Evolution Performance of Symbolic Radial Basis Function Neural Network by Using Evolutionary Algorithms

Radial Basis Function Neural Network(RBFNN)ensembles have long suffered from non-efficient training,where incorrect parameter settings can be computationally disastrous.This paper examines different evolutionary algorithms for training the Symbolic Radial Basis Function Neural Network(SRBFNN)through the behavior’s integration of satisfiability programming.Inspired by evolutionary algorithms,which can iteratively find the nearoptimal solution,different Evolutionary Algorithms(EAs)were designed to optimize the producer output weight of the SRBFNN that corresponds to the embedded logic programming 2Satisfiability representation(SRBFNN-2SAT).The SRBFNN’s objective function that corresponds to Satisfiability logic programming can be minimized by different algorithms,including Genetic Algorithm(GA),Evolution Strategy Algorithm(ES),Differential Evolution Algorithm(DE),and Evolutionary Programming Algorithm(EP).Each of these methods is presented in the steps in the flowchart form which can be used for its straightforward implementation in any programming language.With the use of SRBFNN-2SAT,a training method based on these algorithms has been presented,then training has been compared among algorithms,which were applied in Microsoft Visual C++software using multiple metrics of performance,including Mean Absolute Relative Error(MARE),Root Mean Square Error(RMSE),Mean Absolute Percentage Error(MAPE),Mean Bias Error(MBE),Systematic Error(SD),Schwarz Bayesian Criterion(SBC),and Central Process Unit time(CPU time).Based on the results,the EP algorithm achieved a higher training rate and simple structure compared with the rest of the algorithms.It has been confirmed that the EP algorithm is quite effective in training and obtaining the best output weight,accompanied by the slightest iteration error,which minimizes the objective function of SRBFNN-2SAT.

Integrating Variable Reduction Strategy With Evolutionary Algorithms for Solving Nonlinear Equations Systems

Nonlinear equations systems(NESs)are widely used in real-world problems and they are difficult to solve due to their nonlinearity and multiple roots.Evolutionary algorithms(EAs)are one of the methods for solving NESs,given their global search capabilities and ability to locate multiple roots of a NES simultaneously within one run.Currently,the majority of research on using EAs to solve NESs focuses on transformation techniques and improving the performance of the used EAs.By contrast,problem domain knowledge of NESs is investigated in this study,where we propose the incorporation of a variable reduction strategy(VRS)into EAs to solve NESs.The VRS makes full use of the systems of expressing a NES and uses some variables(i.e.,core variable)to represent other variables(i.e.,reduced variables)through variable relationships that exist in the equation systems.It enables the reduction of partial variables and equations and shrinks the decision space,thereby reducing the complexity of the problem and improving the search efficiency of the EAs.To test the effectiveness of VRS in dealing with NESs,this paper mainly integrates the VRS into two existing state-of-the-art EA methods(i.e.,MONES and DR-JADE)according to the integration framework of the VRS and EA,respectively.Experimental results show that,with the assistance of the VRS,the EA methods can produce better results than the original methods and other compared methods.Furthermore,extensive experiments regarding the influence of different reduction schemes and EAs substantiate that a better EA for solving a NES with more reduced variables tends to provide better performance.

A new evolutionary algorithm for constrained optimization problems

To solve single-objective constrained optimization problems,a new population-based evolutionary algorithm with elite strategy(PEAES) is proposed with the concept of single and multi-objective optimization.Constrained functions are combined to be an objective function.During the evolutionary process,the current optimal solution is found and treated as the reference point to divide the population into three sub-populations:one feasible and two infeasible ones.Different evolutionary operations of single or multi-objective optimization are respectively performed in each sub-population with elite strategy.Thirteen famous benchmark functions are selected to evaluate the performance of PEAES in comparison of other three optimization methods.The results show the proposed method is valid in efficiency,precision and probability for solving single-objective constrained optimization problems.

Practical Meta-Reinforcement Learning of Evolutionary Strategy with Quantum Neural Networks for Stock Trading

We show the practicality of two existing meta-learning algorithms Model- Agnostic Meta-Learning and Fast Context Adaptation Via Meta-learning using an evolutionary strategy for parameter optimization, as well as propose two novel quantum adaptations of those algorithms using continuous quantum neural networks, for learning to trade portfolios of stocks on the stock market. The goal of meta-learning is to train a model on a variety of tasks, such that it can solve new learning tasks using only a small number of training samples. In our classical approach, we trained our meta-learning models on a variety of portfolios that contained 5 randomly sampled Consumer Cyclical stocks from a pool of 60. In our quantum approach, we trained our quantum meta-learning models on a simulated quantum computer with portfolios containing 2 randomly sampled Consumer Cyclical stocks. Our findings suggest that both classical models could learn a new portfolio with 0.01% of the number of training samples to learn the original portfolios and can achieve a comparable performance within 0.1% Return on Investment of the Buy and Hold strategy. We also show that our much smaller quantum meta-learned models with only 60 model parameters and 25 training epochs have a similar learning pattern to our much larger classical meta-learned models that have over 250,000 model parameters and 2500 training epochs. Given these findings, we also discuss the benefits of scaling up our experiments from a simulated quantum computer to a real quantum computer. To the best of our knowledge, we are the first to apply the ideas of both classical meta-learning as well as quantum meta-learning to enhance stock trading.

New Solution Generation Strategy to Improve Brain Storm Optimization Algorithm for Classification

As a new intelligent optimization method,brain storm optimization(BSO)algorithm has been widely concerned for its advantages in solving classical optimization problems.Recently,an evolutionary classification optimization model based on BSO algorithm has been proposed,which proves its effectiveness in solving the classification problem.However,BSO algorithm also has defects.For example,large-scale datasets make the structure of the model complex,which affects its classification performance.In addition,in the process of optimization,the information of the dominant solution cannot be well preserved in BSO,which leads to its limitations in classification performance.Moreover,its generation strategy is inefficient in solving a variety of complex practical problems.Therefore,we briefly introduce the optimization model structure by feature selection.Besides,this paper retains the brainstorming process of BSO algorithm,and embeds the new generation strategy into BSO algorithm.Through the three generation methods of global optimal,local optimal and nearest neighbor,we can better retain the information of the dominant solution and improve the search efficiency.To verify the performance of the proposed generation strategy in solving the classification problem,twelve datasets are used in experiment.Experimental results show that the new generation strategy can improve the performance of BSO algorithm in solving classification problems.

三阶段自适应采样和增量克里金辅助的昂贵高维优化算法

代理辅助进化算法已广泛应用于求解代价高昂的多目标优化问题,但大多数由于代理模型的局限性而仅限于解决决策变量低维的问题。为了解决高维的昂贵多目标优化问题,提出了一种基于三阶段自适应采样策略的改进增量克里金辅助的进化算法。该算法使用改进的增量克里金模型来近似每个目标函数,此模型的超参数根据预测的不确定性进行自适应更新,降低计算复杂度的同时保证模型在高维上的准确性;此外,在模型管理方面提出一种三阶段自适应采样的策略,将采样过程分为不同的优化阶段以更有针对性的选择个体,能够首先保证收敛性,提高算法的收敛速度。为了验证算法的有效性,在包含各种特征的两组测试问题DTLZ(deb-thiele-laumanns-zitzler)、MaF(many-objective function)和路径规划实际工程问题上与最新的同类型算法进行实验对比,结果表明该算法在解决决策变量高维的昂贵多目标优化问题上具有较强的竞争力。

混合整数优化问题的差分进化算法研究

为求解混合整数优化问题,提出了混合整数差分进化算法(Mixed Integer Differential Evolution,MIDE)。该算法结合整数变量的特点,为整数类型变量设计了专用的变异算子,使整数变量可以在差分进化算法中直接进化;为了维持种群多样性,采用了灾变策略;采用双编码方式,使整数变量与连续变量并行进化,进而提出了混合整数差分进化算法。通过与其它混合整数优化算法的比较,证明该算法具有较好的收敛速度、全局收敛性及算法稳定性等优点。

基于成本感知的边缘服务器部署方法

针对移动边缘计算(mobile edge computing,MEC)中边缘服务器(edge server,ES)供应商的成本预算问题,建立一种以最小化时延和部署成本为目标的数学模型。通过归一化方法将其转化为单目标优化问题,提出一种基于交叉算法的鲸鱼优化算法的边缘服务器部署方法;采用精英反向学习策略构造新种群,提高种群的多样性和全局收敛速度;采用改进的非线性收敛因子平衡算法的整体开发能力和局部探索能力;利用纵横交叉策略提高算法跳出局部最优的能力。使用上海电信基站的真实数据集进行仿真,其结果表明,与其它4种算法相比,该算法在时延和部署成本方面的表现均优于其它算法,系统成本下降了42.1%。

基于Bayesian学习的适应性优化协商模型

在复杂的自动协商环境中,设计能够处理不完全信息和动态情形的协商agent有效学习机制正成为具有挑战性的议题.提出了一种基于Bayesian学习的时间依赖的双边多议题协商优化模型(BLMSEAN).通过只观察对手的历史报价,将Bayesian学习和基于混合策略的演化算法相结合,所提模型使得协商agent能够对于对手协商参数的概率分布有更精确的估计(如期限、保留报价和议题权重等),能够适应性地调整让步策略使协商双方都受益,提高了协商的成功率和效用.通过实验可以显示所提的模型学习对手私有信息和适应性调整让步策略的有效性.

ES-SOFM混合模型及其在水环境评价中的应用

提出一种基于进化策略 (EvolutionaryStrategy ,ES)和自组织特征映射 (Self OrganizingFeatureMap ,SOFM)神经网络的混合模型进行水环境评价的新方法 .把SOFM网络嵌入到ES中 ,根据SOFM网络的运行状态构造ES的适应性函数 ,利用ES的强搜索能力克服SOFM网络对初始权向量和样本输入次序敏感的弱点 .在水环境评价中的应用效果表明 。

基于竞争式协同进化的混合变量粒子群优化算法

现实工业生产应用中存在大量的混合变量优化问题,这类问题的决策变量既包含连续变量,又包含离散变量。由于决策变量为混合类型,导致问题的决策空间变得不规则,采用已有的方法很难进行有效求解。引入协同进化策略,提出一种基于竞争式协同进化的混合变量粒子群优化算法(competitive coevolution based PSO,CCPSO)。设计基于容忍度的搜索方向调整机制来判断粒子的进化状态,从而自适应地调整粒子的搜索方向,避免陷入局部最优,平衡了种群的收敛性和多样性;引入基于竞争式协同进化的学习对象生成机制,在检测到粒子进化停滞时为每个粒子生成新的学习对象,从而推动粒子的进一步搜索,提高了种群的多样性;采用基于竞争学习的预测策略为粒子选择合适的学习对象,充分利用了新旧学习对象的学习潜力,保证了算法的收敛速度。实验结果表明:相比其他主流的混合变量优化算法,CCPSO可以获得更优的结果。

一种新的基于预测的动态多目标进化算法

动态多目标优化问题(DMOPs)是指目标函数随时间变化的一类问题,算法求解的目标是持续跟踪移动的Pareto最优解集或Pareto最优前沿。基于预测的方法受到格外的关注,然而这些方法多使用历史环境信息进行预测,考虑到使用历史信息预测会存在预测不准确的问题,加强新环境信息的挖掘和利用,提出了一种新的基于预测的动态多目标进化算法,该算法主要包括两个核心部分,分别记为响应机制和加速机制。响应机制在环境变化后重新初始化群体,一部分的个体由预测策略产生,以生成靠近下一环境Pareto最优解集的个体来提高算法的寻优能力,剩余部分个体采用局部搜索策略生成以增加种群多样性。加速机制用于静态优化过程以提高算法收敛速度。最后,将动态多目标进化算法与其他3种先进的动态多目标优化算法在具有不同动态特征的一系列测试函数上进行实验对比,结果表明,动态多目标进化算法相比其他3个算法在求解动态多目标优化问题中更具有优势。

自适应模型选用辅助的多种群进化算法

代理模型辅助的进化算法是求解目标函数评价昂贵优化问题的有效方法.在这类算法中,算法的搜索策略和填充采样策略是在有限评价次数下获得优化问题较好解的重要因素.为此,本文使用多种群搜索策略用于平衡种群搜索的多样性和收敛性,同时基于个体和训练样本之间目标函数值的距离自适应选择模型进行个体的目标函数值估计,以提高估值的准确度.为了验证算法的有效性,在CEC2005测试函数以及扩频雷达Polly编码优化设计问题上进行测试,并和现有求解昂贵优化问题的算法进行了结果对比.实验结果表明本文提出的算法在目标函数评价次数有限的情况下能够获得昂贵优化问题的较好解.

基于改进双档案多目标进化算法的柔性作业车间批量流混排调度

针对柔性作业车间批量流调度问题,基于快速换模技术,考虑可变子批划分柔性、子批混排加工柔性、自动换模柔性和物料运输柔性,建立以最小化完工时间和加工子批总数为目标的混排调度优化模型,并提出一种改进双档案多目标进化算法以优化目标函数。基于进化算法框架,设计了基于超体积指标和基于改进帕累托支配的双档案筛选机制,以平衡种群的收敛性和多样性;针对批量流混排调度问题特征,在解码阶段提出正/逆解码和子批拆分左移策略,在邻域探索和全局搜索阶段分别设计子批划分和混排调度的自适应进化算子,以提高算法的全局搜索与局部搜索能力。基于不同规模算例,测试了提出算法与经典多目标算法的性能。实验结果表明,该算法在收敛性与多样性上具有明显优势。

基于适应性均衡模型的CMAES约束优化算法

提出一种基于适应性均衡模型的协方差矩阵自适应进化策略(ATM-CMAES)用于求解约束优化问题。ATM-CMAES中的CMAES利用当前代最优子群与上一代分布均值之间的关系更新协方差矩阵来调整种群分布,将协方差矩阵秩1和秩μ2种更新机制相结合,克服了传统进化算法对种群大小的过分依赖;将ATM作为约束处理技术,针对群体不可行、半可行和可行这3种不同情形,采用不同的约束违反度与目标函数值之间的均衡机制来指导群体进化。对13个标准测试函数的实验结果表明:ATM-CMAES具有通用、稳健和高效性能。

基于改进MOEA/D的模糊柔性作业车间调度算法

针对实际生产车间中加工时间的不确定性,将加工时间以模糊数的形式表示,建立以最小化模糊最大完工时间和模糊总材料消耗为优化目标的多目标模糊柔性作业车间调度问题数学模型,提出一种改进基于分解的多目标进化算法(IMOEA/D)进行求解。该算法基于机器和工序两层编码并采用混合的初始化策略提高初始种群的质量,利用插入式贪婪解码策略对机器的选择进行解码,缩短总加工时间;采用基于邻域和外部存档的选择操作结合改进的交叉变异算子进行种群更新,提高搜索效率;设置邻域搜索的启动条件,并基于4种邻域动作进行变邻域搜索,提高局部搜索能力;通过田口实验设计方法研究关键参数对算法性能的影响,同时得到算法的最优性能参数。在Xu 1~Xu 2、Lei 1~Lei 4和Remanu 1~Remanu 4测试集上将所提算法与其他算法进行对比,结果表明,IMOEA/D算法的解集数量和目标函数值均较优,在Lei 2算例获得的解集个数为对比算法的2倍以上。

Parallel Optimization of Program Instructions Using Genetic Algorithms

This paper describes an efficient solution to parallelize softwareprogram instructions, regardless of the programming language in which theyare written. We solve the problem of the optimal distribution of a set ofinstructions on available processors. We propose a genetic algorithm to parallelize computations, using evolution to search the solution space. The stagesof our proposed genetic algorithm are: The choice of the initial populationand its representation in chromosomes, the crossover, and the mutation operations customized to the problem being dealt with. In this paper, geneticalgorithms are applied to the entire search space of the parallelization ofthe program instructions problem. This problem is NP-complete, so thereare no polynomial algorithms that can scan the solution space and solve theproblem. The genetic algorithm-based method is general and it is simple andefficient to implement because it can be scaled to a larger or smaller number ofinstructions that must be parallelized. The parallelization technique proposedin this paper was developed in the C# programming language, and our resultsconfirm the effectiveness of our parallelization method. Experimental resultsobtained and presented for different working scenarios confirm the theoreticalresults, and they provide insight on how to improve the exploration of a searchspace that is too large to be searched exhaustively.

Multi-Knapsack Model of Collaborative Portfolio Configurations in Multi-Strategy Oriented

Aiming at constructing the multi-knapsack model of collaborative portfolio configurations in multi-strategy oriented, the hybrid evolutionary algorithm was designed based on greedy method, combining with the organization of the multiple strategical guidance and multi-knapsack model. Furthermore, the organizing resource utility and risk management of portfolio were considered. The experiments were conducted on three main technological markets which contain communication, transportation and industry. The results demonstrated that the proposed model and algorithm were feasible and reliable.

基于IGD^(+)指标的两阶段选择高维多目标进化算法

针对在高维空间下多目标进化算法难以维持种群收敛性和多样性平衡的问题,本文提出一个基于IGD^(+)指标的两阶段选择高维多目标进化算法(MaOEA–ITS).在第1阶段,算法基于IGD^(+)指标选择收敛性良好的精英个体,其所需的参考点通过引入切割平面截距法构建.在第2阶段,MaOEA–ITS使用模糊c均值算法对参考向量进行聚类,聚类后的参考向量引导种群分解策略对剩余个体进行环境选择,从而维持种群的多样性.另外,为了保护能够提高种群多样性的极值解,本文提出一个参考点分布自适应策略.最后,通过仿真实验来验证MaOEA–ITS的有效性和优越性.

基于新评价指标自适应预测的动态多目标优化算法

现实生活中的多目标优化问题(MOP)大多为动态多目标优化问题(DMOP),此类问题的目标函数、约束条件和决策变量都可能随时间的变化而发生改变,这需要算法在环境变化后快速适应新的环境,且在保证Pareto解集多样性的同时快速收敛到新的Pareto前沿。针对此问题,提出一种基于新评价指标自适应预测的动态多目标优化算法(NEI-APDMOA)。首先,在种群非支配排序过程中提出一种优于拥挤度的新评价指标,并分阶段平衡收敛快速性和种群多样性,使种群的收敛过程更加合理;其次,提出一种可判断环境变化强弱的因子,为预测阶段提供有价值信息,并引导种群更好地适应环境变化;最后,根据环境变化因子匹配3种更加合理的预测策略,使种群快速响应环境变化。将NEI-APDMOA与DNSGA-Ⅱ-A(Dynamic Non-dominated Sorting Genetic Algorithm-Ⅱ-A)、DNSGA-Ⅱ-B(Dynamic Non-dominated Sorting Genetic Algorithm-Ⅱ-B)和PPS(Population Prediction Strategy)算法在9个标准动态测试函数上进行对比。实验结果表明,NEI-APDMOA分别在9、4和8个测试函数上取得了最优的平均反世代距离(IGD)值、平均间距(SP)值和平均世代距离(GD)值,可以更快地响应环境变化。