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A Dimensional Reduction Approach Based on Essential Constraints in Linear Programming
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作者 Eirini I. Nikolopoulou George S. Androulakis 《American Journal of Operations Research》 2024年第1期1-31,共31页
This paper presents a new dimension reduction strategy for medium and large-scale linear programming problems. The proposed method uses a subset of the original constraints and combines two algorithms: the weighted av... This paper presents a new dimension reduction strategy for medium and large-scale linear programming problems. The proposed method uses a subset of the original constraints and combines two algorithms: the weighted average and the cosine simplex algorithm. The first approach identifies binding constraints by using the weighted average of each constraint, whereas the second algorithm is based on the cosine similarity between the vector of the objective function and the constraints. These two approaches are complementary, and when used together, they locate the essential subset of initial constraints required for solving medium and large-scale linear programming problems. After reducing the dimension of the linear programming problem using the subset of the essential constraints, the solution method can be chosen from any suitable method for linear programming. The proposed approach was applied to a set of well-known benchmarks as well as more than 2000 random medium and large-scale linear programming problems. The results are promising, indicating that the new approach contributes to the reduction of both the size of the problems and the total number of iterations required. A tree-based classification model also confirmed the need for combining the two approaches. A detailed numerical example, the general numerical results, and the statistical analysis for the decision tree procedure are presented. 展开更多
关键词 linear programming Binding Constraints Dimension Reduction Cosine Similarity Decision Analysis Decision Trees
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Solving Multi-Objective Linear Programming Problem by Statistical Averaging Method with the Help of Fuzzy Programming Method
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作者 Samsun Nahar Marin Akter Md. Abdul Alim 《American Journal of Operations Research》 2023年第2期19-32,共14页
A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming probl... A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method. 展开更多
关键词 Fuzzy programming Method Fuzzy linear programming Problem Multi-Objective linear programming Problem Statistical Averaging Method New Statistical Averaging Method
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Primal-Dual Interior-Point Algorithms with Dynamic Step-Size Based on Kernel Functions for Linear Programming 被引量:3
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作者 钱忠根 白延琴 《Journal of Shanghai University(English Edition)》 CAS 2005年第5期391-396,共6页
In this paper, primal-dual interior-point algorithm with dynamic step size is implemented for linear programming (LP) problems. The algorithms are based on a few kernel functions, including both serf-regular functio... In this paper, primal-dual interior-point algorithm with dynamic step size is implemented for linear programming (LP) problems. The algorithms are based on a few kernel functions, including both serf-regular functions and non-serf-regular ones. The dynamic step size is compared with fixed step size for the algorithms in inner iteration of Newton step. Numerical tests show that the algorithms with dynaraic step size are more efficient than those with fixed step size. 展开更多
关键词 linear programming (lp interior-point algorithm small-update method large-update method.
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A non-monotone Phase-1 method in linear programming 被引量:4
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作者 潘平奇 李炜 《Journal of Southeast University(English Edition)》 EI CAS 2003年第3期293-296,共4页
To gain superior computational efficiency, it might be necessary to change the underlying philosophy of the simplex method. In this paper, we propose a Phase-1 method along this line. We relax not only the conventiona... To gain superior computational efficiency, it might be necessary to change the underlying philosophy of the simplex method. In this paper, we propose a Phase-1 method along this line. We relax not only the conventional condition that some function value increases monotonically, but also the condition that all feasible variables remain feasible after basis change in Phase-1. That is, taking a purely combinatorial approach to achieving feasibility. This enables us to get rid of ratio test in pivoting, reducing computational cost per iteration to a large extent. Numerical results on a group of problems are encouraging. 展开更多
关键词 linear programming Phase-1 ratio-test-free pivoting rule
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Linear Programming建模研讨 被引量:1
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作者 宋占奎 於全收 +2 位作者 范光 燕嬿 胡杰军 《西安文理学院学报(自然科学版)》 2007年第4期46-49,共4页
研究用图解法、simplex method和匈牙利法建立Linear Programming的数学模型并求得了最优解.结果表明:对仅有两个变量的Linear Programming,既可通过图解法求得最优解;也可用单纯形表简便地求得最优解;而对任务和人数不等的assignment p... 研究用图解法、simplex method和匈牙利法建立Linear Programming的数学模型并求得了最优解.结果表明:对仅有两个变量的Linear Programming,既可通过图解法求得最优解;也可用单纯形表简便地求得最优解;而对任务和人数不等的assignment problem,则用匈牙利法求最优解. 展开更多
关键词 图解法 可行域 linear Progranmfing simplexmethod 匈牙利法
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Solution for integer linear bilevel programming problems using orthogonal genetic algorithm 被引量:9
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作者 Hong Li Li Zhang Yongchang Jiao 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2014年第3期443-451,共9页
An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorith... An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorithm is developed for solving the binary linear implicit programming problem based on the orthogonal design. The orthogonal design with the factor analysis, an experimental design method is applied to the genetic algorithm to make the algorithm more robust, statistical y sound and quickly convergent. A crossover operator formed by the orthogonal array and the factor analysis is presented. First, this crossover operator can generate a smal but representative sample of points as offspring. After al of the better genes of these offspring are selected, a best combination among these offspring is then generated. The simulation results show the effectiveness of the proposed algorithm. 展开更多
关键词 integer linear bilevel programming problem integer optimization genetic algorithm orthogonal experiment design
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An Exact Virtual Network Embedding Algorithm Based on Integer Linear Programming for Virtual Network Request with Location Constraint 被引量:3
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作者 Zeheng Yang Yongan Guo 《China Communications》 SCIE CSCD 2016年第8期177-183,共7页
Network virtualization is known as a promising technology to tackle the ossification of current Internet and will play an important role in the future network area. Virtual network embedding(VNE) is a key issue in net... Network virtualization is known as a promising technology to tackle the ossification of current Internet and will play an important role in the future network area. Virtual network embedding(VNE) is a key issue in network virtualization. VNE is NP-hard and former VNE algorithms are mostly heuristic in the literature.VNE exact algorithms have been developed in recent years. However, the constraints of exact VNE are only node capacity and link bandwidth.Based on these, this paper presents an exact VNE algorithm, ILP-LC, which is based on Integer Linear Programming(ILP), for embedding virtual network request with location constraints. This novel algorithm is aiming at mapping virtual network request(VNR) successfully as many as possible and consuming less substrate resources.The topology of each VNR is randomly generated by Waxman model. Simulation results show that the proposed ILP-LC algorithm outperforms the typical heuristic algorithms in terms of the VNR acceptance ratio, at least 15%. 展开更多
关键词 network virtualization virtual network embedding exact VNE algorithm integer linear programming location constraint VNR acceptance ratio
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Global convergent algorithm for the bilevel linear fractional-linear programming based on modified convex simplex method 被引量:2
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作者 Guangmin Wang Bing Jiang +1 位作者 Kejun Zhu Zhongping Wan 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2010年第2期239-243,共5页
A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equ... A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equaling to zero, the bilevel linear fractional-linear programming is transformed into a traditional sin- gle level programming problem, which can be transformed into a series of linear fractional programming problem. Thus, the modi- fied convex simplex method is used to solve the infinite linear fractional programming to obtain the global convergent solution of the original bilevel linear fractional-linear programming. Finally, an example demonstrates the feasibility of the proposed algorithm. 展开更多
关键词 bilevel linear fractional-linear programming convex simplex method dual problem.
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Solving Intuitionistic Fuzzy Linear Programming Problem 被引量:3
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作者 Arpita Kabiraj Prasun Kumar Nayak Swapan Raha 《International Journal of Intelligence Science》 2019年第1期44-58,共15页
Intuitionistic Fuzzy Set (IFS) can be used as a general tool for modeling problems of decision making under uncertainty where, the degree of rejection is defined simultaneously with the degree of acceptance of a piece... Intuitionistic Fuzzy Set (IFS) can be used as a general tool for modeling problems of decision making under uncertainty where, the degree of rejection is defined simultaneously with the degree of acceptance of a piece of information in such a way that these degrees are not complement to each other. Accordingly, an attempt is made to solve intuitionistic fuzzy linear programming problems using a technique based on an earlier technique proposed by Zimmermann to solve fuzzy linear programming problem. Our proposed technique does not require the existing ranking of intuitionistic fuzzy numbers. This method is also different from the existing weight assignment method or the Angelov’s method. A comparative study is undertaken and interesting results have been presented. 展开更多
关键词 Intuitionistic FUZZY Set Intuitionistic Index Intuitionistic FUZZY NUMBER Intuitionistic FUZZY linear programming PROBLEM FUZZY linear programming PROBLEM
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Linear goal programming approach to obtaining the weights of intuitionistic fuzzy ordered weighted averaging operator 被引量:3
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作者 Yejun Xu Chao Huang +1 位作者 Qingli Da Xinwang Liu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2010年第6期990-994,共5页
The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational law... The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging (IFOWA) operator which is an extension of the well-known ordered weighted averaging (OWA) operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method. 展开更多
关键词 intuitionistic fuzzy set intuitionistic fuzzy ordered weighted averaging(IFOWA) operator linear goal programming WEIGHTS multiple attribute decision making(MADM).
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A New Method for Achieving an Initial Regular Solution of a Linear Programming 被引量:3
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作者 梁平 孙艳华 +1 位作者 魏德宾 张相斌 《Northeastern Mathematical Journal》 CSCD 2008年第1期31-34,共4页
A method is provided for finding an initial regular solution of a linear programming in this paper. The key to this method is to solve an auxiliary linear programming instead of to introduce any artificial variable or... A method is provided for finding an initial regular solution of a linear programming in this paper. The key to this method is to solve an auxiliary linear programming instead of to introduce any artificial variable or constraint. Compared with the traditional method of achieving the regular solution by introducing an artificial constraint, it has advantages of saving the memories and little computational efforts. 展开更多
关键词 initial regular solution auxiliary linear programming artificial variable artificial constrain
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Efficient Algorithm for K-Barrier Coverage Based on Integer Linear Programming 被引量:15
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作者 Yanhua Zhang Xingming Sun Baowei Wang 《China Communications》 SCIE CSCD 2016年第7期16-23,共8页
Barrier coverage of wireless sensor networks is an important issue in the detection of intruders who are attempting to cross a region of interest.However,in certain applications,barrier coverage cannot be satisfied af... Barrier coverage of wireless sensor networks is an important issue in the detection of intruders who are attempting to cross a region of interest.However,in certain applications,barrier coverage cannot be satisfied after random deployment.In this paper,we study how mobile sensors can be efficiently relocated to achieve k-barrier coverage.In particular,two problems are studied:relocation of sensors with minimum number of mobile sensors and formation of k-barrier coverage with minimum energy cost.These two problems were formulated as 0–1 integer linear programming(ILP).The formulation is computationally intractable because of integrality and complicated constraints.Therefore,we relax the integrality and complicated constraints of the formulation and construct a special model known as RELAX-RSMN with a totally unimodular constraint coefficient matrix to solve the relaxed 0–1 ILP rapidly through linear programming.Theoretical analysis and simulation were performed to verify the effectiveness of our approach. 展开更多
关键词 k-barrier coverage linear programming wireless sensor networks
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RIGID-PLASTIC/RIGID-VISCOPLASTIC FEM BASED ON LINEAR PROGRAMMING—THEORETICAL MODELING AND APPLICATION FOR AXISYMMETRICAL PROBLEMS 被引量:1
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作者 Xu Weili Shi Xiangchen Lin Zhongqin School of Mechanical Engineering,Shanghai Jiaotong University Peter Thomson Di Senglin Australia Monash University Australia University of Technology 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2001年第2期184-188,共5页
Compared with the traditional rigid plastic/rigid viscoplastic(RP/RVP) FEM(based on iteration solution),RP/RVP FEM based on linear programming (LP) has some remarkable advantages,such as it's free of convergence... Compared with the traditional rigid plastic/rigid viscoplastic(RP/RVP) FEM(based on iteration solution),RP/RVP FEM based on linear programming (LP) has some remarkable advantages,such as it's free of convergence problem and its convenience in contact,rigid zone,and friction force treatment.The numerical model of RP/RVP FEM based on LP for axisymmetrical metal forming simulation is studied,and some related key factors and its treatment methods in formulation of constraint condition are proposed.Some solution examples are provided to validate its accuracy and efficiency. 展开更多
关键词 RIGID plastic/rigid VISCOPLASTIC FEM Contact treatment linear programming
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A RECOGNITION PROBLEM IN CONVERTING LINEAR PROGRAMMING TO NETWORK FLOW MODELS 被引量:1
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作者 林诒勋 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 1993年第1期76-85,共10页
The main goal of this paper is to study the following combinatorial problem : given a finite set E = (e1, e2, ...,em} and a subset family a - [S1,S2, ... ,Sk} of E , does there exist a tree T with the edge set E such ... The main goal of this paper is to study the following combinatorial problem : given a finite set E = (e1, e2, ...,em} and a subset family a - [S1,S2, ... ,Sk} of E , does there exist a tree T with the edge set E such that each induced subgraph T[Si] of Si is precisely a path (1≤i≤k) ? 展开更多
关键词 linear programming Network Flow Polygon-matrix SEQUENCING Tree.
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Support Vector Machines for Regression: A Succinct Review of Large-Scale and Linear Programming Formulations 被引量:3
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作者 Pablo Rivas-Perea Juan Cota-Ruiz +3 位作者 David Garcia Chaparro Jorge Arturo Perez Venzor Abel Quezada Carreón Jose Gerardo Rosiles 《International Journal of Intelligence Science》 2013年第1期5-14,共10页
Support Vector-based learning methods are an important part of Computational Intelligence techniques. Recent efforts have been dealing with the problem of learning from very large datasets. This paper reviews the most... Support Vector-based learning methods are an important part of Computational Intelligence techniques. Recent efforts have been dealing with the problem of learning from very large datasets. This paper reviews the most commonly used formulations of support vector machines for regression (SVRs) aiming to emphasize its usability on large-scale applications. We review the general concept of support vector machines (SVMs), address the state-of-the-art on training methods SVMs, and explain the fundamental principle of SVRs. The most common learning methods for SVRs are introduced and linear programming-based SVR formulations are explained emphasizing its suitability for large-scale learning. Finally, this paper also discusses some open problems and current trends. 展开更多
关键词 SUPPORT VECTOR MACHINES SUPPORT VECTOR Regression linear programming SUPPORT VECTOR Regression
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Weak optimal inverse problems of interval linear programming based on KKT conditions 被引量:2
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作者 LIU Xiao JIANG Tao LI Hao-hao 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2021年第3期462-474,共13页
In this paper,weak optimal inverse problems of interval linear programming(IvLP)are studied based on KKT conditions.Firstly,the problem is precisely defined.Specifically,by adjusting the minimum change of the current ... In this paper,weak optimal inverse problems of interval linear programming(IvLP)are studied based on KKT conditions.Firstly,the problem is precisely defined.Specifically,by adjusting the minimum change of the current cost coefficient,a given weak solution can become optimal.Then,an equivalent characterization of weak optimal inverse IvLP problems is obtained.Finally,the problem is simplified without adjusting the cost coefficient of null variable. 展开更多
关键词 interval linear programming inverse problems KKT conditions weak optimal solution
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Solving Intuitionistic Fuzzy Linear Programming Problem—II 被引量:1
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作者 Arpita Kabiraj Prasun Kumar Nayak Swapan Raha 《International Journal of Intelligence Science》 2019年第4期93-110,共18页
Under non-random uncertainty, a new idea of finding a possibly optimal solution for linear programming problem is examined in this paper. It is an application of the intuitionistic fuzzy set concept within scope of th... Under non-random uncertainty, a new idea of finding a possibly optimal solution for linear programming problem is examined in this paper. It is an application of the intuitionistic fuzzy set concept within scope of the existing fuzzy optimization. Here, we solve a linear programming problem (LPP) in an intuitionistic fuzzy environment and compare the result with the solution obtained from other existing techniques. In the process, the result of associated fuzzy LPP is also considered for a better understanding. 展开更多
关键词 FUZZY linear programming PROBLEM (FlpP) Intuitionistic FUZZY Set (IFS) Intuitionistic FUZZY Number (IFN) Intuitionistic FUZZY linear programming PROBLEM (IFlpP)
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Short-Term Scheduling of Combined Cycle Units Using Mixed Integer Linear Programming Solution 被引量:1
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作者 Juan Alemany Diego Moitre +1 位作者 Herminio Pinto Fernando Magnago 《Energy and Power Engineering》 2013年第2期161-170,共10页
Combined cycle plants (CCs) are broadly used all over the world. The inclusion of CCs into the optimal resource scheduling causes difficulties because they can be operated in different operating configuration modes ba... Combined cycle plants (CCs) are broadly used all over the world. The inclusion of CCs into the optimal resource scheduling causes difficulties because they can be operated in different operating configuration modes based on the number of combustion and steam turbines. In this paper a model CCs based on a mixed integer linear programming approach to be included into an optimal short term resource optimization problem is presented. The proposed method allows modeling of CCs in different modes of operation taking into account the non convex operating costs for the different combined cycle mode of operation. 展开更多
关键词 Combined CYCLE PLANTS Unit COMMITMENT MIXED INTEGER linear programming
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Linear Programming for Optimum PID Controller Tuning 被引量:1
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作者 Edimar J. Oliveira Leonardo M. Honorio +1 位作者 Alexandre H. Anzai Tamara X. Soares 《Applied Mathematics》 2014年第6期886-897,共12页
This work presents a new methodology based on Linear Programming (LP) to tune Proportional-Integral-Derivative (PID) control parameters. From a specification of a desired output time domain of the plant, a linear opti... This work presents a new methodology based on Linear Programming (LP) to tune Proportional-Integral-Derivative (PID) control parameters. From a specification of a desired output time domain of the plant, a linear optimization system is proposed to adjust the PID controller leading the output signal to stable operation condition with minimum oscillations. The constraint set used in the optimization process is defined by using numerical integration approach. The generated optimization problem is convex and easily solved using an interior point algorithm. Results obtained using familiar plants from literature have shown that the proposed linear programming problem is very effective for tuning PID controllers. 展开更多
关键词 linear programming Optimal Control INTERIOR POINT Method PID Tuning
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A Primal-Dual Simplex Algorithm for Solving Linear Programming Problems with Symmetric Trapezoidal Fuzzy Numbers 被引量:1
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作者 Ali Ebrahimnejad 《Applied Mathematics》 2011年第6期676-684,共9页
Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simpl... Two existing methods for solving a class of fuzzy linear programming (FLP) problems involving symmetric trapezoidal fuzzy numbers without converting them to crisp linear programming problems are the fuzzy primal simplex method proposed by Ganesan and Veeramani [1] and the fuzzy dual simplex method proposed by Ebrahimnejad and Nasseri [2]. The former method is not applicable when a primal basic feasible solution is not easily at hand and the later method needs to an initial dual basic feasible solution. In this paper, we develop a novel approach namely the primal-dual simplex algorithm to overcome mentioned shortcomings. A numerical example is given to illustrate the proposed approach. 展开更多
关键词 FUZZY linear programming FUZZY ARITHMETIC FUZZY ORDERS PRIMAL-DUAL SIMPLEX Algorithm
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