检索结果-内蒙古大学图书馆

large-scale linear-programming - GEOMETRY, WORKING BASES AND FACTORIZATIONS

MATHEMATICAL programming 1983年第1期26卷 1-20页

作者： TODD, MJ UNIV CAMBRIDGE DAMTPCAMBRIDGEENGLAND

This paper is concerned with linear programming problems in which many of the constraints are handled implicitly by requiring that the vector of decision variables lie in a polyhedronX. It is shown that the simplex method can be implemented using a working basis whose size is the number of explicit constraints as long as the local structure ofX around the current point is known. Various ways of describing this local structure lead to known implementations whenX is defined by generalized or variable upper bounds or flow conservation constraints. In the general case a decomposition principle can be used to generate this local structure. We also show how to update factorizations of the working basis.

关键词： large-scale linear programming Geometry Compact Bases Matrix Factorizations

来源：评论

学校读者我要写书评

暂无评论

A FUZZY SATISFICING METHOD FOR large-scale linear-programming PROBLEMS WITH BLOCK ANGULAR STRUCTURE

引用

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 1995年第2期81卷 399-409页

作者： SAKAWA, M SAWADA, K INUIGUCHI, M MATSUSHITA ELECT WORKS LTD CTR INFORMAT SYSTKADOMAOSAKA 571JAPAN

In this paper, we focus on large-scale linear programming problems with block angular structure for which the Dantzig-Wolfe decomposition method has been successfully applied. By considering the vague nature of human judgements, we assume that the decision maker may have a fuzzy goal for the objective function and fuzzy constraints for the coupling constraints. Having elicited the corresponding linear membership functions through the interaction with the decision maker, if we adopt the convex fuzzy decision for combining them, it is shown that, under some appropriate conditions, the formulated problem can be reduced to a number of independent linear subproblems and the overall satisficing solution for the decision maker is directly obtained just only solving the subproblems.

关键词： large-scale linear programming BLOCK ANGULAR STRUCTURE FUZZY GOAL FUZZY CONSTRAINTS CONVEX FUZZY DECISION FUZZY SATISFICING METHOD

来源：评论

学校读者我要写书评

暂无评论

Balance constraints reduction of large-scale linear programming problems

引用

Annals of Operations Research 1993年第3期43卷 147-170页

作者： Andrei, N. Barbulescu, M. Research Institute for Informatics Analysis and Mathematical Modeling of Systems Bucharest 71316 8-10 Bdl. Averescu Romania

This paper describes a method and the corresponding algorithms for simplification of large-scale linear programming models. It consists of the elimination of the balance constraints (i.e. constraints with zero RHS term). The idea is to apply some linear transformations to the original problem in order to nullify the balance constraints. These transformations are able to simultaneously eliminate more balance rows. The core of this contribution is the introduction of the reduction matrix and the associated theorems on the equivalent linear programs (original and reduced). The numerical experiments with this method of simplification proved this approach to be beneficial for a large class of LP problems. © 1993 J.C. Baltzer AG, Science Publishers.

关键词： interactive systems for LP large-scale linear programming reduction and simplification

来源：评论

学校读者我要写书评

暂无评论

AN INTERACTIVE FUZZY SATISFICING METHOD FOR large-scale MULTIOBJECTIVE linear-programming PROBLEMS WITH BLOCK ANGULAR STRUCTURE

引用

FUZZY SETS AND SYSTEMS 1994年第1期67卷 5-17页

作者： SAKAWA, M SAWADA, K MATSUSHITA ELECT WORKS LTD CTR INFORMAT SYSTOSAKA 571JAPAN

In this paper, we present an interactive fuzzy satisficing method for large-scale multiobjective linear programming problems with the block angular structure. By considering the vague nature of human judgements, we assume that the decision maker (DM) may have a fuzzy goal for each of the objective functions. Having elicited the corresponding linear membership functions, if the DM specifies the reference membership levels for all the membership functions, the corresponding Pareto optimal solution which is, in the minimax sense, nearest to the requirement or better than that if the reference membership levels are attainable can be obtained by solving the minimax problem. Here it is shown that the formulated minimax problem can be reduced to one master problem and a number of linear subproblems and the Pareto optimal solution together with the trade-off rate information between the membership functions can be obtained by applying the Dantzig-Wolfe decomposition method. In this way, the satisficing solution for the DM can be derived from Pareto optimal solutions by updating the current reference membership levels on the basis of the current levels of the membership functions together with the trade-off rates between the membership functions.

关键词： large-scale linear programming MULTIOBJECTIVE linear programming BLOCK ANGULAR STRUCTURE FUZZY GOALS INTERACTIVE FUZZY SATISFICING METHOD

来源：评论

学校读者我要写书评

暂无评论

A fuzzy satisficing method for large-scale multiobjective linear programming problems with block angular structure

引用

FUZZY SETS AND SYSTEMS 1996年第3期78卷 279-288页

作者： Sakawa, M Inuiguchi, M Sawada, K MATSUSHITEA ELECT WORKS LTD INFORMAT SYST CTROSAKA 571JAPAN

In this paper, we focus on large-scale multiobjective linear programming problems with the block angular structure. By considering the imprecise nature of human judgements, we assume that the decision maker may have a fuzzy goal for each of the objective functions. Having elicited the corresponding linear membership functions through the interaction with the decision maker, we adopt the fuzzy decision for aggregating them. Then it is shown that the formulated problem can be reduced to one master problem and a number of linear subproblems and the satisficing solution for the decision maker can be obtained by directly applying the Dantzig-Wolfe decomposition method.

关键词： large-scale linear programming multiobjective linear programming block angular structure fuzzy goals fuzzy decision fuzzy satisficing method

来源：评论

学校读者我要写书评

暂无评论

Fuzzy programming for large-scale Multiobjective linear programming Problems with Fuzzy Parameters

引用

IFAC Proceedings Volumes 1995年第10期28卷 401-406页

作者： Masatoshi Sakawa Kosuke Kato Department of Industrial and Systems Engineering Faculty of Engineering Hiroshima University Higashi-Hiroshima 739 Japan

In this paper, a large-scale multiobjective block-angular linear programming problem involving fuzzy parameters is formulated by considering the experts' vague understanding of the nature of the parameters in the problem-formulation process. Using the α-level sets of fuzzy numbers, the corresponding nonfuzzy α-programming problem is introduced and the fuzzy goals of the decision maker are quantified by eliciting the membership functions. Through the introduction of an extended Pareto optimality concept, if the decision maker specifies the degree a and the reference membership values, the corresponding extended Pareto optimal solution can be obtained by solving the minimax problems for which the Dantzig-Wolfe decomposition method is applicable. Then a linear programming-based interactive fuzzy satisficing method for deriving a satisficing solution for the decision maker from an extended Pareto optimal solution set is presented.

关键词： multiobjective linear programming large-scale linear programming fuzzy parameters fuzzy goals fuzzy satisficing methods

来源：评论

学校读者我要写书评

暂无评论

Constraint Optimal Selection Techniques (COSTs) for nonnegative linear programming problems

引用

APPLIED MATHEMATICS AND COMPUTATION 2015年 251卷 586-598页

作者： Saito, G. Corley, H. W. Rosenberger, Jay M. Sung, Tai-Kuan Noroziroshan, Alireza Univ Texas Arlington IMSE Dept Arlington TX 76019 USA Nan Kai Univ Technol Caotun Taiwan

We describe an active-set, cutting-plane approach called Constraint Optimal Selection Techniques (COSTs) and develop an efficient new COST for solving nonnegative linear programming problems. We give a geometric interpretation of the new selection rule and provide computational comparisons of the new COST with existing linear programming algorithms for some large-scale sample problems. (C) 2014 Elsevier Inc. All rights reserved.

关键词： linear programming large-scale linear programming Cutting planes Active-set methods Constraint selection

来源：评论

学校读者我要写书评

暂无评论

A primal deficient-basis simplex algorithm for linear programming

引用

APPLIED MATHEMATICS AND COMPUTATION 2008年第2期196卷 898-912页

作者： Pan, Ping-Qi Southeast Univ Dept Math Nanjing 210096 Peoples R China

The standard basis, which plays a fundamental role in simplex methodology, was recently extended to include a deficient case (with fewer columns than rows) by taking advantage of primal degeneracy. Computational results have been favorable with dense implementations. In this paper, we propose a primal simplex algorithm using sparse LU factors of deficient bases. Amenable to real-world linear programming problems, which are often degenerate or even highly degenerate, the algorithm would solve them with potentially improved stability compared to the simplex algorithm. The proposed algorithm has been implemented and tested on a set of 50 Netlib test problems as well as a set of 15 much larger real-world problems, including 8 Kennington and 5 BPMPD problems. It significantly outperformed MINOS 5.3 in terms of both iteration counts and run time. In particular,. these results reveal that there is no inevitable correlation between an algorithm's inefficiency and degeneracy (contradicting common belief). (C) 2007 Elsevier Inc. All rights reserved.

关键词： large-scale linear programming simplex algorithm primal degeneracy deficient-basis LU factorization

来源：评论

学校读者我要写书评

暂无评论

A FAST SIMPLEX ALGORITHM FOR linear programming

引用

Journal of Computational Mathematics 2010年第6期28卷 837-847页

作者： Pingqi Pan Department of Mathematics Southeast University Nanjing 210096 China

Recently, computational results demonstrated remarkable superiority of a so-called ＂largest-distance＂ rule and ＂nested pricing＂ rule to other major rules commonly used in practice, such as Dantzig＇s original rule, the steepest-edge rule and Devex rule. Our computational experiments show that the simplex algorithm using a combination of these rules turned out to be even more efficient.

关键词： large-scale linear programming Simplex algorithm Pivot rule Nested largestdistance Scaling.

来源：评论

学校读者我要写书评

暂无评论

A revised dual projective pivot algorithm for linear programming

引用

SIAM JOURNAL ON OPTIMIZATION 2005年第1期16卷 49-68页

作者： Pan, PQ Southeast Univ Dept Math Nanjing 210096 Peoples R China

We revise the dual projective pivot algorithm using sparse rectangular LU factors. In each iteration, the proposed algorithm solves at most three triangular systems, while simplex algorithms solve four. Instead of the classical basis, it uses a so-called pseudobasis ( a rectangular matrix having fewer columns than rows), thereby solving smaller linear systems with a potentially improved stability compared to simplex algorithms. Most importantly, it generates good search directions at a low cost. We report encouraging computational results on a set of 50 Netlib standard test problems as well as a set of 15 much larger real-world problems. A code named RDPPA 1.10 based on the proposed algorithm outperformed MINOS 5.51 significantly in terms of both iterations and run time. In particular, it appears that a high proportion of degenerate iterations need not imply many total iterations ( contradicting the common belief).

关键词： large-scale linear programming dual algorithm projection pivot pseudobasis deficient basis LU factorization

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：