混合差分进化算法

为了克服差分进化算法容易出现早熟和收敛速度慢的问题,提出了一种混合差分进化算法.该算法在趋药性差分进化算法(CDE)的基础上,通过对较优个体进行变异操作,维护了种群多样性、避免早熟;通过将较差的个体与较优个体进行杂交,提高了开采能力、加快了收敛速度.基于这两种策略,算法的开采能力与探索能力达到了平衡.用该算法解决标准函数优化问题,并将仿真结果与其他算法进行比较,数值结果表明该文算法具有较快的收敛速度和很强的跳出局部最优的能力.     

Colonial competitive differential evolution: An experimental study for optimal economic load dispatch

Differential evolution (DE) algorithm is a population-based algorithm designed for global optimization of the optimization problems. This paper proposes a different DE algorithm based on mathematical modeling of socio-political evolution which is called Colonial Competitive Differential Evolution (CCDE). The two typical CCDE algorithms are benchmarked on three well-known test functions, and the results are verified by a comparative study with two original DE algorithms which include DE/best/1 and DE/rand/2. Also, the effectiveness of CCDE algorithms is tested on Economic Load Dispatch (ELD) problem including 10, 15, 40, and 140-unit test systems. In this study, the constraints and operational limitations, such as valve-point loading, transmission losses, ramp rate limits, and prohibited operating zones are considered. The comparative results show that the CCDE algorithms have good performance and are reliable tools in solving ELD problem.     

多策略协方差矩阵学习差分进化算法

针对差分进化算法（DE）存在的早熟收敛和搜索停滞的问题,提出了多策略协方差矩阵学习的差分进化算法。通过协方差矩阵建立特征坐标系,通过在特征坐标系中执行变异和交叉操作,来充分利用当前种群的分布信息以及各变量之间的关系,保证种群能朝着全局最优解的方向进化;根据历史进化信息来选择变异策略的方式使得个体能选择当前最合适的变异策略,提高找到最优解的概率;交叉概率的自适应也一定程度上平衡算法的全局探索能力和局部探索能力。对算法的收敛性进行了证明,同时将算法在CEC2017测试集上进行了仿真实验,并将实验结果跟其他优秀的差分进化算法进行了对比,对比结果表明了该算法的有效性。     

Solution of economic load dispatch using hybrid chemical reaction optimization approach

In this paper, a new and efficient optimization technique based on hybridization of chemical reaction optimization (CRO) with differential evolution (DE) is developed and demonstrated to solve the ELD problem with thermal cost function having valve point loading effect together with and without multiple fuel options and with and without considering prohibited operating zone and ramp rate constraint. When valve-point effects, multi-fuel operations and the constraints of prohibited operating zone and ramp rate are taken into account, ELD problem become more complex than conventional ELD problem. To show the priority of the proposed algorithm, it is implemented on six different test systems for solving ELD problems. Comparative studies are carried out to examine the effectiveness of the proposed HCRO-DE approach with conventional DE, CRO and the other algorithms reported in the literature. The simulation results show that the proposed HCRO-DE method is capable of obtaining better quality solutions than DE, CRO and the other well popular optimization techniques.     

求解高维多模优化问题的自适应差分进化算法

在基变量选择方差理论分析的基础上,提出一种自适应差分进化算法(ADE).ADE算法通过设计自适应收敛因子构建自调整的权重质心变异策略,同时在交叉策略中引入发射、收缩两种单纯形操作算子,保证算法全局搜索能力的同时,能钉效提高算法后期的局部增强能力.30个优化问题的数值研究结果表明ADE算法具有比DE、DERL以及DERB三种算法更快的收敛速度和可靠性,尤其适合于高维多模优化问题的求解.     

An improved teaching-learning-based optimization algorithm for numerical and engineering optimization problems

The teaching-learning-based optimization (TLBO) algorithm, one of the recently proposed population-based algorithms, simulates the teaching-learning process in the classroom. This study proposes an improved TLBO (ITLBO), in which a feedback phase, mutation crossover operation of differential evolution (DE) algorithms, and chaotic perturbation mechanism are incorporated to significantly improve the performance of the algorithm. The feedback phase is used to enhance the learning style of the students and to promote the exploration capacity of the TLBO. The mutation crossover operation of DE is introduced to increase population diversity and to prevent premature convergence. The chaotic perturbation mechanism is used to ensure that the algorithm can escape the local optimal. Simulation results based on ten unconstrained benchmark problems and five constrained engineering design problems show that the ITLBO algorithm is better than, or at least comparable to, other state-of-the-art algorithms.     

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.     

采用概率判定法的分组变异自适应差分进化算法

为了平衡差分进化算法(DE)的全局探索和局部开发过程,提高算法避免陷入局部最优的能力,文中提出采用概率判定法的分组变异自适应差分进化算法(GVADE).GVADE采用概率判定法判定个体进化状态为较好、较差或一般,并根据个体进化状态为个体选择合适的变异算子和控制参数组.同时,为了满足进化状态较差个体变异的需要,设计具有较强全局探索能力的变异算子.在CEC2005标准测试集合上的实验表明,GVADE优于现有的其它DE算法,可以更好地平衡全局探索和局部开发,具有更高的收敛精度.     

Opposition-Based Differential Evolution

Evolutionary algorithms (EAs) are well-known optimization approaches to deal with nonlinear and complex problems. However, these population-based algorithms are computationally expensive due to the slow nature of the evolutionary process. This paper presents a novel algorithm to accelerate the differential evolution (DE). The proposed opposition-based DE (ODE) employs opposition-based learning (OBL) for population initialization and also for generation jumping. In this work, opposite numbers have been utilized to improve the convergence rate of DE. A comprehensive set of 58 complex benchmark functions including a wide range of dimensions is employed for experimental verification. The influence of dimensionality, population size, jumping rate, and various mutation strategies are also investigated. Additionally, the contribution of opposite numbers is empirically verified. We also provide a comparison of ODE to fuzzy adaptive DE (FADE). Experimental results confirm that the ODE outperforms the original DE and FADE in terms of convergence speed and solution accuracy.     

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.     

一种多策略混合的粒子群优化算法

针对传统粒子群优化算法在解决一些复杂优化问题时易陷入局部最优且收敛速度较慢的问题,提出一种多策略混合的粒子群优化算法(Hybrid Particle Swarm Optimization with Multiply Strategies,HPSO)。该算法利用反向学习策略产生反向解群,扩大粒子群搜索的范围,增强算法的全局勘探能力;同时,为避免种群陷入局部最优,算法对种群中部分较差的个体实施柯西变异,以产生远离局部极值的个体,而对群体中较好的个体施以差分进化变异,以增强算法的局部开采能力。对这3种策略进行了有机结合以更好地平衡粒子群算法全局勘探和局部开采的能力。将HPSO算法与其他3种知名的粒子群算法在10个标准测试函数上进行了性能比较实验,结果表明HPSO算法在求解精度和收敛速度上具有较显著的优势。     

A hybrid differential evolution algorithm based on particle swarm optimization for nonconvex economic dispatch problems

This paper presents the design and application of an efficient hybrid heuristic search method to solve the practical economic dispatch problem considering many nonlinear characteristics of power generators, and their operational constraints, such as transmission losses, valve-point effects, multi-fuel options, prohibited operating zones, ramp rate limits and spinning reserve. These practical operation constraints which can usually be found at the same time in realistic power system operations make the economic load dispatch problem a nonsmooth optimization problem having complex and nonconvex features with heavy equality and inequality constraints.The proposed approach combines in the most effective way the properties of two of the most popular evolutionary optimization techniques now in use for power system optimization, the Differential Evolution (DE) and Particle Swarm Optimization (PSO) algorithms. To improve the global optimization property of DE, the PSO procedure is integrated as additional mutation operator.The effectiveness of the proposed algorithm (termed DEPSO) is demonstrated by solving four kinds of ELD problems with nonsmooth and nonconvex solution spaces. The comparative results with some of the most recently published methods confirm the effectiveness of the proposed strategy to find accurate and feasible optimal solutions for practical ELD problems.     

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。     

基于随机邻域变异和趋优反向学习的差分进化算法

传统差分进化（DE）算法在迭代过程中不能充分平衡全局勘探与局部开发,存在易陷入局部最优、求解精度低、收敛速度慢等缺点。为提升算法性能,提出一种基于随机邻域变异和趋优反向学习的差分进化（RNODE）算法并对其进行复杂度分析。首先,为种群中每个个体生成随机邻域,用全局最佳个体引导邻域最佳个体生成复合基向量,结合控制参数自适应更新机制构成随机邻域变异策略,使算法在引导种群向最优方向趋近的同时保持一定的勘探能力;其次,为了进一步帮助算法跳出局部最优,对种群中较差个体执行趋优反向学习操作,扩大搜索区域;最后,将RNODE与九种算法进行对比以验证RNODE的有效性和先进性。在23个Benchmark函数和两个实际工程优化问题上的实验结果表明,RNODE算法收敛精度更高、速度更快、稳定性更优。     

多策略自适应变异的差分进化算法及其应用

针对传统DE算法在求解复杂函数时会出现早熟收敛、收敛精度低、收敛速度慢等缺陷，提出了一种多策略自适应变异的差分进化算法MsA-DE。将3种变异策略两两结合，随机分配所占比重，以增加种群的多样性；通过引入进化程度阈值，自适应地选择最合适的变异策略，平衡算法的全局搜索和局部搜索能力；对越界的变异个体进行处理，保证种群的多样性和有效性。加入扰动机制提高算法跳出局部最优的能力，同时提高最优解的精度。将该算法用于14个测试函数的优化中，结果表明，MsA-DE算法与其它4种算法相比具有更高的收敛精度和跳出局部最优的能力。将该算法应用于铁路功率调节器RPC的容量优化问题中，结果表明，该算法能够减小RPC补偿装置的容量，提高装置的经济性。     

自适应变异尺度系数和混合选择的回溯搜索算法

回溯搜索算法（Backtracking Search Optimization Algorithm,BSA）是一种基于种群的进化算法。该算法有良好的全局搜索性能,但存在收敛速度慢的缺点。针对这一缺点,提出了自适应变异尺度系数和混合选择的改进的回溯搜索算法。改进的变异尺度系数是基于Metropolis准则提出的,它的总体趋势自适应减小。改进的选择策略是整体[q]%择优法与锦标赛选择法的混合选择机制,在选择过程中使一定比例的优秀个体优先进入下一代,剩余个体对位选取适应度较高的个体。对5个复杂的约束优化问题进行仿真实验,得到的实验结果分别与原算法和众多同类算法进行了比较,实验结果表明了改进算法的有效性和良好竞争力。     

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...     

基于模拟退火的混合差分进化算法及其在联合补货-配送集成优化中的应用

针对差分进化 (Differential evolution, DE)算法搜索效率较低和容易陷入局部最优的缺点,设计了基于SA的混合差分进化算法(SA-based Hybrid DE, SAHDE),以提高DE算法的全局寻优能力。该算法采用自适应变异算子和交叉算子,并结合模拟退火(Simulated Annealing, SA)算法的Metropolis 准则。首先通过标准测试函数对改进的SAHDE进行性能测试,证明了该算法比DE、自适应混合DE (Adaptive Hybrid DE, AHDE)和遗传算法(Genetic Algorithm, GA)更有效。进而将该算法运用到联合补货-配送集成优化(典型NP-hard)问题的求解中,通过大规模的算例分析,证实SAHDE在解决联合补货-配送优化问题比DE、AHDE和GA更有效。     

基于双变异模式协同的自适应微分进化算法

针对微分进化算法(DE)易陷入局部最优解、进化后期收敛速度慢、求解精度低等缺点,结合DE/rand/1和DE/best/1两种变异模式分别具有全局探索能力和局部开发能力的优点,引入精英存档策略和控制参数自适应策略,提出一种双变异模式协同自适应微分进化(DMCSaDE)算法.15个典型benchmark测试函数的实验结果表明,DMCSaDE能够有效提高算法的全局探索能力和局部开发能力,避免早熟收敛,大大提高算法的收敛性能和鲁棒性,同时,精英种群的大小对DMCSaDE的优化性能具有明显的影响.     

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。