A self-adaptive differential evolution algorithm for continuous optimization problems

This paper proposes a new self-adaptive differential evolution algorithm (DE) for continuous optimization problems. The proposed self-adaptive differential evolution algorithm extends the concept of the DE/current-to-best/1 mutation strategy to allow the adaptation of the mutation parameters. The control parameters in the mutation operation are gradually self-adapted according to the feedback from the evolutionary search. Moreover, the proposed differential evolution algorithm also consists of a new local search based on the krill herd algorithm. In this study, the proposed algorithm has been evaluated and compared with the traditional DE algorithm and two other adaptive DE algorithms. The experimental results on 21 benchmark problems show that the proposed algorithm is very effective in solving complex optimization problems.     

一种求解背包问题的混合差异演化算法

为增强差异演化算法在求解背包问题时的局部搜索能力,提出拉马克-鲍德温混合差异演化算法。该算法采用双种群协同进化,以差异演化算法为主体,在演化过程中分别引入拉马克进化和鲍德温效应2种局部搜索算子,引导种群进化方向。仿真实验结果表明,该算法求解精度高,收敛速度快,能够高效求解背包问题。     

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.     

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.     

Distributed memetic differential evolution with the synergy of Lamarckian and Baldwinian learning

As a population-based optimizer, the differential evolution (DE) algorithm has a very good reputation for its competence in global search and numerical robustness. In view of the fact that each member of the population is evaluated individually, DE can be easily parallelized in a distributed way. This paper proposes a novel distributed memetic differential evolution algorithm which integrates Lamarckian learning and Baldwinian learning. In the proposed algorithm, the whole population is divided into several subpopulations according to the von Neumann topology. In order to achieve a better tradeoff between exploration and exploitation, the differential evolution as an evolutionary frame is assisted by the Hooke–Jeeves algorithm which has powerful local search ability. We incorporate the Lamarckian learning and Baldwinian learning by analyzing their characteristics in the process of migration among subpopulations as well as in the hybridization of DE and Hooke–Jeeves local search. The proposed algorithm was run on a set of classic benchmark functions and compared with several state-of-the-art distributed DE schemes. Numerical results show that the proposed algorithm has excellent performance in terms of solution quality and convergence speed for all test problems given in this study.     

Multi-objective no-wait flow-shop scheduling with a memetic algorithm based on differential evolution

In this paper, a memetic algorithm (MA) based on differential evolution (DE), namely MADE, is proposed for the multi-objective no-wait flow-shop scheduling problems (MNFSSPs). Firstly, a largest-order-value rule is presented to convert individuals in DE from real vectors to job permutations so that the DE can be applied for solving flow-shop scheduling problems (FSSPs). Secondly, the DE-based parallel evolution mechanism is applied to perform effective exploration, and several local searchers developed according to the landscape of multi-objective FSSPs are applied to emphasize local exploitation. Thirdly, a speed-up computing method is developed based on the property of the no-wait FSSPs. In addition, the concept of Pareto dominance is used to handle the updating of solutions in sense of multi-objective optimization. Due to the well balance between DE-based global search and problem-dependent local search as well as the utilization of the speed-up evaluation, the MNFSSPs can be solved effectively and efficiently. Simulation results and comparisons demonstrate the effectiveness and efficiency of the proposed MADE.     

A variable iterated greedy algorithm with differential evolution for the no-idle permutation flowshop scheduling problem

This paper presents a variable iterated greedy algorithm (IG) with differential evolution (vIG_DE), designed to solve the no-idle permutation flowshop scheduling problem. In an IG algorithm, size d of jobs are removed from a sequence and re-inserted into all possible positions of the remaining sequences of jobs, which affects the performance of the algorithm. The basic concept behind the proposed vIG_DE algorithm is to employ differential evolution (DE) to determine two important parameters for the IG algorithm, which are the destruction size and the probability of applying the IG algorithm to an individual. While DE optimizes the destruction size and the probability on a continuous domain by using DE mutation and crossover operators, these two parameters are used to generate a trial individual by directly applying the IG algorithm to each target individual depending on the probability. Next, the trial individual is replaced with the corresponding target individual if it is better in terms of fitness. A unique multi-vector chromosome representation is presented in such a way that the first vector represents the destruction size and the probability, which is a DE vector, whereas the second vector simply consists of a job permutation assigned to each individual in the target population. Furthermore, the traditional IG and a variable IG from the literature are re-implemented as well. The proposed algorithms are applied to the no-idle permutation flowshop scheduling (NIPFS) problem with the makespan and total flowtime criteria. The performances of the proposed algorithms are tested on the Ruben Ruiz benchmark suite and compared to the best-known solutions available at http://soa.iti.es/rruiz as well as to those from a recent discrete differential evolution algorithm (HDDE) from the literature. The computational results show that all three IG variants represent state-of-art methods for the NIPFS problem.     

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.     

批量流水线调度问题的混合差分进化算法

针对E/T指标的批量流水线调度问题,提出了差分进化调度算法。该算法采用基于实数的编码方式,利用最优目标个体的扰动产生变异个体,通过变异个体与目标个体的交叉产生试验个体,提高了最优目标个体信息共享,并结合模拟退火算法给出了两种混合求解策略。仿真试验表明了所得算法的可行性和高效性。     

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 hybrid DE–random search approach for unit commitment problem

Differential evolution (DE) is a population-based stochastic search algorithm, whose simple yet powerful and straightforward features make it very attractive for numerical optimization. DE uses a rather greedy and less stochastic approach to problem-solving than other evolutionary algorithms. DE combines simple arithmetic operators with the classical operators of recombination, mutation and selection to evolve from a randomly generated starting population to a final solution. Although global exploration ability of DE algorithm is adequate, its local exploitation ability is feeble and convergence velocity is too low and it suffers from the problem of untime convergence for multimodal objective function, in which search process may be trapped in local optima and it loses its diversity. Also, it suffers from the stagnation problem, where the search process may infrequently stop proceeding toward the global optimum even though the population has not converged to a local optimum or any other point. To improve the exploitation ability and global performance of DE algorithm, a novel and hybrid version of DE algorithm is presented in the proposed research. This research paper presents a hybrid version of DE algorithm combined with random search for the solution of single-area unit commitment problem. The hybrid DE–random search algorithm is tested with IEEE benchmark systems consisting of 4, 10, 20 and 40 generating units. The effectiveness of proposed hybrid algorithm is compared with other well-known evolutionary, heuristics and meta-heuristics search algorithms, and by experimental analysis, it has been found that proposed algorithm yields global results for the solution of unit commitment problem.

     

一种求解多模态复杂问题的混合和声差分算法

针对多模态复杂优化问题,提出了一种基于和声搜索和差分进化的混合优化算法:HHSDE算法。在不同的进化阶段,HHSDE算法依据累积加权更新成功率来自适应地选择和声算法或差分算法作为更新下一代种群的方式,并改进了差分算法的变异策略来平衡差分算法的全局与局部搜索能力。通过对10个多模态Benchmark函数进行测试,利用Wilcoxon秩和检验对不同算法的计算结果进行比较,结果表明HHSDE算法具有收敛速度快,求解精度高,稳定性好等优势。     

差分进化混合粒子群算法求解项目调度问题*

针对求解资源受限项目调度问题（RCPSP）,提出了基于差分进化（DE）的混合粒子群算法（PSODE）。通过在PSO种群和DE种群之间建立一种信息交流机制,使信息能够在两个种群中传递,以避免个体因错误的信息判断而陷入局部最优点。采用标准测试函数和具体算例进行检验,结果表明PSODE算法可以较好地解决RCPS问题。     

改进自适应微分进化算法求解全局优化问题

针对微分进化(DE: differential evolution)算法在进化后期收敛速度慢,收敛精度低,易陷入局部最优解等缺点。本文通过改进DE的变异方程,并引入一种新的控制参数自适应策略,提出了一种改进自适应微分进化(IADE: improved adaptive differential evolution)算法。进化过程中IADE将根据个体适应值与父代平均适应值之间的关系动态地调整控制参数。同时,采用10个常用于优化算法比较的标准函数对IADE和其它改进DE算法进行对比试验,实验结果表明IADE算法不仅能够显著地提高收敛速度和收敛精度,而且具有非常好的鲁棒性,从而使得该算法能够满足过程优化的实时性、准确性以及稳定性要求。     

自适应调整控制参数的差异演化算法

控制参数选取是包括差异演化在内的演化算法设计时所面临的一个重要问题,对算法的性能有着重大影响.针对差异演化算法参数选取问题,提出一种利用个体适应度作为参数调整决策依据,并结合一定的调整概率对F和CR进行自适应调整的方法,解决了手工设置控制参数的不便.同时利用交叉操作生成双子代个体与父代个体竞争形成新一代种群,加快了算法的收敛.对标准测试函数的仿真实验结果表明,该算法无论在最优解质量和收敛速度上都优于相关算法,尤其对于高维函数而言.     

基于简化群优化算法和协方差矩阵学习的差分进化算法

把SSO算法的交叉策略、协方差矩阵学习策略与传统的DE算法结合,提出一个新的DE算法的变种,我们把它称作SCDE算法。正如我们所知,DE算法的变异策略在DE算法中占据了非常重要的位置,然而,传统的DE算法的变异策略都是用相对位置来产生候选解,本文尝试利用个体历史最优解来诱导变异产生候选解,这将大大提高种群跳出局部最优的能力。此外,将算法的变异和交叉操作放在由种群的协方差矩阵的所有特征向量组成的坐标系中执行,这将使算法的交叉和变异操作具有旋转不变性。实验结果表明,本文提出的新的交叉和变异策略可以大大提高DE算法在CEC 2013中28个测试函数的全局寻优能力。     

一种具有混合编码的二进制差分演化算法

差分演化(DE)是Storn和Price于1997年提出的一种基于个体差异重组思想的演化算法,非常适用于求解连续域上的最优化问题.首先引入"差异算子"等概念,给出DE的一种简洁算法描述,并分析了它所具有的特性.然后,为了使DE能够求解离散域上的最优化问题,基于数学变换思想引入"辅助搜索空间"和"个体混合编码"等概念,通过定义一个特殊的满射变换,在辅助搜索空间的作用下将连续域上的高效差分演化搜索变换为离散域上的同步演化搜索,由此提出了第1个二进制差分演化算法:具有混合编码的二进制差分演化算法(HBDE).接着,给出了HBDE的依概率收敛和完全收敛的定义,并利用离散Markov随机理论证明了HBDE是完全收敛的. HBDE不仅完全具有DE的各种特性和所有优点,而且非常适用于求解离散域上的最优化问题,对随机生成的大规模3-SAT问题实例和典型0/1背包问题实例的数值计算表明:该算法具有很好的全局收敛性和稳定性,其性能远远超过二进制粒子群优化算法和遗传算法.     

A HYBRID METAHEURISTIC FOR THE SINGLE-MACHINE TOTAL WEIGHTED TARDINESS PROBLEM

This article presents a new hybrid algorithm for combinatorial optimization that combines differential evolution (DE) with variable neighborhood search (VNS). DE (a population heuristic for optimization over continuous search spaces) is used as global optimizer for solution evolution guiding the search toward the optimal regions of the search space; VNS (a random local search heuristic based on the systematic change of neighborhood) is used as a local optimizer performing a sequence of local changes on individual DE solutions until a local optimum is found. The effectiveness of a DE-VNS approach is demonstrated on the solution of the single-machine total weighted tardiness scheduling problem. The concepts of Lamarckian and Baldwinian learning are also investigated and discussed. Experiments on known benchmark data sets show that DE-VNS with Lamarckian learning can produce high-quality schedules in a rather short computation time. DE-VNS uses a self-adapted mechanism for tuning the required control parameters, a critical feature rendering it applicable to real-life scheduling problems.     

基于改进量子差分进化的含分布式电源的配电网无功优化

差分进化算法（DE）已被证明为解决无功优化问题的有效方法.随着越来越多的分布式电源并网,对配电网潮流、电压均有一定改变,同时也影响了DE的鲁棒性和性能.本文在研究DE基础上,针对其收敛过早、局部搜索能力较差的缺陷,分析了量子计算思想和人工蜂群算法的优势,提出改进量子差分进化混合算法（IQDE）.通过量子编码思想提高了种群个体的多样性,人工蜂群算法的观察蜂加速进化操作和侦查蜂随机搜索操作分别提高了算法的局部搜索和全局搜索性能.建立以有功网损最小为目标的数学模型,将IQDE算法和DE算法分别用于14节点和30节点标准数据集进行大量仿真实验.实验结果表明,IQDE算法用更少的收敛时间、更小的种群规模便可以获得与DE算法相同甚至更佳的优化效果,并且可以很好的应用于解决难分布式电源的配电网无功优化问题.     

Differential evolution and quantum-inquired differential evolution for evolving Takagi–Sugeno fuzzy models

The differential evolution (DE) is a global optimization algorithm to solve numerical optimization problems. Recently the quantum-inquired differential evolution (QDE) has been proposed for binary optimization. This paper proposes DE/QDE to learn the Takagi–Sugeno (T–S) fuzzy model. DE/QDE can simultaneously optimize the structure and the parameters of the model. Moreover a new encoding scheme is given to allow DE/QDE to be easily performed. The two benchmark problems are used to validate the performance of DE/QDE. Compared to some existing methods, DE/QDE shows the competitive performance in terms of accuracy.