应急资源调度问题的改进进化规划算法研究

针对应急资源调度问题,建立一种多资源时间-成本调度模型。设计了进化规划算法的全局变异算子和局部变异算子,根据全局变异前后个体适应度值和分量值的变化趋势,实现定向变异。构建了具有惩罚系数的适应度函数,给出了改进的进化规划算法种群进化策略。计算实验表明,改进的进化规划算法具有较强的局部寻优能力,在收敛速度和求解精度方面优于比较的遗传算法、差分进化算法和进化规划算法,解决了标准进化算法的早熟收敛问题。     

一种基于DE算法和NSGA-Ⅱ的多目标混合进化算法

设计了一种新颖的基于差分进化算法和NSGA-Ⅱ的混合进化算法用来解决多目标优化问题。在此算法中,根据算法的搜索情况设计相应的自适应变异算子,以便在突变操作中找到Pareto解。同时,选择操作将基于NSGA-Ⅱ快速非优超排序和拥挤机制将父代与子代的双种群进行截短,确保最优解不会丢失并保证解的多样性。三个经典测试函数的仿真结果表明,文中算法在实现多目标优化问题的两个目标(获得收敛于真实Pareto前沿的解和解沿着前沿均匀扩展)方面表现出良好的综合性能。     

求解高维全局优化问题的改进飞蛾火焰优化算法

针对标准飞蛾火焰优化算法在求解高维全局优化问题时存在收敛速度慢、解精度低和易陷入局部最优等缺点,提出一种改进的飞蛾火焰优化算法(简记为IMFO).该算法首先引入动态惯性权重对飞蛾位置更新方程进行修改以平衡算法的勘探和开采能力.受差分进化算法启发,设计出一种新的随机差分变异策略,以帮助种群跳出局部最优.选取18个高维(100、500和1000维)全局优化问题进行数值测试,结果表明,在相同的适应度函数评价次数下,IMFO在收敛速度和求解精度指标上明显优于基本MFO算法和其他对比算法.     

求解旅行商问题的搜寻者遗传算法

针对简单遗传算法易陷入局部最优及收敛速度慢的不足,提出一种改进遗传算法-基于启发式策略的搜寻者遗传算法.首先将搜寻者优化算法中的模糊思想和近邻策略相结合改进变异算子,增强种群多样性,避免陷入局部最优;然后针对路径优化问题基于启发式策略设计反转算子,使得路径中不存在交叉边,加快收敛速度;最后将改进遗传算法用于求解旅行商问题.结果表明,改进遗传算法的求解精度和求解效率明显优于基本遗传算法.     

基于动态自适应t分布变异的人群搜索算法

针对人群搜索算法在进化后期大量个体聚集局部最优时,易陷入局部最优,搜索精度低的缺陷,提出一种基于t分布变异的人群搜索算法.算法使用动态自适应方式确定变异步长,引入t分布变异算子以融合柯西变异和高斯变异的优点,促进算法在进化早期具备良好的全局探索能力,在进化后期收获较强的局部开发能力,增加种群的多样性;采用边界缓冲墙策略处理越界问题,避免越界个体聚集在边界值上的缺陷.实验结果表明,算法比基本人群搜索算法具有更高的寻优精度和收敛速度,是一种有效的算法.     

基于精英区域学习的多种群自适应的差分进化算法

为了进一步提高差分进化算法的收敛速度、算法精度和稳定性,采用多种群技术来增加算法收敛速度和降低复杂度;利用精英区域学习策略来对算法的全局搜索能力和算法精度进一步提升,引进自适应免疫搜索策略,以实现自适应修正差分算法的变异因子和交叉因子。通过五个测试函数,把本文算法与最新文献中的算法进行对比,表明算法在收敛速度、精度和高维问题寻优能力方面的优越性。     

改进的布谷鸟算法求解物流配送中心选址问题

针对基本布谷鸟算法求解物流配送中心选址问题时存在搜索精度低、易陷入局部最优值的缺陷,提出一种改进的布谷鸟算法.算法采用基于寄生巢适应度值排序的自适应方法改进基本布谷鸟算法的惯性权重,以平衡算法的全局开发能力和局部探索能力;利用NEH领域搜索以提高算法的搜索精度和收敛速度;引入停止阻止策略对全局最优寄生巢位置进行变异避免算法陷入局部最优值、增加种群的多样性.通过实验仿真表明,改进的布谷鸟算法在求解物流配送中心选址问题上要优与基本布谷鸟算法以及其它智群算法,是一种有效的算法.     

混合变异粒子群优化算法及其应用

为改善粒子群优化算法在解决复杂优化问题时收敛质量不高的不足,提出了一种改进的粒子群优化算法,即混合变异粒子群优化算法(HMPSO).HMPSO算法采用了带有随机因子的惯性权重取值更新策略,降低了标准粒子群优化算法中由于粒子飞行速度过大而错过最优解的概率,从而加速了算法的收敛速度.此外,通过混合变异进化环节的引入,缓解了粒子种群在进化过程中的多样性与收敛性这一矛盾,使得算法的全局探索与局部开发得到有效平衡.利用经典的基准测试函数和平面冗余机械臂逆运动学问题的求解来验证提出算法的有效性,试验结果表明:与其他算法相比,HMPSO算法具有更快的收敛速度、更高的收敛精度、更强的收敛稳定性以及更低的计算成本.     

嵌入差分进化算子的混合蜂群算法及其在VRPSDP的应用

针对人工蜂群算法进化速度慢、容易陷入搜索停滞的问题,通过嵌入差分进化算子,提出了一种混合蜂群算法(Hybrid Artificial Bee Colony algorithm, HABC).基本思想是:在迭代中嵌入差分进化算子,充分利用差分算法全局收敛性和鲁棒性强的特点,寻求全局最优蜜源;此外,在标准蜂群算方法基础上进行两点改进:在采蜜蜂阶段搜索策略中加入最优位置引导,提高搜索的效率;对超边界的个体重新进行变异,以增强种群的多样性.将混合算法应用于带同时送取货的车辆路径问题(VRPSDP),计算结果表明了混合算法的有效性.     

基于自适应子种群和动态反向学习的改进鸡群算法

针对鸡群算法(Chicken swarm optimization,CSO)求解复杂高维问题收敛精度低、容易陷入局部极值等问题,提出了一种基于自适应子种群和动态反向学习的改进鸡群(ICSO)算法.根据鸡群算法迭代进化进程,自适应确定公鸡种群规模大小,并据此将母鸡种群和小鸡分成若干个子种群;设计进化停滞判定机制,并引入动态反向学习因子以改进算法个体更新方式,有效保持鸡群样本多样性和算法全局深度搜索能力.典型测试函数仿真实验结果表明,与SFLA算法、PSO等智能优化算法相比,ICSO算法具有更高的收敛精度和更优的复杂函数优化能力.     

Self-adaptive randomized and rank-based differential evolution for multimodal problems

Differential Evolution (DE) is a widely used successful evolutionary algorithm (EA) based on a population of individuals, which is especially well suited to solve problems that have non-linear, multimodal cost functions. However, for a given population, the set of possible new populations is finite and a true subset of the cost function domain. Furthermore, the update formula of DE does not use any information about the fitness of the population. This paper presents a novel extension of DE called Randomized and Rank-based Differential Evolution (R2DE) and its self-adaptive version SAR2DE to improve robustness and global convergence speed on multimodal problems by introducing two multiplicative terms in the DE update formula. The first term is based on a random variate of a Cauchy distribution, which leads to a randomization. The second term is based on ranking of individuals, so that R2DE exploits additional information provided by the population fitness. In extensive experiments conducted with a wide range of complexity settings, we show that the proposed heuristics lead to an overall improvement in robustness and speed of convergence compared to several global optimization techniques, including DE, Opposition based Differential Evolution (ODE), DE with Random Scale Factor (DERSF) and the self-adaptive Cauchy distribution based DE (NSDE).     

Differential Evolution algorithm with Separated Groups for multi-dimensional optimization problems

The classical Differential Evolution (DE) algorithm, one of population-based Evolutionary Computation methods, proved to be a successful approach for relatively simple problems, but does not perform well for difficult multi-dimensional non-convex functions. A number of significant modifications of DE have been proposed in recent years, including very few approaches referring to the idea of distributed Evolutionary Algorithms. The present paper presents a new algorithm to improve optimization performance, namely DE with Separated Groups (DE-SG), which distributes population into small groups, defines rules of exchange of information and individuals between the groups and uses two different strategies to keep balance between exploration and exploitation capabilities. The performance of DE-SG is compared to that of eight algorithms belonging to the class of Evolutionary Strategies (Covariance Matrix Adaptation ES), Particle Swarm Optimization (Comprehensive Learning PSO and Efficient Population Utilization Strategy PSO), Differential Evolution (Distributed DE with explorative-exploitative population families, Self-adaptive DE, DE with global and local neighbours and Grouping Differential Evolution) and multi-algorithms (AMALGAM). The comparison is carried out for a set of 10-, 30- and 50-dimensional rotated test problems of varying difficulty, including 10- and 30-dimensional composition functions from CEC2005. Although slow for simple functions, the proposed DE-SG algorithm achieves a great success rate for more difficult 30- and 50-dimensional problems.     

Fitness based Differential Evolution

Differential Evolution (DE) is a well known and simple population based probabilistic approach for global optimization. It has reportedly outperformed a few Evolutionary Algorithms and other search heuristics like Particle Swarm Optimization when tested over both benchmark and real world problems. But, DE, like other probabilistic optimization algorithms, sometimes exhibits premature convergence and stagnates at suboptimal point. In order to avoid stagnation behavior while maintaining a good convergence speed, a new position update process is introduced, named fitness based position update process in DE. In the proposed strategy, position of the solutions are updated in two phases. In the first phase all the solutions update their positions using the basic DE and in the second phase, all the solutions update their positions based on their fitness. In this way, a better solution participates more times in the position update process. The position update equation is inspired from the Artificial Bee Colony algorithm. The proposed strategy is named as Fitness Based Differential Evolution ( $FBDE$ ). To prove efficiency and efficacy of $FBDE$ , it is tested over 22 benchmark optimization problems. A comparative analysis has also been carried out among proposed FBDE, basic DE, Simulated Annealing Differential Evolution and Scale Factor Local Search Differential Evolution. Further, $FBDE$ is also applied to solve a well known electrical engineering problem called Model Order Reduction problem for Single Input Single Output Systems.     

An efficient Differential Evolution based algorithm for solving multi-objective optimization problems

In the present study, a modified variant of Differential Evolution (DE) algorithm for solving multi-objective optimization problems is presented. The proposed algorithm, named Multi-Objective Differential Evolution Algorithm (MODEA) utilizes the advantages of Opposition-Based Learning for generating an initial population of potential candidates and the concept of random localization in mutation step. Finally, it introduces a new selection mechanism for generating a well distributed Pareto optimal front. The performance of proposed algorithm is investigated on a set of nine bi-objective and five tri-objective benchmark test functions and the results are compared with some recently modified versions of DE for MOPs and some other Multi Objective Evolutionary Algorithms (MOEAs). The empirical analysis of the numerical results shows the efficiency of the proposed algorithm.     

Self Balanced Differential Evolution

Differential Evolution (DE) is a well known and simple population based probabilistic approach for global optimization. It has reportedly outperformed a few Evolutionary Algorithms (EAs) and other search heuristics like the Particle Swarm Optimization (PSO) when tested over both benchmark and real world problems. But, DE, like other probabilistic optimization algorithms, sometimes behave prematurely in convergence. Therefore, in order to avoid stagnation while keeping a good convergence speed for DE, two modifications are proposed: one is the introduction of a new control parameter, Cognitive Learning Factor (CLF) and the other is dynamic setting of scale factor. Both modifications are proposed in mutation process of DE. Cognitive learning is a powerful mechanism that adjust the current position of individuals by a means of some specified knowledge. The proposed strategy, named as Self Balanced Differential Evolution (SBDE), balances the exploration and exploitation capability of the DE. To prove efficiency and efficacy of SBDE, it is tested over 30 benchmark optimization problems and compared the results with the basic DE and advanced variants of DE namely, SFLSDE, OBDE and jDE. Further, a real-world optimization problem, namely, Spread Spectrum Radar Polly phase Code Design, is solved to show the wide applicability of the SBDE.     

A Differential Evolution algorithm to deal with box, linear and quadratic-convex constraints for boundary optimization

We both propose and test an implicit strategy that is based on changing the search space from points to directions, which in combination with the Differential Evolution (DE) algorithm, is easily implemented for solving boundary optimization of a generic continuous function. In particular, we see that the DE method can be efficiently implemented to find solutions on the boundary of a convex and bounded feasible set resulting when the constraints are bounds on the variables, linear inequalities and quadratic convex inequalities. The computational results are performed on different classes of boundary minimization problems. The proposed technique is compared with the Generalized Differential Evolution method.     

基于种群自适应调整的多目标差分进化算法

为提高已有多目标进化算法在求解复杂多目标优化问题上的收敛性和解集分布性,提出一种基于种群自适应调整的多目标差分进化算法。该算法设计一个种群扩增策略,它在决策空间生成一些新个体帮助搜索更优的非支配解;设计了一个种群收缩策略,它依据对非支配解集的贡献程度淘汰较差的个体以减少计算负荷,并预留一些空间给新的带有种群多样性的扰动个体;引入精英学习策略,防止算法陷入局部收敛。通过典型的多目标优化函数对算法进行测试验证,结果表明所提算法相对于其他算法具有明显的优势,其性能优越,能够在保证良好收敛性的同时,使获得的Pareto最优解集具有更均匀的分布性和更广的覆盖范围,尤其适合于高维复杂多目标优化问题的求解。     

Differential evolution using a superior–inferior crossover scheme

Differential evolution (DE) is a new population-based stochastic optimization, which has difficulties in solving large-scale and multimodal optimization problems. The reason is that the population diversity decreases rapidly, which leads to the failure of the clustered individuals to reproduce better individuals. In order to improve the population diversity of DE, this paper aims to present a superior–inferior (SI) crossover scheme based on DE. Specifically, when population diversity degree is small, the SI crossover is performed to improve the search space of population. Otherwise, the superior–superior crossover is used to enhance its exploitation ability. In order to test the effectiveness of our SI scheme, we combine the SI with adaptive differential evolution (JADE), which is a recently developed DE variant for numerical optimization. In addition, the theoretical analysis of SI scheme is provided to show how the population’s diversity can be improved. In order to make the selection of parameters in our scheme more intelligently, a self-adaptive SI crossover scheme is proposed. Finally, comparative comprehensive experiments are given to illustrate the advantages of our proposed method over various DEs on a suite of 24 numerical optimization problems.     

Step-size Adaptation in a Multi-objective Differential Evolution Algorithm

If Differential Evolution (DE) is applied to multi-objective optimization problems, some of its features like automatic problem-specific step-size adaptation gets lost. This can be resolved by modifying the DE equations. Three strategies are proposed and compared with existing algorithms. It is shown, that the proposed strategies deliver a superior convergence and preserve the positive characteristics of DE known from solving mono-objective optimization problems. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Global optimization of higher order moments in portfolio selection

We discuss the global optimization of the higher order moments of a portfolio of financial assets. The proposed model is an extension of the celebrated mean variance model of Markowitz. Asset returns typically exhibit excess kurtosis and are often skewed. Moreover investors would prefer positive skewness and try to reduce kurtosis of their portfolio returns. Therefore the mean variance model (assuming either normally distributed returns or quadratic utility functions) might be too simplifying. The inclusion of higher order moments has therefore been proposed as a possible augmentation of the classical model in order to make it more widely applicable. The resulting problem is non-convex, large scale, and highly relevant in financial optimization. We discuss the solution of the model using two stochastic algorithms. The first algorithm is Differential Evolution (DE). DE is a population based metaheuristic originally designed for continuous optimization problems. New solutions are generated by combining up to four existing solutions plus noise, and acceptance is based on evolutionary principles. The second algorithm is based on the asymptotic behavior of a suitably defined Stochastic Differential Equation (SDE). The SDE consists of three terms. The first term tries to reduce the value of the objective function, the second enforces feasibility of the iterates, while the third adds noise in order to enable the trajectory to climb hills.