Pareto solution

An Interval Algorithm For Solving Pareto Solution Set of Multiobjective Optimization Problems

求凸多目标优化有效解集的区间算法

Discussion on the Application of a Pareto Solution to DEA

有关Pareto解在DEA中的应用的探讨

And the best compromise solution is selected from Pareto solution set with multiple attribute decision making method .

利用基于直觉模糊集的多重属性决策方法，从Pareto解集中选取最佳的折衷解。

Traditional optimization techniques can only find a Pareto solution , but with the evolutionary algorithm can find out more Pareto non-inferior solutions .

传统优化技术一般每次只能得到Pareto解集中的一个，而用进化算法求解，可以得到更多的Pareto非劣解。

Based on genetic algorithm and variable neighborhood search , a genetic-variable neighborhood search algorithm is developed to get Pareto solution set of the model .

设计了遗传-变邻域搜索算法，利用产生式方法求解模型的Pareto解集。

This paper is concerned with the Pareto solution set of multiobjective optimization problem with unconstrains , in which the objective functions are convex functions .

主要讨论了求解无约束多目标优化问题Pareto最优解集的区间算法，该问题的目标函数是C1连续的凸函数。

Established a mathematical model of the problem based on the external tractors separated scheduling mode , and computed solutions with QEA for solving Pareto solution .

在对外集卡分离式调度模式的基础上，建立了该问题的数学模型，设计了一种基于QEA求解Pareto解的运算方案。

Inspired with the defined distance between current and ideal solution , the ant colony algorithm is well suited for searching and finding the Pareto solution in reasonable solution set .

通过定义多目标解与理想解的相对距离为蚁群算法的启发函数，激励蚁群搜索可行解空间并发现最优解集；

On the basis of the criterion of the decision maker , a final solution can be got by analysis of the efficient solution and the value of functions at one pareto solution .

该方法可以保证每一步得到的解均为有效极点解，且根据决策者的偏好不断得到改进，直至最终得到满意的最终解。

Examples were given to prove that these modified methods could promote the genetic algorithm to find better global optimum quickly and effectively , and eventually improve the quality of the Pareto solution set . (?)

经过实例检验，这些改进方法能够促进遗传算法快速、有效地找到全局更优解，提高Pareto解集的质量。

In the algorithm , high-quality initial solution is created by four heuristic algorithms ; elitist solution set is set up to store Pareto solution and update it with adaptive niche method .

算法采用四种启发式算法生成高质量的初始解，并建立精英解集储存Pareto解，通过自适应小生境方法对精英解集进行维护。

Based on the algorithm for transit efficient path search and computational procedure for integrated network system performance , a genetic-variable neighborhood search algorithm is developed to get Pareto solution set of the proposed model .

在给出公交一体化网络有效路径搜索与网络性能计算的基础上，设计了遗传-变邻域搜索算法求解模型的Pareto解。

The experimental data obtained by the simulation of MATLAB showed this genetic algorithm can solve the optimal Pareto solution aggregate of the ULD region ' multiple inbound tasks freight lot allocation problem .

通过MATLAB编程仿真所得到的实验数据表明这种遗传算法可较好地求解出集装区多ULD入库作业任务货位调度问题的最优Pareto解集。

Investors , venture capitalists and entrepreneurs form double-sided agency relation , these bring on several kinds of asymmetric information and complicate interest conflicts , the optimal Pareto solution cannot be achieved .

其相关的决策主体风险投资者、风险投资家和风险企业家之间形成了双层委托代理关系，由此存在严重的信息非对称性，进而导致他们之间存在复杂的利益冲突，最终使帕累托最优不能实现。

Through analyzing the uncertainty factors of multi-objective optimization problems , it shows that Pareto solution should be generalized to fuzzy multi-objective optimization model , and the model is used to find the satisfactory solution through soft computing .

通过对多目标优化问题不确定性因素的分析，将有效解问题扩展到模糊多目标优化模型软计算满意解求解问题。

The inspection cost transfer model and quality level model under sample inspection mode in series manufacturing were analyzed . The ant colony multi-object optimization method based on Pareto solution evaluation was proposed to realize optimization of inspection planning .

针对常见的串行多工序抽样检验方式，建立了工序间质量水平传递模型和质量检验成本模型，提出基于Pareto解评价的多目标优化蚁群算法；

The grey fuzzy optimal selection model of the Pareto solution is formed by integrating the information in local and holistic , and its correctness is proved by mathematical illation , the corresponding GA is given .

通过整合局部和整体信息，建立了Pareto解的灰色模糊优选模型，并对其正确性进行了数学证明，给出了相应的遗传算法。

As for the characteristic of the layout problem , this paper proposes the solving method based on multi-objective evolutionary algorithm NSGA-II and presents the Pareto solution selection method based on fuzzy objective preference and distributing distance of the allocated objects .

利用多目标进化算法NSGA-Ⅱ进行求解，并给出了基于模糊目标偏好和待布物分布距离支配的Pareto最优解选择方法。

The Pareto solution set of composite barrel is obtained by optimal solving . The optimization examples show that the uniformly distributed Pareto front is obtained by using NSG ⅱ, and the corresponding design solution of composite barrel is improved in stiffness and weight .

优化算例表明，采用NSGA-Ⅱ获得的Pareto前沿面曲线分布均匀，其所对应的复合材料身管设计方案在刚度和重量方面均有改善。

This kind of scheduling strategy can shorten the total execution time , making the layout of the shelves more reasonable . And due to the optimal Pareto solution aggregate with multiple solutions , the operator can select different scheduling scheme according to different job purpose .

这种调度策略缩短了多ULD入库作业任务的总执行时间，使得货架上货物的布局更加合理，并且现场人员可依据不同的工作目的在所求的的Pareto解集中选择不同的调度方案。

The approach adds Pareto solution sets and Niche technology besides traditional operators . It can search the optimum solution sets that distribute uniformly . The approach ensures storage location assignment optimization and offers an optimization decision making scheme for AS / RS. 3 .

该算法除了常规遗传操作以外，设计了Pareto解集过滤器和小生境技术，求得均匀分布的Pareto最优解集，较好地解决了货位分配多目标优化问题，并为AS/RS提供多种动态优化解决方案。

The conditions of choosing a new Pareto solution are that the solution is not dominated by the original solution and the solution from which the original solution was generated , and at the same time , the solution has minimal value with at least one of the two objectives .

选择新的Pareto解的条件是该解既不被原解支配，也不被产生原解的解支配，同时对某个目标改进最大。

The property of Sam-C ~ 2 W model and its relation with traditional DEA models are analyzed , and the relation between the SC ~ 2W-DEA efficiency based on Sam-C ~ 2 W model and the corresponding Pareto solution to multi-objective programming is discussed .

分析了（Sam-C~2W）模型的性质以及它与传统DEA模型之间的关系，探讨了（Sam-C~2W）模型刻画的SC~2W-DEA有效性与相应的多目标规划Pareto解之间的关系。

Several sufficient conditions of Pareto optimum solution of multi objective programming

多目标规划Pareto最优解的几个充分条件

Banker law is one of the effective methods to tectonic Pareto optimal solution sets .

庄家法则是构造Pareto最优解集的高效方法之一。

Moreover , we obtain the connectedness of Pareto efficient solution set .

此外，利用所得的结果，还得出一个多目标最优化问题帕莱托有效解集连通的新结果。

The concepts of local Pareto optimal solution set and local Pareto optimal state set are presented .

提出局部Pareto最优解集与局部Pareto最优态集概念。

Finally , a new result about the connectedness of Pareto efficient solution set is gained .

同时，还给出一个关于Pareto有效解集连通性的新结果。

The k - Major - Optimality of Pareto Efficient Solution for Multiobjective Programming

多目标规划的Pareto有效解的k－较多最优性

By this result , a new and simple method is proposed for solving the Pareto optimal solution of the multi-objective control problems .

最优均衡解方法是求解多目标问题Pareto最优解的新的、简单方法。