基于极大熵差分进化混合算法求解非线性方程组*

针对非线性方程组,给出了一种新的算法——极大熵差分进化混合算法。首先把非线性方程组转换为一个不可微优化问题;然后用一个称之为凝聚函数的光滑函数直接代替不可微的极大值函数,从而可把非线性方程组的求解转换为无约束优化问题,利用差分进化算法对其进行求解。计算结果表明,该算法在求解的准确性和有效性均优于其他算法。     

求解非线性方程组的BFGS差分进化算法

针对差分进化算法进化后期收敛缓慢和稳定性不强的缺陷,将BFGS算法插入差分进化算法当中,提出了一种BFGS差分进化算法,用来求解非线性方程组。通过5个非线性方程组和一个工程实例的实验,说明：算法收敛精度较高、收敛速度较快、鲁棒性强、收敛成功率高,是一种较好的解决非线性方程组的方法。     

求解非线性方程组系统的改进差分进化算法

针对基于邻域拥挤的差分进化算法求解非线性方程组系统时存在丢根、陷入局部最优等不足,提出一种改进的差分进化算法.首先,提出一种个体预判机制,判断当前群体的个体属于哪一类,并分别采取不同的操作;其次,设计一种新的混合差分变异算子,以增强算法跳出局部最优的能力;然后,改进外部存档策略,延长了父代优秀个体在种群的保存时间,有利...     

求解互补问题的极大熵差分进化算法*

针对传统算法无法获得互补问题多个最优解的困难, 提出了求解互补问题的差分进化算法。首先利用NCP函数, 将互补问题转换为一个非光滑方程组问题, 然后用凝聚函数对其进行光滑化, 进而把互补问题的求解转换为无约束优化问题, 利用差分进化算法对其进行求解。该算法对目标函数的解析性质没有要求且容易实现, 数值结果表明了该方法在求解互补问题中的有效性。     

正交差分演化算法在工程优化设计中的应用

提出一种基于正交设计的快速差分演化算法,并把它应用于工程优化设计中。新算法在保留传统差分演化算法简单、有效等特性的同时,还具有以下一些特点：（1）引入一种基于正交设计的杂交算子,并结合约束统计优生法来产生最好子个体;（2）提出一种简单的多样性规则,以处理约束条件;（3）简化基本差分演化算法的缩放因子,尽量减少算法的控制参数,方便工程人员的使用。通过对2个工程优化实例进行实验,并与其他算法的结果作比较,其结果表明,新算法在解的精度、稳定性、收敛性和收敛速度上表现出很好的性能,并且对所优化的问题没有特殊的要求,具有很好的普适性。     

多模态多目标差分进化算法求解非线性方程组

针对当前算法在求解非线性方程组时面临解的个数不完整、精确度不高、收敛速度慢等问题进行了研究,提出一种多模态多目标差分进化算法。首先将非线性方程组转换为多模态多目标优化问题,初始化一个随机种群并对种群中全部个体进行评价;然后通过非支配解排序和决策空间拥挤距离选择机制,挑选种群中的一半优质个体进行变异;接着在变异过程中采用一种新的变异策略和边界处理方法以增加解的多样性;最后通过交叉和选择机制使优质个体进行进化,直到搜索到全部最优解。在所选测试函数集和工程实例上的实验结果表明,该算法能有效地搜索到非线性方程组的解,并通过与当前四个算法进行比较,该算法在解的数量和成功率上具有优越性。     

基于邻域交叉的双变异差分进化算法求解非线性方程组

非线性方程组问题的求解难点在于多根联解的同步解出, 针对邻域拥挤差分进化算法存在的多根解出不完整、丢根及易陷入局部最优等问题, 提出一种基于邻域交叉的双变异差分进化算法. 双变异策略基于个体适应度值综合学习邻域和全局的进化信息, 以提高种群多样性并同步增强其局部最优规避性能; 邻域交叉策略通过种群分组与不同交叉操作实现进化个体的差异性引导, 以规避多根的联解丢失并改善计算资源的利用效率. 实验结果表明, 所提算法能够有效实现非线性方程组的多根联解, 且在找根率和成功率指标上表现优异.     

基于正交差分演化无迹卡尔曼滤波的短时交通流量预测算法

针对复杂交通路段下的短时交通流量模型的参数估计问题,建立了基于宏观交通流量预测的状态空间模型,提出了基于正交自适应差分演化的无迹卡尔曼滤波(UKF)算法,解决交通流量预测动态模型的参数优化问题.对差分演化算法(DE)的初始化过程,使用基于正交设计和量化技术的交叉算子最大限度地提高种群的多样性,平衡差分演化算法的开采性和勘探性,更高效地搜索无迹卡尔曼滤波的模型参数.并针对UKF、DE的不同情况,分别采用不同的自适应策略提高调节算法性能.实验结果表明,相对于单独使用随机分布的方式初始化,或者根据经验设置模型参数的方法,使用正交设计方法的初始化策略、变异算子以及参数自适应控制策略的差分演化算法能够有效地节省计算资源,提升预测性能和精度,具有更高的鲁棒性.     

基于粒子群算法的非线性方程组求解

将非线性方程组的求解问题转化为无约束极大极小优化问题,并应用一种新的进化计算（EC）方法——粒子群算法（PSO）求解此优化问题。数值实验的结果验证了该方法的可行性和有效性。     

改进差分进化算法求解整数任务分配

针对0-1任务规划模型存在维数灾维的问题,提出了一种基于改进差分进化算法的整数任务分配算法。将任务分配的0-1规划模型转化整数规划模型,不仅大幅降低了优化变量的维数,还减小了整式约束条件;将差分进化算法常用的变异算子DE/rand/1/bin和DE/best/2/bin结合起来组成新的变异算子,使得DE既保持了种群的多样性,又有较快的收敛速度和搜索精度,并用改进的差分进化算法求解整数规划;通过典型的任务分配实例验证了该算法在优化大规模任务分配的有效性和快速性。     

Differential evolution based on ε-domination and orthogonal design method for power environmentally-friendly dispatch

This paper proposes a differential evolution algorithm based on ε-domination and orthogonal design method (ε-ODEMO) to solve power dispatch problem considering environment protection and saving energy. Besides the operation costs of thermal power plant, contaminative gas emission is also optimized as an objective. In the proposed algorithm, ε-dominance is adopted to make genetic algorithm obtain a good distribution of Pareto-optimal solutions in a small computational time, and the orthogonal design method can generate an initial population of points that are scattered uniformly over the feasible solution space, these modify the differential evolution algorithm (DE) to make it suit for multi-objective optimization (MOO) problems and improve its performance. A test hydrothermal system is used to verify the feasibility and effectiveness of the proposed method. Compared with other methods, the results obtained demonstrate the effectiveness of the proposed algorithm for solving the power environmentally-friendly dispatch problem.     

求解大规模优化问题的正交反向混合差分进化算法*

差分进化算法简单高效,然而在求解大规模优化问题时,其求解性能迅速降低。针对该问题,提出一种正交反向差分进化算法。首先,该算法利用正交交叉算子,加强了算法的局部搜索能力。其次,为防止过强的局部搜索使算法陷入早熟收敛,利用反向学习策略调节种群多样性,从而有效地平衡算法的全局和局部搜索能力。利用11个标准测试函数进行实验,并和差分进化算法的4种优秀改进版本进行比较,实验结果表明该算法求解精度高、收敛速率快,是一种求解大规模优化问题的有效算法。     

基于改进最大熵算法系统传输速率优化研究

研究系统速率优化提高问题。随着用户对系统的传输速率要求越来越高,传统的系统优化传输速率算法由于参数设置难,而造成算法复杂度特别高,使得系统的传输速率降低,为了解决上述问题,在基于误比特率和功率的分析基础上,提出了一种改进的最大熵算法优化系统传输速率方法。方法首先给出系统模型并提出自适应最大熵调制算法理论,然后在发送端和接收端能够完全知道信道状态信息的情况下,给出了最大化传输速率的低复杂度比特和功率分配算法。仿真结果表明,提出的算法可以有效地满足系统地误比特率要求,同时大大降低了系统的计算复杂度,是一种有效地系统传输速率优化方法。     

Application of maximum entropy principle for reliability-based design optimization

The maximum entropy principle (MEP) is used to generate a natural probability distribution among the many possible that have the same moment conditions. The MEP can accommodate higher order moment information and therefore facilitate a higher quality PDF model. The performance of the MEP for PDF estimation is studied by using more than four moments. For the case with four moments, the results are compared with those by the Pearson system. It is observed that as accommodating higher order moment, the estimated PDF converges to the original one. A sensitivity analysis formulation of the failure probability based on the MEP is derived for reliability-based design optimization (RBDO) and the accuracy is compared with that by finite difference method (FDM). Two RBDO examples including a realistic three-dimensional wing design are solved by using the derived sensitivity formula and the MEP-based moment method. The results are compared with other methods such as TR-SQP, FAMM + Pearson system, FFMM + Pearson system in terms of accuracy and efficiency. It is also shown that an improvement in the accuracy by including more moment terms can increase numerical efficiency of optimization for the three-dimensional wing design. The moment method equipped with the MEP is found flexible and well adoptable for reliability analysis and design.     

残损模糊图像的最大熵恢复

模糊图像存在较大的信息冗余,这一特点有助于残损模糊图像的恢复处理。最大熵恢复是复原残损模糊图像的理想法之一。本文在简单描述基于微分方程初值问题的最大熵恢复方法的基础上,对其进行了推广,给出了在非周期反卷积模型下该方法的一个实现算法,并用实验验证了其在处理局部受损的模糊图像时的有效性。该算法计算量适中,恢复效果好,可在一段的PC机上快速进行。     

Maximum Bayesian entropy method for determining ordered weighted averaging operator weights

Determination of the ordered weighted averaging (OWA) operators is an important issue in the theory of the OWA operator weights. In this paper, the main existing models for determining the OWA operator weights are outlined and the concept of the Bayesian entropy is introduced. Based upon the Bayesian entropy the maximum Bayesian entropy approach for obtaining the OWA operator weights is proposed. In this model it is assumed, according to previous experiences or from theoretical considerations that a decision maker may have reasons to consider a given prior OWA vector. Finally the new model is solved according to the prior OWA vector with specific level of orness comparing the results with other methods. The results demonstrate the efficiency of our model in generating the OWA operator weights. An applied example is also presented to illustrate the applications of the proposed model.     

Pontryagin-type necessary conditions for differential inclusion problems

We give a new proof of the Pontryagin-type adjoint equation and maximum condition for differential inclusion problems first established by Kaskosz and Lojasiewicz. Our argument is much simpler than the original proof based on generalized control systems, and has the further advantage of illustrating the relationship between the separated necessary conditions and the familiar Hamiltonian inclusion due to Clarke.     

基于均匀设计的差分进化算法的参数设定

差分进化算法参数的设定多采用经验选取方式,其缺点是试验运行量大以及难以得到最优参数组合,从而在很大程度上影响了算法的寻优能力。将均匀设计的试验方法引入差分进化算法的参数设定中,通过对单峰函数、多峰函数和病态函数等3种不同类型的标准测试函数进行均匀设计试验,找出适合不同类型标准测试函数的最优参数组合,从而达到对差分进化算法的参数进行设定的目的。结果显示,将经过均匀设计试验得到的两组最优的参数组合用于差分进化算法时,所获得的平均全局最优解为4.3215,平均标准差为3.650。可见,利用均匀试验设计方法对基本差分进化算法的参数进行设定是可行且有效的,同时具有较好的稳定性。     

A two-dimensional multilevel thresholding method for image segmentation

In this work, we develop a two-dimensional multilevel thresholding technique based on Rényi and Tsallis entropies. The formulation of the proposed method gives rise to an NP-hard combinatorial optimization problem. In order to solve efficiently this problem, two leading evolutionary algorithms, namely the quantum genetic algorithm (QGA) and the differential evolution (DE) have been employed and compared. The effectiveness of both the proposed method and the optimizers was demonstrated on a sample of real-world and synthetic images showing different types of gray-level distributions. Moreover, the contribution of the two-dimensional histogram to the segmentation quality has been highlighted on some images corrupted by noise and containing shadow or reflection effects. Experimental results demonstrated, first, that DE is less time consuming than QGA which is slightly more efficient on complex problems. Second, the Rényi and Tsallis entropies leads to similar image segmentation quality. Finally, we have shown that the proposed method is more appropriate than bilevel thresholding for multimodal and noisy images segmentation.