湖南大学硕士学位论文差分进化算法及应用研究姓名：吴亮红申请学位级别：硕士专业：控制理论与控制工程指导教师：王耀南20070310硕士学位论文摘要论文首先介绍了智能优化算法的产生对现代优化技术的重要影响，阐述了智能优化算法的研究和发展对现代优化技术和工程实践应用的必要性，归纳总结了智能优化算法的主要特点，简要介绍了智能优化算法的主要研究内容及应用领域。

对差分进化算法的原理进行了详细的介绍，给出了差分进化算法的伪代码。

针对混合整数非线性规划问题的特点，在差分进化算法的变异操作中加入取整运算，提出了一种适合于求解各种混合整数非线性规划问题的改进差分进化算法。

同时，采用时变交叉概率因子的方法以提高算法的全局搜索能力和收敛速率。

用四个典型测试函数进行了实验研究，实验结果表明，改进的差分进化算法用于求解混合整数非线性规划问题时收敛速度快，精度高，鲁棒性强。

采用非固定多段映射罚函数法处理问题的约束条件，提出了一种用改进差分进化算法求解非线性约束优化问题的新方法。

结合差分进化算法两种不同变异方式的特点，引入模拟退火策略，使算法在搜索的初始阶段有较强的全局搜索能力，而在后阶段有较强的局部搜索能力，以提高算法的全局收敛性和收敛速率。

用几个典型Benchmarks函数进行了测试，实验结果表明，该方法全局搜索能力强，鲁棒性好，精度高，收敛速度快，是一种求解非线性约束优化问题的有效方法。

为保持所求得的多目标优化问题Pareto最优解的多样性，提出了一种精英保留和根据目标函数值进行排序的多目标优化差分进化算法。

对排序策略中目标函数的选择方式进行了分析和比较，并提出了一种确定进化过程中求得的精英解是否进入Pareto最优解集的阈值确定方法。

用多个经典测试函数进行了实验分析，并与NSGA-Ⅱ算法进行了比较。

实验结果表明，本文方法收敛到问题的Pareto前沿效果良好，获得解的散布范围广，能有效保持所求得的Pareto最优解的多样性。

提出了一种新的基于群体适应度方差自适应二次变异的差分进化算法。

该算法在运行过程中根据群体适应度方差的大小，增加一种新的变异算子对最优个体和部分其它个体同时进行变异操作，以提高种群多样性，增强差分进化算法跳出局部最优解的能力。

对几种典型Benchmarks函数进行了测试，实验结果表明，该方法能有效避免早熟收敛，显著提高算法的全局搜索能力。

提出了将该改进算法用来整定不完全微分PID控制器最优或近似最优参数的新方法。

为克服频域中常用的积分性能指标如IAE，ISE和ITSE的不足，提出了一种新的时域性能指标对控制器性能进行测试和评价。

用三个典型的控制系统对提出的ASMDE-PID控制器进行了测试。

实验结果表明，该方法实现容易，收敛性能稳定，计算效率高。

与ZN，GA和ASA方法相比，DE在提高系统单位阶跃响应性能方面效率更高，鲁棒性更强。

为了提高差分进化算法的全局搜索能力和收敛速率，提出了一种双群体伪并行差分差分进化算法及应用研究进化算法。

该算法结合差分进化算法DE/best/2/bin变异方式局部搜索能力强，收敛速度快，和DE/rand/1/bin变异方式全局搜索能力强，鲁棒性好的特点，采用串行算法结构实现并行差分进化算法独立进化、信息交换的思想。

为使初始化个体均匀分布在搜索空间，提高算法收敛到全局最优解的鲁棒性，提出了一种基于平均熵的初始化策略。

典型Benchmarks函数测试和非线性系统模型参数估计结果表明，该方法能显著提高算法的收敛速率和全局搜索能力。

基本差分进化算法的控制参数在进化过程中是保持不变的，对于不同的优化问题要确定合适的控制参数是件不容易的事。

根据生成差分矢量的两个不同个体矢量在搜索空间中的相对位置，对缩放因子F提出了一种自适应策略；根据目标个体矢量的收敛情况，提出了一种自适应交叉概率CR策略，使适应度好的目标个体矢量的CR小而适应度差的目标个体矢量的CR大。

同时，为提高算法的收敛速率，对基本差分进化算法的变异操作进行了改进，提出了一种新的变异操作。

典型的Benchmarks函数测试及三关节平面冗余机械手的轨迹规划实验表明，本文提出的方法能显著提高算法的鲁棒性和收敛速率。

关键词：差分进化算法；混合整数非线性规划；非线性约束优化；多目标优化；不完全微分PID；参数估计；冗余机械手硕士学位论文AbstractThis paper firstly introduced the important impact of intelligent optimization algorithms for modern optimization technique. And then, the necessary of the research and development of intelligent optimization technique for modern optimization technique and real engineer application is expatiated. Lastly, the characteristics of intelligent optimization algorithms are induced, and the application areaes of intelligent optimization algorithms are introduced briefly.The differential evolution algorithm (DE) is introduced in detail, and the pseudocode of DE is given. Aiming to the characteristics of mixed-integer nonlinear programming (MINP), a rounding operation was added to the mutation operator, and a modified differential evolution (MDE) algorithm fitted to the MINP is proposed. At the same time, the method of time-varying crossover probability factor was adopted to improve the global searching ability and convergence speed of MDE. The experiments researching were done by four classic testing functions. The experiment results show that the MDE has fast convergence speed, high precision and good robustness for solving MINP.Using non-stationary multi-stage assignment penalty function to deal with the constrained conditions, a modified differential evolution (MDE) for nonlinear constrained optimization is proposed. In order to improve global convergence and convergence speed of the algorithm, two different mutation scheme of DE were combined, and simulation anneal tactics was adapted, which ensure the algorithm has good global exploring ability at the beginning stage and good local exploring ability at the last stage. Several classic Benchmarks functions were tested, the experiment results show that the MDE has powerful global exploring ability, good robustness, high precision, and fast convergence speed. So it is an effective way for nonlinear constrained optimization problems.In order to preserve the diversity of Pareto optimality of multi-objective optimization problems (MOP), a differential evolution algorithm for MOP adopting elitist archive and sorting tactic based on objective function value is presented. The selection methods to the objective function in the sorting tactic were analyzed and compared. And the same time, a threshold determining way was proposed to decide whether a elitist solve found in the evolutionary process added to the Pareto set or not. The experiments were done using several classic test functions, and the comparisons were done with NSGA-Ⅱ. The experiment results show that, the proposed approach can convergence to the Pareto front and preserve the diversity of Pareto optimality efficiently, the obtained optimality has wider bound.差分进化算法及应用研究A new adaptive second mutation differential evolution algorithm (ASMDE) based on the variance of the population’s fitness is presented. In order to improve the population’s diversity and the ability of breaking away from the local optimum, according to the value of the variance of the population’s fitness during the running time, a new mutation operator is adapted to mutate both the best individual and partial other individuals. Several classic Benchmarks functions are tested, the results show that the new algorithm can avoid the premature convergence and improve the global convergence ability greatly. The proposed ASMDE was applied to optimize parameters of PID controller with incomplete derivation. To overcome the disadvantages of the integral performance criteria in the frequency domain such as IAE, ISE, and ITSE, a new performance criterion in the time domain was proposed. Three typical control systems were chosen to test and evaluate the adaptation and robustness of the proposed DE-PID controller. The simulation results show that the proposed approach had superior features, including easy implementation, stable convergence characteristic and good computational efficiency. Compared with the ZN, GA, and ASA, the proposed design method was indeed more efficient and robust in improving the step response of a control system.To improve the global searching ability and convergence speed of DE, a pseudo parallel differential evolution algorithm with dual subpopulations (DSPPDE) is proposed. Combining with the properties of good local searching ability and fast convergence speed of DE/best/2/bin mutation scheme and the properties of good global searching ability and robustness of DE/rand/1/bin mutation scheme, the algorithm applied the ideal of isolated evolution and information exchanging in parallel DE algorithm by serial program structure. To diversify the initial individuals in the search space and improve the robustness of convergence to the global optimum, an initialization tactic based on the mean entropy is proposed. The tests of several classic Benchmarks function and the parameters estimation result of a nonlinear system model show that the proposed algorithm can improve the convergence speed and the global searching ability greatly.Control parameters of original DE are kept fixed throughout the entire evolutionary process. However, it is not an easy task to properly set control parameters in DE for different optimization problems. According to relative position of the two different individual vectors selected to generate a difference vector in the searching place, a self-adapting strategy for the amplification factor F of the difference vector is proposed. In term of the convergence status of target vector, a self-adapting crossover probability constant CR strategy is proposed. Therefore, good target vectors have lower CR while worse target vectors have large CR. And the same time, the mutation operation was modified to improve the convergence speed. The performance of these proposed approaches are studied with the use of some benchmark硕士学位论文problems and applied to trajectory planning of a three-joint redundant manipulator. The experiment results show that the proposed approaches can improve robustness and convergence speed greatly.Keywords: Differential evolution; Mixed-integer nonlinear programming; Nonlinear constrained optimization; Multi-objective optimization; PID controller withincomplete derivation; Parameter estimation; Redundant manipulator湖南大学学位论文原创性声明本人郑重声明：所呈交的论文是本人在导师的指导下独立进行研究所取得的研究成果。