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1)  Pareto optimal set
Pareto最优集
2)  Pareto-optimal set
Pareto-最优集
3)  Pareto solution set
Pareto最优解集
1.
This paper is concerned with the Pareto solution set of multiobjective optimization problem with unconstrain, in which the objective functions functions are C1.
主要讨论了无约束多目标优化问题Pareto最优解集的求解方法,其中问题的目标函数是C1连续函数。
4)  Pareto-optimal solution
Pareto最优解
1.
Results indicate that this method can obtain uniformly distributed Pareto-optimal solutions.
结果表明:该算法求得的Pareto最优解分布均匀、收敛速度快、寻优能力强,决策者可根据不同的侧重点在Pareto解集中选择最终的满意解。
2.
The numerical experiments show that this algorithm can find more and wider Pareto-optimal solutions than the original one.
数值实验表明该混合遗传算法能求得问题的数量更多、分布更广的Pareto最优解。
3.
Aim It is desirable to find more Pareto-optimal solutions which scattered uniformly over Pareto-front in solving multiobjective programming.
结论 该方法能够找到问题的分布较均匀的Pareto最优解。
5)  Pareto optimal solution
Pareto最优解
1.
The optimal equilibrium solutions set is a connected convex set consisting of the Pareto optimal solutions in a certain convex condition.
在某种凸性条件下最优均衡解集是Pareto最优解的凸本质连通区域。
2.
This is a multi-objective optimization problem, so a set of Pareto optimal solutions have to be sought.
这是一个多目标优化问题,需要寻求一组Pareto最优解,应用多目标进化算法求解该问题可以得到多种满足条件的PMU配置可行方案。
3.
Thus how to find a sufficient number of uniformly distributed and representative Pareto optimal solutions under the condition of the continuously changing time for the decision maker is very important.
在动态多目标优化中,各目标通常相互冲突,其最优解往往有无穷多个,如何在时间连续发生变化的情况下依然能求出分布均匀且数量多的Pareto最优解供决策者选择十分重要。
6)  Pareto optimum
Pareto最优
1.
To solve the problem of ignored product quality in cost-tolerance model,a multi-objective model of tolerance design was presented,which was based on Taguchi's quality view and the conception of Pareto optimum set.
为解决成本—公差设计模型中忽视产品质量的问题,以新型的田口质量观和Pareto最优解集概念为基础,提出了一种公差设计多目标模型。
2.
The relationship between general equilibrium and the pareto optimum in private ownership economy system is discussed with the method of constructing mathematic model and proved with the method of the first and second welfare theorems of private ownership economy.
用构建数学模型的方法探讨了私有制经济系统中一般均衡和pareto最优的关系,并以私有制经济第一、第二福利定理的形式对其进行了证明。
3.
With the help of the gaming analysis and based on the small-world optimization algorithm,it tries to find a QoS unicast path with the Pareto optimum under the Nash equilibrium on both the network provider utility and the user utility achieved or approached.
设计一种ABC支持型QoS单播路由机制,采用区间形式描述用户QoS需求和边(链路)参数,引入用户满意度和边评价,通过博弈分析,基于小世界优化算法寻找使用户和网络提供方效用达到或接近Nash均衡下Pareto最优的QoS单播路径。
补充资料:Pareto分布


Pareto分布
Pareto destribution

  h比加分布「r恤犯勿山洲的h心阅;naPe功p舰uPe解爬-皿e} 一种连续概率分布(pro恤biljtydis颐bution),其密度为 {二厂二、一二。<二<二. n(x)=之xo\x/ Lo,x簇二。,它依赖于两个参数:x。>0和“>0.在那种“截断”解释中,PaJ吧to分布可看作密度为 l戈p一I ~瓦石万石花石万不了,召,“>”,”<尤<田,的第二种B分布(玫恤~distribution)族的拼=l时的独立分布.对于任何固定的x。,通过变换x=x。/夕,P肚eto分布归结为第一种B分布.在P口n扣。曲线(B汾乃。ncur代‘)系统中,PaJ弋to分布属于“类型VI”和“类型xI”的分布.几化to分布的数学期望对于:>1有限,并等于二x。/(二一l);方差对于二>2有限,并等于:x孟/(,一1)“(二一2):中位数是2’‘’、‘,.Pal℃to分布函数由下列公式来确定: /义二、: 尸之X戈了、,戊>U. \x/自从W.Rlreto(1882)关于收人分配的工作以来,Pareto分布已经广‘泛地应用在各种经济统计问题中.人们有时认为,几reto分布在下列意义下完美地描述了收人超过某一水平后的分布:它必须随着x一的有阶为1/x’的尾巴.
  
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