基于多目标优化的控制器设计方法

多目标优化方法对所用的目标函数和约束要进行分析和改进, 为了多个目标的同时实现和分析本文研究了一种新的基于组织型 P 系统的多目标优化算法来设计 PID 控制器. 控制器参数被编码后按照与膜结构相关的规则进化, 组织型 P 系统具有独特的动态膜结构, 整个参数群体被动态膜结构划分成几个子群体计算降低了计算复杂性. 仿真结果表明所提算法收敛快, 解的精度高, 而且在 Pareto 前沿上均匀分布, 所得的控制器具有令人满意的控制性能. 实验结果显示新算法适于研究不同性能指标和调节参数之间的关系, 可以用于设计和评估不同的控制器.     

求解多目标问题的Memetic免疫优化算法

将基于Pareto支配关系的局部下山算子和差分算子引入免疫多目标优化算法之中,提出了一种求解多目标问题的Memetic免疫优化算法(Memetic immune algorithm for multiobjective optimization,简称MIAMO).该算法利用种群中抗体在决策空间上的位置关系设计了两种有效的启发式局部搜索策略,提高了免疫多目标优化算法的求解效率.仿真实验结果表明,MIAMO与其他4种有效的多目标优化算法相比,不仅在求得Pareto最优解集的逼近性、均匀性和宽广性上有明显优势,而且算法的收敛速度与免疫多目标优化算法相比明显加快.     

Convergence Acceleration for Hyperbolic Systems Using Semicirculant Approximations

The iterative solution of systems of equations arising from systems of hyperbolic, time-independent partial differential equations (PDEs) is studied. The PDEs are discretized using a finite volume or finite difference approximation on a structured grid. A convergence acceleration technique where a semicirculant approximation of the spatial difference operator is employed as preconditioner is considered. The spectrum of the preconditioned coefficient matrix is analyzed for a model problem. It is shown that, asymptotically, the time step for the forward Euler method could be chosen as a constant, which is independent of the number of grid points and the artificial viscosity parameter. By linearizing the Euler equations around an approximate solution, a system of linear PDEs with variable coefficients is formed. When utilizing the semicirculant (SC) preconditioner for this problem, which has properties very similar to the full nonlinear equations, numerical experiments show that the favorable convergence properties hold also here. We compare the results for the SC method to those of a multigrid (MG) scheme. The number of iterations and the arithmetic complexities are considered, and it is clear that the SC method is more efficient for the problems studied. Also, the MG scheme is sensitive to the amount of artificial dissipation added, while the SC method is not.     

动态系统控制器的多目标优化设计方法

1　引言在控制系统理论与应用中 ,有两种多目标优化控制的提法 ,其一是将控制系统的传递函数的 l1 范数、H∞ 范数和 H2 范数作为目标函数的多目标优化控制 ,这方面的工作可参考文 [1 ]及所引用文献 ;其二是将控制系统的一些时域性能指标作为优化目标的多目标优化控制 .本文考虑后一种形式的多目标优化控制问题 .众所周知 ,对一个动态系统设计控制器时 ,一般有多个指标需要考虑 .最优控制器的设计可以是将这些指标加相应的权系数作和求解最小问题 .但是 ,这样处理存在两个问题 :对于某些问题 ,采取重要目标加大权往往达不到期望的目的 ;另…     

一种解决多目标优化问题改进的进化规划算法

目前,大多数多目标进化算法采用非优超排序的方法逼近Pareto前沿,此方法存在的一个致命弱点是需要花费大量的时间检验非劣解,效率很低。论文提出了一种新的多目标进化规划算法,将初始群体划分为可替换部分与不可替换部分,并用外部文件存储进化过程中得到的非劣解,大大减少了检验非劣解所需的工作,加快了算法的收敛速度。仿真试验表明,与传统的基于非优超排序的多目标进化规划算法相比,该算法在效率上有很大的改善,并能更好地逼近Pareto前沿。     

On Set-Based Multiobjective Optimization

Assuming that evolutionary multiobjective optimization (EMO) mainly deals with set problems, one can identify three core questions in this area of research: 1) how to formalize what type of Pareto set approximation is sought; 2) how to use this information within an algorithm to efficiently search for a good Pareto set approximation; and 3) how to compare the Pareto set approximations generated by different optimizers with respect to the formalized optimization goal. There is a vast amount of studies addressing these issues from different angles, but so far only a few studies can be found that consider all questions under one roof. This paper is an attempt to summarize recent developments in the EMO field within a unifying theory of set-based multiobjective search. It discusses how preference relations on sets can be formally defined, gives examples for selected user preferences, and proposes a general preference-independent hill climber for multiobjective optimization with theoretical convergence properties. Furthermore, it shows how to use set preference relations for statistical performance assessment and provides corresponding experimental results. The proposed methodology brings together preference articulation, algorithm design, and performance assessment under one framework and thereby opens up a new perspective on EMO.      

基于最大最小适应度函数的多目标粒子群算法

针对多目标优化问题提出了一种基于最大最小适应度函数（F_maximin）的粒子群算法，将此算法简称为IMPSO。它在求解多目标问题的非劣解前沿（Pareto Front）时表现出很好的性能。通过经典测试函数计算表明该算法保证收敛到多目标优化问题的Pareto最优前沿；同时，使用两个性能指标（GD和Diversity）验证了此算法优于其他的多目标粒子群优化算法。     

基于进化算法的多目标优化方法

进化算法在解决多目标优化问题中有其特有的优势.首先对多目标优化问题进行了描述;然后结合研究现状讨论了目前几种主要的基于进化算法的多目标优化方法,以及它们的优缺点;最后给出了多目标进化优化算法的一些应用,以及进化多目标优化算法的未来发展方向.     

A Multiobjective Optimization-Based Evolutionary Algorithm for Constrained Optimization

A considerable number of constrained optimization evolutionary algorithms (COEAs) have been proposed due to increasing interest in solving constrained optimization problems (COPs) by evolutionary algorithms (EAs). In this paper, we first review existing COEAs. Then, a novel EA for constrained optimization is presented. In the process of population evolution, our algorithm is based on multiobjective optimization techniques, i.e., an individual in the parent population may be replaced if it is dominated by a nondominated individual in the offspring population. In addition, three models of a population-based algorithm-generator and an infeasible solution archiving and replacement mechanism are introduced. Furthermore, the simplex crossover is used as a recombination operator to enrich the exploration and exploitation abilities of the approach proposed. The new approach is tested on 13 well-known benchmark functions, and the empirical evidence suggests that it is robust, efficient, and generic when handling linear/nonlinear equality/inequality constraints. Compared with some other state-of-the-art algorithms, our algorithm remarkably outperforms them in terms of the best, mean, and worst objective function values and the standard deviations. It is noteworthy that our algorithm does not require the transformation of equality constraints into inequality constraints     

A Competitive-Cooperative Coevolutionary Paradigm for Dynamic Multiobjective Optimization

In addition to the need for satisfying several competing objectives, many real-world applications are also dynamic and require the optimization algorithm to track the changing optimum over time. This paper proposes a new coevolutionary paradigm that hybridizes competitive and cooperative mechanisms observed in nature to solve multiobjective optimization problems and to track the Pareto front in a dynamic environment. The main idea of competitive-cooperative coevolution is to allow the decomposition process of the optimization problem to adapt and emerge rather than being hand designed and fixed at the start of the evolutionary optimization process. In particular, each species subpopulation will compete to represent a particular subcomponent of the multiobjective problem, while the eventual winners will cooperate to evolve for better solutions. Through such an iterative process of competition and cooperation, the various subcomponents are optimized by different species subpopulations based on the optimization requirements of that particular time instant, enabling the coevolutionary algorithm to handle both the static and dynamic multiobjective problems. The effectiveness of the competitive-cooperation coevolutionary algorithm (COEA) in static environments is validated against various multiobjective evolutionary algorithms upon different benchmark problems characterized by various difficulties in local optimality, discontinuity, nonconvexity, and high-dimensionality. In addition, extensive studies are also conducted to examine the capability of dynamic COEA (dCOEA) in tracking the Pareto front as it changes with time in dynamic environments.      

A Jumping Gene Paradigm for Evolutionary Multiobjective Optimization

A new evolutionary computing algorithm on the basis of the ldquojumping genesrdquo (JG) phenomenon is proposed in this paper. It emulates the gene transposition in the genome that was discovered by Nobel Laureate, Barbara McClintock, in her work on the corn plants. The principle of JGs that is adopted for evolutionary computing is outlined. The procedures for executing the computational optimization are provided. A large number of constrained and unconstrained test functions have been utilized to verify this new scheme. Its performances on convergence and diversity have been statistically examined and comparisons with other evolutionary algorithms are carried out. It has been discovered that this new scheme is robust and able to provide outcomes quickly and accurately. A stringent measure of binary-indicator is also applied for algorithm classification. The outcome from this test indicates that the JG paradigm is a very competitive scheme for multiobjective optimization and also a compatible evolutionary computing scheme when speed in convergence, diversity, and accuracy are simultaneously required.     

改进的和声搜索算法求解多目标优化问题

针对和声搜索算法在求解多目标问题时效率不高、易陷入局部最优、在算法后期收敛精度不够等不足.提出一种改进的多目标和声搜索算法,其思想是通过引入自适应操作,加强算法的全局搜索能力,增加解的多样性;同时对解集根据Pareto最优解进行非支配排序,提高算法效率,增加算法在后期的收敛精度.在数值仿真实验中选取4个测试函数进行实验...     

A Tabu-Based Exploratory Evolutionary Algorithm for Multiobjective Optimization

This paper presents an exploratorymultiobjective evolutionary algorithm (EMOEA)that integrates the features of tabu search andevolutionary algorithm for multiobjective (MO)optimization. The method incorporates the taburestriction in individual examination andpreservation in order to maintain the searchdiversity in evolutionary MO optimization,which subsequently helps to prevent the searchfrom trapping in local optima as well as topromote the evolution towards the globaltrade-offs concurrently. In addition, a newlateral interference is presented in the paperto distribute nondominated individuals alongthe discovered Pareto-front uniformly. Unlikemany niching or sharing methods, the lateralinterference can be performed without the needof parameter settings and can be flexiblyapplied in either the parameter or objectivedomain. The features of the proposed algorithmare examined based upon three benchmarkproblems. Experimental results show that EMOEAperforms well in searching and distributingnondominated solutions along the trade-offsuniformly, and offers a competitive behavior toescape from local optima in a noisyenvironment.     

进化多目标优化设计满意解的模糊决策

文章提出了一种进化多目标优化满意解的模糊决策方法。首先,根据各个子目标满意度对所有pareto最优解的性能做出模糊评价,并在此基础上将整个pareto解集划分为若干个具有不同性能特征的类;然后根据决策者对目标的模糊偏好,从相应的类中选择最有代表性的个体作为最终的满意解。最后以两杆桁架多目标优化问题为例,说明了该方法的应用。     

Generalized Equivalence Set Method for Solving Multiobjective Optimization Problems

Journal of Computer and Systems Sciences International - Various aspects of solving multiobjective discrete optimization problems are considered. Advantages of the equivalence set method are shown...     

多目标原油选择与混合优化方法

为保证原料的稳定供应,炼厂经常需要寻找相似原油替代库存量少的原油.以混合原油与目标原油质量偏差最小以及混合原料成本最低为目标,构建了一个多目标原油选择与混合优化模型.模型为混合整数非线性规划模型,可以将寻找替代原油转化为原油选择与混合优化问题.在原始多目标布谷鸟搜索(MOCS)算法基础上,对编码以及Lévy飞行进行了改进,结合非支配排序方法提出了一种改进的多目标布谷鸟搜索(IMOCS)算法.利用IMOCS算法求解模型,可同时确定原油的选择和混合比例,且一次计算可得到一组Pareto最优解.通过仿真,与非支配排序遗传算法(NSGA-Ⅱ)进行对比,验证算法的寻优效果.计算得到的混合方案可为炼厂寻找替代原油提供参考.     

一种新的求解约束多目标优化问题的遗传算法

由于采用罚函数法将有约束多目标优化问题转化为无约束多目标优化问题会使求解不合理,因此,文章首先在无约束Pareto排序遗传算法的基础上,提出了一个简单、实用的能分别考虑目标函数和约束函数,而又可以避免采用罚函数的全新排序方法。接着,针对小生境技术在遗传后期依旧会出现遗传漂移现象和共享半径不易确定等缺陷,提出了一种易于实现的超量惩罚策略来替代小生境技术,用以改进种群的多样性。此外,还采用了Pareto解集过滤器、邻域变异和群体重组等策略对算法的寻优能力进行改进,并最终形成了一种求解有约束多目标优化问题的Pareto遗传算法(CMOPGA),还给出了具体的算法流程图。最后采用两个数值算例对算法的求解性能进行了测试。数值试验表明,采用CMOPGA可方便地求得问题的Pareto前沿,并能使求得的Pareto最优解集具有可靠、均布、多样等特点。     

解约束最优化问题的一个新的多目标进化算法

把约束函数作为目标函数,将约束优化问题转化为多目标规划问题。对这个多目标规划,根据带权极小极大策略构造了一个同进化代数有关的变适应值函数。利用广义球面坐标变换和均匀设计法来选择权重,使得由此权重确定的适应值函数能使种群中的容许解逐渐增加并且保持其多样性。用均匀设计法构造的带有自适应性的变异算子增强了算法的局部搜索能力。该方法能有效处理约束,特别是紧约束。计算机仿真显示了该方法是有效的。     

多目标蚁群优化研究综述

多目标蚁群优化是一类重要的多目标进化算法,它在解决多目标优化问题,尤其是多目标组合优化方面,具有优异的性能。首先,通过总结多目标蚁群优化的研究成果,将多目标蚁群优化分为基于帕累托的方法、基于指标函数的方法和目标分解法3类,并阐述了每类方法的特点和代表性算法;然后,展现了多目标蚁群优化在实际问题中的广泛应用;最后,探讨了目前多目标蚁群优化存在的问题。     

Constraint Handling in Multiobjective Evolutionary Optimization

This paper proposes a constraint handling technique for multiobjective evolutionary algorithms based on an adaptive penalty function and a distance measure. These two functions vary dependent upon the objective function value and the sum of constraint violations of an individual. Through this design, the objective space is modified to account for the performance and constraint violation of each individual. The modified objective functions are used in the nondominance sorting to facilitate the search of optimal solutions not only in the feasible space but also in the infeasible regions. The search in the infeasible space is designed to exploit those individuals with better objective values and lower constraint violations. The number of feasible individuals in the population is used to guide the search process either toward finding more feasible solutions or favor in search for optimal solutions. The proposed method is simple to implement and does not need any parameter tuning. The constraint handling technique is tested on several constrained multiobjective optimization problems and has shown superior results compared to some chosen state-of-the-art designs.