Modified differential evolution approach for optimization of planar parallel manipulators force capabilities

The global optimization problem is not easy to solve and is still an open challenge for researchers since an analytical optimal solution is difficult to obtain even for relatively simple application problems. Conventional deterministic numerical algorithms tend to stop the search in local minimum nearest to the input starting point, mainly when the optimization problem presents nonlinear, non-convex and non-differential functions, multimodal and nonlinear. Nowadays, the use of evolutionary algorithms (EAs) to solve optimization problems is a common practice due to their competitive performance on complex search spaces. EAs are well known for their ability to deal with nonlinear and complex optimization problems. The primary advantage of EAs over other numerical methods is that they just require the objective function values, while properties such as differentiability and continuity are not necessary. In this context, the differential evolution (DE), a paradigm of the evolutionary computation, has been widely used for solving numerical global optimization problems in continuous search space. DE is a powerful population-based stochastic direct search method. DE simulates natural evolution combined with a mechanism to generate multiple search directions based on the distribution of solutions in the current population. Among DE advantages are its simple structure, ease of use, speed, and robustness, which allows its application on several continuous nonlinear optimization problems. However, the performance of DE greatly depends on its control parameters, such as crossover rate, mutation factor, and population size and it often suffers from being trapped in local optima. Conventionally, users have to determine the parameters for problem at hand empirically. Recently, several adaptive variants of DE have been proposed. In this paper, a modified differential evolution (MDE) approach using generation-varying control parameters (mutation factor and crossover rate) is proposed and evaluated. The proposed MDE presents an efficient strategy to improve the search performance in preventing of premature convergence to local minima. The efficiency and feasibility of the proposed MDE approach is demonstrated on a force optimization problem in Robotics, where the force capabilities of a planar 3-RRR parallel manipulator are evaluated considering actuation limits and different assembly modes. Furthermore, some comparison results of MDE approach with classical DE to the mentioned force optimization problem are presented and discussed.     

Micro-differential evolution: Diversity enhancement and a comparative study

Differential evolution (DE) algorithm suffers from high computational time due to slow nature of evaluation. Micro-DE (MDE) algorithms utilize a very small population size, which can converge faster to a reasonable solution. Such algorithms are vulnerable to premature convergence and high risk of stagnation. This paper proposes a MDE algorithm with vectorized random mutation factor (MDEVM), which utilizes the small size population benefit while empowers the exploration ability of mutation factor through randomizing it in the decision variable level. The idea is supported by analyzing mutation factor using Monte-Carlo based simulations. To facilitate the usage of MDE algorithms with very-small population sizes, a new mutation scheme for population sizes less than four is also proposed. Furthermore, comprehensive comparative simulations and analysis on performance of the MDE algorithms over various mutation schemes, population sizes, problem types (i.e. uni-modal, multi-modal, and composite), problem dimensionalities, and mutation factor ranges are conducted by considering population diversity analysis for stagnation and pre-mature convergence. The MDEVM is implemented using a population-based parallel model and studies are conducted on 28 benchmark functions provided for the IEEE CEC-2013 competition. Experimental results demonstrate high performance in convergence speed of the proposed MDEVM algorithm.     

一种改进的约束优化差分进化算法

提出一种改进的差分进化算法用于求解约束优化问题.该算法在处理约束时不引入惩罚因子,使约束处理问题简单化.利用佳点集方法初始化个体以维持种群的多样性.结合差分进化算法两种不同变异策略的特点,对可行个体与不可行个体分别采用DE/best/1变异策略和DE/rand/1策略,以提高算法的全局收敛性能和收敛速率.用几个标准的Benchmark问题进行了测试,实验结果表明该算法是一种求解约束优化问题的有效方法.     

基于最优高斯随机游走和个体筛选策略的差分进化算法

针对差分进化算法开发能力较差的问题, 提出一种具有快速收敛的新型差分进化算法. 首先, 利用最优高斯随机游走策略提高算法的开发能力; 然后, 采用基于个体优化性能的简化交叉变异策略实现种群的进化操作以加强其局部搜索能力; 最后, 通过个体筛选策略进一步提高算法的探索能力以避免陷入局部最优. 12 个标准测试函 数和两种带约束的工程优化问题的实验结果表明, 所提出的算法在收敛速度、算法可靠性及收敛精度方面均优于EPSDE、SaDE、JADE、BSA、CoBiDE、GSA和ABC等算法, 在加强算法探索能力的同时能够有效地提高算法的开发能力.

     

A novel clustering-based differential evolution with 2 multi-parent crossovers for global optimization

Differential evolution (DE) is a simple and efficient global optimization algorithm. However, DE has been shown to have certain weaknesses, especially if the global optimum should be located using a limited number of function evaluations (NFEs). Hence hybridization with other methods is a research direction for the improvement of differential evolution. In this paper, a hybrid DE based on the one-step k-means clustering and 2 multi-parent crossovers, called clustering-based differential evolution with 2 multi-parent crossovers (2-MPCs-CDE) is proposed for the unconstrained global optimization problems. In 2-MPCs-CDE, k cluster centers and several new individuals generate two search spaces. These spaces are then searched in turn. This method utilizes the information of the population effectively and improves search efficiency. Hence it can enhance the performance of DE. A comprehensive set of 35 benchmark functions is employed for experimental verification. Experimental results indicate that 2-MPCs-CDE is effective and efficient. Compared with other state-of-the-art evolutionary algorithms, 2-MPCs-CDE performs better, or at least comparably, in terms of the solution accuracy and the convergence rate.     

Optimal short-term hydro-thermal scheduling using quasi-oppositional teaching learning based optimization

This paper presents a new approach for solving short-term hydrothermal scheduling (HTS) using an integrated algorithm based on teaching learning based optimization (TLBO) and oppositional based learning (OBL). The practical hydrothermal system is highly complex and possesses nonlinear relationship of the problem variables, cascading nature of hydro reservoirs, water transport delay and scheduling time linkage that make the problem of optimization difficult using standard optimization methods. To overcome these problems, the proposed quasi-oppositional teaching learning based optimization (QOTLBO) is employed. To show its efficiency and robustness, the proposed QOTLBO algorithm is applied on two test systems. Numerical results of QOTLBO are compared with those obtained by two phase neural network, augmented Lagrange method, particle swarm optimization (PSO), improved self-adaptive PSO (ISAPSO), improved PSO (IPSO), differential evolution (DE), modified DE (MDE), fuzzy based evolutionary programming (Fuzzy EP), clonal selection algorithm (CSA) and TLBO approaches. The simulation results reveal that the proposed algorithm appears to be the best in terms of convergence speed, solution time and minimum cost when compared with other established methods. This method is considered to be a promising alternative approach for solving the short-term HTS problems in practical power system.     

A hybrid memory-based dragonfly algorithm with differential evolution for engineering application

The dragonfly algorithm (DA) is a swarm-based stochastic algorithm which possesses static and dynamic behavior of swarm and is gaining meaningful popularity due to its low computational cost and fast convergence in solving complex optimization problems. However, it lacks internal memory and is thereby not able to keep track of its best solutions in previous generations. Furthermore, the solution also lacks in diversity and thereby has a propensity of getting trapped in the local optimal solution. In this paper, an iterative-level hybridization of dragonfly algorithm (DA) with differential evolution (DE) is proposed and named as hybrid memory-based dragonfly algorithm with differential evolution (DADE). The reason behind selecting DE is for its computational ability, fast convergence and capability in exploring the solution space through the use of crossover and mutation techniques. Unlike DA, in DADE the best solution in a particular iteration is stored in memory and proceeded with DE which enhances population diversity with improved mutation and accordingly increases the probability of reaching global optima efficiently. The efficiency of the proposed algorithm is measured based on its response to standard set of 74 benchmark functions including 23 standard mathematical benchmark functions, 6 composite benchmark function of CEC2005, 15 benchmark functions of CEC2015 and 30 benchmark function of CEC2017. The DADE algorithm is applied to engineering design problems such as welded beam deign, pressure vessel design, and tension/compression spring design. The algorithm is also applied to the emerging problem of secondary user throughput maximization in an energy-harvesting cognitive radio network. A comparative performance analysis between DADE and other most popular state-of-the-art optimization algorithms is carried out and significance of the results is deliberated. The result demonstrates significant improvement and prominent advantages of DADE compared to conventional DE, PSO and DA in terms of various performance measuring parameters. The results of the DADE algorithm applied on some important engineering design problems are encouraging and validate its appropriateness in the context of solving interesting practical engineering challenges. Lastly, the statistical analysis of the algorithm is also performed and is compared with other powerful optimization algorithms to establish its superiority.

     

一种改进的多目标约束优化差分进化算法

提出一种新的多目标优化差分进化算法用于求解约束优化问题.该算法利用佳点集方法初始化个体以维持种群的多样性.将约束优化问题转化为两个目标的多目标优化问题.基于Pareto支配关系,将种群分为Pareto子集和Non-Pareto子集,结合差分进化算法两种不同变异策略的特点,对Non-Pareto子集和Pareto子集分别采用DE/best/1变异策略和DE/rand/1变异策略.数值实验结果表明该算法具有较好的寻优效果.     

一种改进的微分进化算法

相对于其他优化算法来说,微分进化算法具有控制参数少、易于使用以及鲁棒性强等特点,但在搜索过程中存在着局部搜索能力弱的缺点。针对微分进化算法局部搜索能力弱的缺点,提出了一种基于局部变异的微分进化算法,该算法使个体具有良好快速收敛能力。使用典型优化函数对比较算法进行了测试,算法分析和仿真结果表明,改进以后的算法具有寻优能力...     

求解高维优化问题的改进正弦余弦算法*

提出一种改进的正弦余弦算法(简记为ISCA)。受粒子群优化(PSO)算法的启发,引入惯性权重以提高正弦余弦算法的收敛精度和加快收敛速度。此外,采取反向学习策略产生初始个体以提高种群的多样性和解的质量。采用8个高维基准测试函数进行仿真实验：在相同的最大适应度函数评价次数下,ISCA总体性能上均优于基本SCA算法和HGWO算法;当维数较高(D=1000)时,ISCA所用计算量远小于HDEOO。实验结果表明ISCA在收敛精度和收敛速度指标上均优于对比算法。     

Hybrid differential evolution and Nelder�CMead algorithm with re-optimization

Nonlinear optimization algorithms could be divided into local exploitation methods such as Nelder–Mead (NM) algorithm and global exploration ones, such as differential evolution (DE). The former searches fast yet could be easily trapped by local optimum, whereas the latter possesses better convergence quality. This paper proposes hybrid differential evolution and NM algorithm with re-optimization, called as DE-NMR. At first a modified NM, called NMR is presented. It re-optimizes from the optimum point at the first time and thus being able to jump out of local optimum, exhibits better properties than NM. Then, NMR is combined with DE. To deal with equal constraints, adaptive penalty function method is adopted in DE-NMR, which relaxes equal constraints into unequal constrained functions with an adaptive relaxation parameter that varies with iteration. Benchmark optimization problems as well as engineering design problems are used to experiment the performance of DE-NMR, with the number of function evaluation times being employed as the main index of measuring convergence speed, and objective function values as the main index of optimum’s quality. Non-parametric tests are employed in comparing results with other global optimization algorithms. Results illustrate the fast convergence speed of DE-NMR.     

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.     

应用反向学习和差分进化的群搜索优化算法

针对标准群搜索优化算法在解决一些复杂优化问题时容易陷入局部最优且收敛速度较慢的问题,提出一种应用反向学习和差分进化的群搜索优化算法(Group Search Optimization with Opposition-based Learning and Diffe-rential Evolution,OBDGSO)。该算法利用一般动态反向学习机制产生反向种群,扩大算法的全局勘探范围;对种群中较优解个体实施差分进化的变异操作,实现在较优解附近的局部开采,以改善算法的求解精度和收敛速度。这两种策略在GSO算法中相互协同,以更好地平衡算法的全局搜索能力和局部开采能力。将OBDGSO算法和另外4种群智能算法在12个基准测试函数上进行实验,结果表明OBDGSO算法在求解精度和收敛速度上具有较显著的性能优势。     

带基向量种群的改进差分进化算法

在基向量随机选择中,差分进化算法的收敛速度较慢。为此,提出一种改进的差分进化算法。从当前种群中选择一定数量个体组成基向量种群,在进行变异操作时,从该基向量种群中选择个体作为基向量。使用标准测试函数对算法进行验证,结果表明,该算法能缩小基向量选择范围,减少迭代次数。     

基于精英种群策略的协同差分进化算法

针对差分进化算法在处理函数优化时存在的过早收敛和易陷入局部最优的问题,提出了一种基于精英种群策略的协同差分进化算法。在优化过程中,首先对种群进行适应度值评估和排序,提取前N个优秀个体组成精英种群,其余个体随机分为3个等大的子种群,每个子种群采取不同的进化策略,以此来保证种群的多样性;然后每隔一定代数,根据新的适应度值更新精英种群和其余3个子种群,这样可以有效地避免算法陷入局部最优;最后,将所提出的算法与4个先进的差分进化算法在CEC2014的30个标准测试函数上进行对比实验。实验结果表明,所提出的算法能够有效提高收敛速度,具有较高的收敛精度和较好的优化性能。     

阶段波动差分进化算法及函数优化

差分进化算法被认为是一种简单高效的全局优化算法,但其在解决高维复杂优化问题收敛精度过低,为此提出了阶段波动差分进化算法.新算法利用柯西分布随机数设计用于生成变异率的算子,并对变异率进行上下波动.进化过程中引入分段思想,每个阶段分别根据不同的配置利用算子生成变异率并选择对应的交叉比率改善算法性能.同时为了加快收敛速度,设计了一种新的变异处理策略.通过对一组经典Benchmark函数的测试,实验结果显示了本文算法在解决复杂高维问题时具有优于或相当于其他DE算法的性能.     

采用双变异策略的自适应差分进化算法及应用

为了克服差分进化算法早熟收敛和寻优精度低的缺点,提出一种采用双变异策略的自适应差分进化算法（Adaptive Differential Evolution Algorithm using Double mutation strategies,DADE）。DADE引入基于种群相似度和中心解的双变异策略,有效平衡了算法的全局搜索和局部搜索;自适应交叉概率使种群个体向更新成功的个体学习,有利于后续种群的进化。在7个测试函数和3个电力系统动态经济调度（Dynamic Economic Dispatch,DED）问题上的优化结果表明,DADE算法与其他4种DE算法相比具有更强的全局寻优能力,且对电力系统动态经济调度问题的优化结果优于文献中所报道的结果。     

基于新变异策略的动态自适应差分进化算法

针对差分进化算法在复杂优化问题求解时后期收敛速度慢、易陷入局部最优和参数设置繁琐等问题,提出一种基于新变异策略的动态自适应差分进化算法p-ADE.首先,新变异策略中通过利用种群的全局最优解和目标个体的历史最优解引导种群搜索方向,为下一代个体的生成引入更多有效的方向性信息,避免差分向量中个体随机选择导致的搜索盲目性.其次,为加快收敛速度、提高算法稳定性、避免参数设置的繁琐与不精确,提出一种参数动态自适应调整策略,动态平衡算法局部搜索与全局搜索间的关系,有效调节个体在进化过程中的变异程度.在10个Benchmark函数上的实验结果表明,p-ADE相对于多种先进DE优化策略和全局优化算法在收敛精度、速度和鲁棒性上均具有明显优势.     

基于双种群两阶段变异策略的差分进化算法

针对差分进化算法差分策略优化问题上的不足, 解决DE/best/1策略全局探测能力差, DE/rand/1局部搜索能力弱而带来的鲁棒性降低及陷入局部最优等问题, 本文在差分策略上进行改进, 并且加入邻域分治思想提高进化效率, 提出一种基于双种群两阶段变异策略的差分进化算法(TPSDE). 第一个阶段利用DE/best/1的优势对邻域向量划分完成的子种群区域进行局部优化, 第二个阶段借鉴DE/rand/1的思想实现全局优化, 最终两阶段向量加权得到最终变异个体使得算法避免了过早收敛和搜索停滞等问题的出现. 6个测试函数的仿真实验结果表明TPSDE在收敛速度、优化精度和鲁棒性方面都得到了明显改善.     

分阶段二次变异的多目标混沌差分进化算法

提出一种结合分阶段二次变异和混沌理论的改进差分进化(DE)算法,以解决多目标约束优化问题.其核心思想是,在DE进化前期采用基于非支配解的随机二次变异来提高算法的全局寻优能力,进化后期采用基于非支配解的混沌二次变异来提高DE的局部寻优能力.通过对典型测试问题的仿真实验验证了所提出的算法能在全局搜索性能与局部搜索性能之间维持较好平衡,而且保持了DE算法的简洁性能,其收敛性、分布度和均衡性均优于标准DE.