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1.
多目标最优化中的共轭对偶理论   总被引:3,自引:0,他引:3  
引言本文将在一般“非支配解” (Nondominated Solution) 意义下建立多目标最优化共轭对偶理论框架.全文共三部分.首先在§1中提出共轭映照、Λ-凸和次微分等概念,导出它们之间的一些重要关系.然后在§2中利用摄动方法,把原多目标极值问题嵌入到一族摄动问题中去,由摄动后的目标函数的共轭映照来定义原问题的对偶问题,建立并证明多目标最优化共轭对偶理论中的弱对偶定理、强对偶定理和鞍点定理.作为例子,在§3中讨论一类广义凸多目标数学规划问题的共轭对偶性.  相似文献   

2.
本文把拓展熵规划转化为锥最优化问题,再对该锥最优化问题构造一个锥自对偶嵌入模型,证明了锥自对偶嵌入模型的障碍函数满足自协调性,这保证了用某些内点法求解时算法是多项式时间的.这种方法的另一个优点是不需要寻找初始可行解.  相似文献   

3.
针对均衡约束数学规划模型难以满足约束规范及难于求解的问题,基于Mond和Weir提出的标准非线性规划的对偶形式,利用其S稳定性,建立了均衡约束数学规划问题的一类广义Mond-Weir型对偶,从而为求解均衡约束优化问题提供了一种新的方法.在Hanson-Mond广义凸性条件下,利用次线性函数,分别提出了弱对偶性、强对偶性和严格逆对偶性定理,并给出了相应证明.该对偶化方法的推广为研究均衡约束数学规划问题的解提供了理论依据.  相似文献   

4.
多约束非线性整数规划是一类非常重要的问题,非线性背包问题是它的一类特殊而重要的问题.定义在有限整数集上极大化一个可分离非线性函数的多约束最优化问题.这类问题常常用于资源分配、工业生产及计算机网络的最优化模型中,运用一种新的割平面法来求解对偶问题以得到上界,不仅减少了对偶间隙,而且保证了算法的收敛性.利用区域割丢掉某些整数箱子,并把剩下的区域划分为一些整数箱子的并集,以便使拉格朗日松弛问题能有效求解,且使算法在有限步内收敛到最优解.算法把改进的割平面法用于求解对偶问题并与区域分割有效结合解决了多约束非线性背包问题的求解.数值结果表明了改进的割平面方法对对偶搜索更加有效.  相似文献   

5.
具有(F,α,ρ,d)—凸的分式规划问题的最优性条件和对偶性   总被引:1,自引:0,他引:1  
给出了一类非线性分式规划问题的参数形式和非参数形式的最优性条件,在此基础上,构造出了一个参数对偶模型和一个非参数对偶模型,并分别证明了其相应的对偶定理,这些结果是建立在次线性函数和广义凸函数的基础上的.  相似文献   

6.
本文基于消失约束的结构特征,提出消失约束数学规划一个不涉及未知指标集的拉格朗日型对偶,并在合适条件下建立了弱对偶和强对偶定理.另外,也讨论了消失约束数学规划的鞍点最优性判据.最后,我们通过某些例子验证了这些结果的合理性.  相似文献   

7.
一个数学规划问题称为是自身对偶的,如果它可以从它的对偶问题中增加或减去某些约束条件而得到,而且它和它的对偶问题有相同的最优解和相同的最优值.凡是自身对偶的数学规划问题都有这样一些重要性质:它的最优值等于零,它的最优解在约束集合的边界上,等等。因此,自身对偶是一类非常重要的对偶模型,它在数学规划的对偶理论中,占有极其重要的地位。文章[1,2]分别讨论了自身对偶的线性规划问题和二次规划问题。文章[3]推广了文章[1]和[2]的结果,建立了如下一类自身对偶的凸规划问题  相似文献   

8.
针对一类系数为梯形模糊数的两层多随从线性规划问题,利用模糊结构元理论定义了模糊结构元加权序,证明了一类系数为梯形模糊数的两层多随从线性规划问题的最优解等价于两层多随从线性规划问题的最优解.根据线性规划的对偶定理和互补松弛性质,得到了两层多随从线性规划模型的最优化条件.最后,利用两层多随从线性规划模型的最优化条件,设计了求解一类系数为梯形模糊数的两层多随从线性规划问题的算法,并通过算例验证了该方法的可行性和合理性.  相似文献   

9.
本文建立了目标和约束为不对称的群体多目标最优化问题的Lagrange对偶规划,在问题的联合弱有效解意义下,得到群体多目标最优化Lagrange型的弱对偶定理、基本对偶定理、直接对偶定理和逆对偶定理。  相似文献   

10.
稀疏优化模型是目前最优化领域中非常热门的研究前沿课题,在压缩感知、图像处理、机器学习和统计建模等领域都获得了成功的应用.本文以光谱分析技术、数字信号处理和推荐系统等多个应用问题为例,阐述稀疏优化模型的建模过程与核心思想.稀疏优化模型属于组合优化模型,非常难以求解(NP-难).正则化方法是稀疏优化模型的一类常用的求解方法.我们将介绍正则化方法的原理与几类常见的正则化模型,并阐述正则化模型的稳定性理论与多种先进算法.数值实验表明,这些算法都具有快速、高效、稳健等显著优点.稀疏正则化模型将在大数据时代中发挥更显著的计算优势与应用价值.  相似文献   

11.
非凸极小极大问题是近期国际上优化与机器学习、信号处理等交叉领域的一个重要研究前沿和热点,包括对抗学习、强化学习、分布式非凸优化等前沿研究方向的一些关键科学问题都归结为该类问题。国际上凸-凹极小极大问题的研究已取得很好的成果,但非凸极小极大问题不同于凸-凹极小极大问题,是有其自身结构的非凸非光滑优化问题,理论研究和求解难度都更具挑战性,一般都是NP-难的。重点介绍非凸极小极大问题的优化算法和复杂度分析方面的最新进展。  相似文献   

12.
锻压机床由于生产效率高和材料利用率高的特点,被广泛应用于各领域.然而,锻压机床发生故障时,其故障种类繁多、故障数据量大,所以对锻压机床故障源的快速、准确诊断较困难.针对该问题,文章提出一种将故障树分析法和混沌粒子群算法相融合的方法,对锻压机床的故障源进行故障诊断.该方法是先通过故障树分析法对锻压机床的故障进行分析从而得到故障模式及其故障概率,然后由得到的故障模式和已知的故障维修经验分析归纳出故障模式的学习样本,再根据得到的故障概率运用混沌粒子群算法的遍历性快速、准确地诊断出锻压机床发生故障的精确位置.文章提出的方法以锻压机床的伺服系统为例进行了故障诊断实验,将该实验结果与遗传算法、粒子群算法进行对比.实验结果表明,文章的算法在锻压机床伺服系统的故障诊断中准确度更高、速度更快.  相似文献   

13.
Convex optimization methods are used for many machine learning models such as support vector machine. However, the requirement of a convex formulation can place limitations on machine learning models. In recent years, a number of machine learning methods not requiring convexity have emerged. In this paper, we study non-convex optimization problems on the Stiefel manifold in which the feasible set consists of a set of rectangular matrices with orthonormal column vectors. We present examples of non-convex optimization problems in machine learning and apply three nonlinear optimization methods for finding a local optimal solution; geometric gradient descent method, augmented Lagrangian method of multipliers, and alternating direction method of multipliers. Although the geometric gradient method is often used to solve non-convex optimization problems on the Stiefel manifold, we show that the alternating direction method of multipliers generally produces higher quality numerical solutions within a reasonable computation time.  相似文献   

14.
During the last years, interest on hybrid metaheuristics has risen considerably in the field of optimization and machine learning. The best results found for many optimization problems in science and industry are obtained by hybrid optimization algorithms. Combinations of optimization tools such as metaheuristics, mathematical programming, constraint programming and machine learning, have provided very efficient optimization algorithms. Four different types of combinations are considered in this paper: (i) Combining metaheuristics with complementary metaheuristics. (ii) Combining metaheuristics with exact methods from mathematical programming approaches which are mostly used in the operations research community. (iii) Combining metaheuristics with constraint programming approaches developed in the artificial intelligence community. (iv) Combining metaheuristics with machine learning and data mining techniques.  相似文献   

15.
We present here a computational study comparing the performance of leading machine learning techniques to that of recently developed graph-based combinatorial optimization algorithms (SNC and KSNC). The surprising result of this study is that SNC and KSNC consistently show the best or close to best performance in terms of their F1-scores, accuracy, and recall. Furthermore, the performance of SNC and KSNC is considerably more robust than that of the other algorithms; the others may perform well on average but tend to vary greatly across data sets. This demonstrates that combinatorial optimization techniques can be competitive as compared to state-of-the-art machine learning techniques. The code developed for SNC and KSNC is publicly available.  相似文献   

16.
A Tutorial on the Cross-Entropy Method   总被引:34,自引:0,他引:34  
The cross-entropy (CE) method is a new generic approach to combinatorial and multi-extremal optimization and rare event simulation. The purpose of this tutorial is to give a gentle introduction to the CE method. We present the CE methodology, the basic algorithm and its modifications, and discuss applications in combinatorial optimization and machine learning.  相似文献   

17.
In this paper, we derive a portfolio optimization model by minimizing upper and lower bounds of loss probability. These bounds are obtained under a nonparametric assumption of underlying return distribution by modifying the so-called generalization error bounds for the support vector machine, which has been developed in the field of statistical learning. Based on the bounds, two fractional programs are derived for constructing portfolios, where the numerator of the ratio in the objective includes the value-at-risk (VaR) or conditional value-at-risk (CVaR) while the denominator is any norm of portfolio vector. Depending on the parameter values in the model, the derived formulations can result in a nonconvex constrained optimization, and an algorithm for dealing with such a case is proposed. Some computational experiments are conducted on real stock market data, demonstrating that the CVaR-based fractional programming model outperforms the empirical probability minimization.  相似文献   

18.
针对汽车涂装车间中的作业优化排序问题,提出一种基于启发式Q学习的优化算法。首先,建立包括满足总装车间生产顺序和最小化喷枪颜色切换次数的多目标整数规划模型。将涂装作业优化排序问题抽象为马尔可夫过程,建立基于启发式Q算法的求解方法。通过具体案例,对比分析了启发式Q学习、Q学习、遗传算法三种方案的优劣。结果表明:在大规模问题域中,启发式Q学习算法具有寻优效率更高、效果更好的优势。本研究为机器学习算法在汽车涂装作业优化排序问题的应用提出了新思路。  相似文献   

19.
The learnable evolution model is a stochastic optimization method which employs machine learning to guide the optimization process. LEM3, its newest implementation, combines its machine learning mode with other search operators. The presented research concerns its application within a multi-agent system for autonomous control of container on-carriage operations. Specifically, LEM3 is used by transport management agents that act on behalf of the trucks of a forwarding agency for the planning of individual transport schedules.  相似文献   

20.
Support vector machine (SVM) is a popular tool for machine learning task. It has been successfully applied in many fields, but the parameter optimization for SVM is an ongoing research issue. In this paper, to tune the parameters of SVM, one form of inter-cluster distance in the feature space is calculated for all the SVM classifiers of multi-class problems. Inter-cluster distance in the feature space shows the degree the classes are separated. A larger inter-cluster distance value implies a pair of more separated classes. For each classifier, the optimal kernel parameter which results in the largest inter-cluster distance is found. Then, a new continuous search interval of kernel parameter which covers the optimal kernel parameter of each class pair is determined. Self-adaptive differential evolution algorithm is used to search the optimal parameter combination in the continuous intervals of kernel parameter and penalty parameter. At last, the proposed method is applied to several real word datasets as well as fault diagnosis for rolling element bearings. The results show that it is both effective and computationally efficient for parameter optimization of multi-class SVM.  相似文献   

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