最优解。与其它进化算法的对比实验结果表明，本文的差分进化算法有效提高了benchmark函数的最优值精度，加快了收敛速度。在弹簧设计问题中，利用改进的差分进化混合算法得到了较好的结构参数。

A hybrid algorithm combining conjugate gradientmethod and feedback differential evolution andits application in tension string design

We analyze the mutation characteristics of multiple differential evolution methods and their respective appropriate search state. In order to enable individual's efficient searching with self learning and self regulation, we establish a feedback loop, which can help the population choose mutation strategies dynamically according to its own search conditions. Moreover, we also use the conjugate gradient method to find out the optimal search routes in the neighborhood of the best individuals of each generation, and it is useful for searching locally in the neighborhood of optimal solution. Results of the next generation theoretically prove that the proposed hybrid algorithm converges to the global optimal solution at a probability of 1. Experiments on benchmark functions show that the proposed algorithm can improve the efficiency and precision in searching the optimum value. Applied to tension string design problem, the proposed algorithm is able to achieve good structure parameters.