基于差分演化和克隆选择机制的优化算法

为了解决函数优化过程中的“早熟收敛”和“搜索迟钝”问题,将差分演化算法与克隆选择算法进行了结合,提出了一种新的差分演化克隆选择算法。该算法将克隆选择操作引入到差分演化算法中,达到了既能够选出最好个体又能够保证种群多样性的效果。实验结果表明该算法在多峰值函数优化问题中,具有求解精度较高,收敛速度较快等优点。     

基于差分演化的果蝇优化算法

针对基本果蝇优化算法在求解高维函数时存在求解精度低、迭代收敛速度较慢等问题,提出一种基于差分演化的果蝇优化算法。该算法将差分演化策略融合到果蝇优化算法中,对每代产生的群体进行变异、交叉、选择操作,增加种群的多样性,使其能更快、更有效地求解高维函数问题。对12个基准函数进行了仿真验证,结果表明,与基本的果蝇优化算法和差分演化算法相比,新算法在收敛速度、求解精度上都具有明显的优越性。     

保存基因的2-Opt一般反向差分演化算法

为了进一步提高差分演化算法的性能,提出一种采用保存基因的2-Opt一般反向差分演化算法,并把它应用于函数优化问题中.新算法具有以下特征:(1)采用保存被选择个体基因的方式组成参加演化的新个体.保存基因的方法可以很好的保持种群多样性;(2)采用一般反向学习(GOBL)机制进行初始化,提高了初始化效率;(3)采用2-Opt算法加速差分演化算法的收敛速度,提高搜索效率.通过测试函数的实验,并与其他差分演化算法进行比较.实验结果证实了新算法的高效性,通用性和稳健性.     

基于差分演化算法的粗糙集属性约简

属性约简是粗糙集(RS)理论的核心内容之一。应用差分演化(DE)算法求解最小属性约简是一个新的方向。对差分演化算法进行了改进,给出了一种新的适应值函数的定义形式;并在此基础上提出了基于差分演化算法的属性约简算法。最后利用多组数据对该算法进行了仿真实验,并与现有算法进行了比较分析。实验结果表明该算法是有效的,能快速地进行属性约简。     

基于单形正交实验设计的差分演化算法

为了克服传统差分演化(DE)算法在求解约束优化问题时出现的收敛性慢和容易陷入早熟等缺陷,提出一种新的基于单形正交实验设计的差分演化(SO-DE)算法。该算法设计了一种结合单形交叉和正交实验设计的混合交叉算子来提高差分演化算法的搜索能力;同时采用了一种改进的个体优劣比较准则对种群个体进行比较和选择。这种新的混合交叉算子利用多个父代个体进行单形交叉产生多个子代个体,从两者中选择优秀个体进行正交实验设计得到下一代种群个体。改进的个体优劣比较准则对不同状态下的种群采用不同的处理方案,其目的在于能够有效地权衡目标函数值和约束违反量之间的关系,从而选择优秀个体进入下一代种群。通过对13个标准测试函数和2个工程设计问题进行仿真实验,实验结果表明SO-DE算法求解的精度和标准方差都要优于HEAA算法和COEA/OED算法。SO-DE算法具有更高的精度以及更好的稳定性。     

基于ε占优的正交多目标差分演化算法研究

演化多目标优化是目前演化计算中热门研究方向之一.但是,要设计一种高效、鲁棒的演化多目标优化算法,使其找到接近最优和完整的非劣解集是一项很困难的任务.为了能有效求解多目标优化问题,提出了一种新的多目标差分演化算法.新算法具有如下特征:1)利用正交实验设计和连续空间量化的方法产生初始群体,使得初始群体中的个体可以均匀分布于搜索空间,并且可以使好的个体在演化过程中得到利用;2)采用Archive群体保存非劣解,并利用ε占优方法更新Archive群体,从而可以使算法较快获得分布很好的Pareto解集;3)为了加快算法收敛,提出一种基于随机选择和精英选择的混合选择机制.通过8个标准测试函数对新算法进行测试,并与其他一些多目标演化算法进行比较,其结果表明新算法可以有效逼近真实Pareto前沿且分布均匀,并且在收敛性和多样性的求解精度和稳     

基于差分演化与猫群算法融合的群体智能算法

提出一种基于差分演化与猫群算法融合的群体智能算法。该算法基于猫群算法的两种行为模式,引进差分演化的思想,根据分组率随机把群体分成两个种群,一个种群执行猫群算法搜寻模式,另一种群执行差分变异模式,算法采用一种信息共享机制,使两个种群在搜索最优解时可以实现协同进化,信息交流。既实现了不同进化模式间的优势互补,又可以增加种群的多样性。对5个基准函数进行仿真实验并分别与DE和CSO进行比较,表明混合算法同时具有全局搜索和局部搜索最优解性能,收敛速度快,计算精度高,更适合用于求解高维复杂函数。     

差分演化算法在约束优化问题中的应用

差分演化算法的变异机制没有充分利用种群的信息,导致变异是盲目的。受到粒子群算法信息共享机制的启发,文中提出了一种多群体差分演化算法,新算法将整个种群分成多个子种群,每个子种群通过借鉴本种群的内部经验与整个种群的外部经验对变异进行指导。一方面,由于变异操作借鉴了子种群的局部信息和整个种群的全局信息,提高了算法收敛的速度;另一方面,多个子群体增强了种群的多样性,提升了算法的全局搜索能力。数值实验表明新算法具有很强的稳定性和全局搜索能力,在相同计算复杂度情况下的全局搜索能力较原始差分演化算法有明显提升,可以有效求解约束优化问题。     

差分演化算法在约束优化问题中的应用

差分演化算法的变异机制没有充分利用种群的信息,导致变异是盲目的.受到粒子群算法信息共享机制的启发,文中提出了一种多群体差分演化算法,新算法将整个种群分成多个子种群,每个子种群通过借鉴本种群的内部经验与整个种群的外部经验对变异进行指导.一方面,由于变异操作借鉴了子种群的局部信息和整个种群的全局信息,提高了算法收敛的速度;另一方面,多个子群体增强了种群的多样性,提升了算法的全局搜索能力.数值实验表明新算法具有很强的稳定性和全局搜索能力,在相同计算复杂度情况下的全局搜索能力较原始差分演化算法有明显提升,可以有效求解约束优化问题.     

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。     

Multiobjective differential evolution using homeostasis based mutation for application in software cost estimation

The problem in software cost estimation revolves around accuracy. To improve the accuracy, heuristic/meta-heuristic algorithms have been known to yield better results when it is applied in the domain of software cost estimation. For the sake of accuracy in results, we are still modifying these algorithms. Here we have proposed a new meta-heuristic algorithm based on Differential Evolution (DE) by Homeostasis mutation operator. Software development requires high prediction and low Root Mean Squared Error (RMSE) and mean magnitude relative error(MMRE). The problem in software cost estimation relates to accurate prediction and minimization of RMSE and MMRE, which are used to solve multiobjective optimization. Many versions of DE were proposed, however multi-objective versions where the concept of Pareto optimality is used, are most popular. Pareto-Based Differential Evolution (PBDE) is one of them. Although the performance of this algorithm is very good, its convergence rate can be further improved by minimizing the time complexity of nondominated sorting, and by improving the diversity of solutions. This has been implemented by using efficient nondominated algorithm whose time complexity is better than the previous one and a new mutation scheme is implemented in DE which can provide more diversity among solutions. The proposed variant multiplies the Homeostasis value with one more vector, named the Homeostasis mutation vector, in the existing mutation vector to provide more bandwidth for selecting effective mutant solutions. The proposed approach provides more promising solutions to guide the evolution and helps DE escape the situation of stagnation. The performance of the proposed algorithm is evaluated on twelve benchmark test functions (bi-objective and tri-objective) on the Pareto-optimal front. The performance of the proposed algorithm is compared with other state-of-the-art algorithms on five multi-objective evolutionary algorithms (MOEAs). The result verifies that our proposed Homeostasis mutation strategy performs better than other state-of-the-art algorithms. Finally, application of MODE-HBM is applied to solve in terms of Pareto front, representing the trade-off between development RMSE, MMRE, and prediction for COCOMO model.     

Disturbed Exploitation compact Differential Evolution for limited memory optimization problems

This paper proposes a novel and unconventional Memetic Computing approach for solving continuous optimization problems characterized by memory limitations. The proposed algorithm, unlike employing an explorative evolutionary framework and a set of local search algorithms, employs multiple exploitative search within the main framework and performs a multiple step global search by means of a randomized perturbation of the virtual population corresponding to a periodical randomization of the search for the exploitative operators. The proposed Memetic Computing approach is based on a populationless (compact) evolutionary framework which, instead of processing a population of solutions, handles its statistical model. This evolutionary framework is based on a Differential Evolution which cooperatively employs two exploitative search operators: the first is based on a standard Differential Evolution mutation and exponential crossover, and the second is the trigonometric mutation. These two search operators have an exploitative action on the algorithmic framework and thus contribute to the rapid convergence of the virtual population towards promising candidate solutions. The action of these search operators is counterbalanced by a periodical stochastic perturbation of the virtual population, which has the role of “disturbing” the excessively exploitative action of the framework and thus inhibits its premature convergence. The proposed algorithm, namely Disturbed Exploitation compact Differential Evolution, is a simple and memory-wise cheap structure that makes use of the Memetic Computing paradigm in order to solve complex optimization problems. The proposed approach has been tested on a set of various test problems and compared with state-of-the-art compact algorithms and with some modern population based meta-heuristics. Numerical results show that Disturbed Exploitation compact Differential Evolution significantly outperforms all the other compact algorithms present in literature and reaches a competitive performance with respect to modern population algorithms, including some memetic approaches and complex modern Differential Evolution based algorithms. In order to show the potential of the proposed approach in real-world applications, Disturbed Exploitation compact Differential Evolution has been implemented for performing the control of a space robot by simulating the implementation within the robot micro-controller. Numerical results show the superiority of the proposed algorithm with respect to other modern compact algorithms present in literature.     

Design of microwave broadband absorbers using a self‐adaptive differential evolution algorithm

Microwave broadband absorber design for a desired frequency and angle range is presented. The design technique is based on a self‐adaptive Differential Evolution (DE) algorithm. Numerical examples are compared with the existing in the literature and with those found by the other evolutionary algorithms. The results show that the new DE algorithm version outerperforms other global optimizers like Particle swarm optimization (PSO) variants and the classical DE algorithm. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2009.     

基于多变异策略的自适应差分进化算法

为了克服差分进化算法寻优精度低、收敛速度慢、稳定性差等不足,提出一种基于多变异策略的自适应差分进化算法（ADE-MM）。首先,在3个变异策略的选择过程中添加2个具有学习功能的扰动阈值,以提高种群多样性,扩大搜索范围;然后,根据上次迭代的成功参数自适应调整当前参数,提高寻优精度和寻优速度;最后,利用向量粒子池法和中心粒子法产生新的向量粒子,进一步提高寻优效果。使用8个函数、5种对比算法（RMDE、OLCPDE、JADE、SaDE、MDE_pBX）进行测试,且每种例子都独立执行30次。ADE-MM算法在均值和方差的比较中取得了全胜,其中在30维的情况下取得了5个独立胜利,3个并列胜利;在50维的情况下取得了6个独立胜利,2个并列胜利;在100维的情况下全部为独立胜利。同时在Wilcoxon rank sum test、胜率和算法耗时分析中,ADE-MM算法也取得优异的表现。实验结果表明,相对于其他5种对比算法,ADE-MM算法具有更强的全局寻优能力、收敛性和稳定性。     

Evolutionary and population dynamics of 3 parents differential evolution (3PDE) using self-adaptive tuning methodologies

Differential Evolution is known for its simplicity and effectiveness as an evolutionary optimizer. In recent years, many researchers have focused on the exploration of Differential Evolution (DE). The objective of this paper is to show the evolutionary and population dynamics for the empirical testing on 3-Parents Differential Evolution (3PDE) for unconstrained function optimization (Teng et al. 2007). In this paper, 50 repeated evolutionary runs for each of 20 well-known benchmarks were carried out to test the proposed algorithms against the original 4-parents DE algorithm. As a result of the observed evolutionary dynamics, 3PDE-SAF performed the best among the preliminary proposed algorithms that included 3PDE-SACr and 3PDE-SACrF. Subsequently, 3PDE-SAF is chosen for the self-adaptive population size for testing dynamic population sizing methods using the absolute (3PDE-SAF-Abs) and relative (3PDE-SAF-Rel) population size encodings. The final result shows that 3PDE-SAF-Rel produced a better performance and convergence overall compared to all the other proposed algorithms, including the original DE. In terms of population dynamics, the population size in 3PDE-SAF-Abs exhibited disadvantageously high dynamics that caused less efficient results. On the other hand, the population size in 3PDE-SAF-Rel was observed to be approximately constant at ten times the number of variables being optimized, hence giving a better and more stable performance.     

基于新颖S型转换函数的二进制粒子群优化算法求解具有单连续变量的背包问题

为了高效求解具有单连续变量的背包问题（KPC）,首先基于高斯误差函数提出了一个新颖S型转换函数,给出了利用该转换函数将一个实向量转换为0-1向量的新方法,由此提出了一个新的二进制粒子群优化（NBPSO）算法;然后,利用KPC的第二数学模型,并且把NBPSO与处理KPC不可行解的有效算法相结合,提出了求解KPC的一个新方法。为了检验NBPSO求解KPC的性能,利用NBPSO求解四类大规模KPC实例,并把所得计算结果与基于其他S、V型转换函数的二进制粒子群优化算法（BPSO）、具有混合编码的单种群二进制差分演化算法（S-HBDE）、具有混合编码的双种群二进制差分演化算法（B-HBDE）和二进制粒子群优化算法（BPSO）等的计算结果相比较。比较结果表明NBPSO不仅平均计算结果更优,而且稳定性更佳,说明NBPSO的性能比其他算法有显著提升。     

基于差异进化的克隆选择算法

针对免疫算法在全局优化过程中多样性不足的问题,将差异进化引入克隆变异操作中,提出了一个新的改进的克隆选择算法——基于差异进化的克隆选择算法(DECSA),算法将差异进化和克隆超变异相结合,促进了抗体与抗体之间的信息融合,使得子代抗体继承父代抗体的信息的同时,携带着不同父代个体信息,丰富了抗体种群的多样性,实现了在同一父代抗体周围的多个方向同时进行全局和局部搜索。对13个标准测试函数的测试结果及与已有的算法的比较表明,该算法表现出较好的局部搜索和全局搜索能力。     

基于最小距离和聚合策略的分解多目标进化算法

针对基于帕累托（Pareto）支配的多目标进化算法在解决高维问题时选择压力降低,以及基于分解的多目标进化算法在提高收敛性和分布性的同时降低了种群多样性的问题,提出了一种基于最小距离和聚合策略的分解多目标进化算法。首先,使用基于角度分解的技术将目标空间分解为指定个数的子空间来提高种群的多样性;然后,在生成新解的过程中加入基于聚合的交叉邻域方法,使生成的新解更接近于父代解;最后,分两阶段在每个子空间内基于最小距离和聚合策略来选择解以提高收敛性和分布性。为了验证所提算法的可行性,采用标准测试函数ZDT和DTLZ进行仿真实验,结果表明所提算法的总体性能均优于经典的基于分解的多目标进化算法（MOEA/D）、MOEA/D-DE、NSGA-Ⅲ和GrEA。可见,所提算法在提高多样性的同时可以有效平衡收敛性和多样性。     

一种改进的基于差分进化的多目标进化算法

近年来运用进化算法（EAs）解决多目标优化问题（Multi-objective Optimization Problems MOPs）引起了各国学者们的关注。作为一种基于种群的优化方法,EAs提供了一种在一次运行后得到一组优化的解的方法。差分进化（DE）算法是EA的一个分支,最开始是用来解决连续函数空间的问题。提出了一种改进的基于差分进化的多目标进化算法（CDE）,并且将它与另外两个经典的多目标进化算法（MOEAs）NSGA-II和SPEA2进行了对比实验。     

A new hybrid differential evolution algorithm with self-adaptation for function optimization

In this study, a new hybrid algorithm, hDEBSA, is proposed with the aid of two evolutionary algorithms, Differential Evolution (DE) and Backtracking Search Optimization Algorithm (BSA). The control parameters of both algorithms are simultaneously considered as a self-adaptation basis such that the values of the parameters update automatically during the optimization process to improve performance and convergence speed. To validate the proposed algorithm, twenty-eight CEC2013 test functions are considered. The performance results of hDEBSA are validated by comparing them with several state-of-the-art algorithms that are available in literature. Finally, hDEBSA is applied to solve four real-world optimization problems, and the results are compared with the other algorithms, where it was found that the hDEBSA performance is better than that of the other algorithms.