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Global Optimization Algorithm for Minimizing Linear Fractional Programming 认领 引用
1
作者 ZHAO Peng SHEN Pei-ping ZHONG Zhe-wei 《Chinese Quarterly Journal of Mathematics》 2026年第1期50-59,共10页
In this paper,we study a class of Linear Fractional Programming on a nonempty bounded set,called the Problem(LFP),and design a branch and bound algorithm to find the global optimal solution of the problem(LFP).First,w... In this paper,we study a class of Linear Fractional Programming on a nonempty bounded set,called the Problem(LFP),and design a branch and bound algorithm to find the global optimal solution of the problem(LFP).First,we convert the problem(LFP)to the equivalent problem(EP2).Secondly,by applying the linear relaxation technique to the problem(EP2),the linear relaxation programming problem(LRP2Y)was obtained.Then,the overall framework of the algorithm is given,and the convergence and complexity of the algorithm are analyzed.Finally,experimental results are listed to illustrate the effectiveness of the algorithm. 展开更多
关键词 Global optimization Linear Fractional Programming Branch and bound algorithm Linear relaxation
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Solution for integer linear bilevel programming problems using orthogonal genetic algorithm 认领 引用 被引量：10
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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 adaptive genetic algorithm for solving bilevel linear programming problem 认领 引用 被引量：2
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作者 王广民 王先甲 +1 位作者 万仲平 贾世会 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2007年第12期1605-1612,共8页
Bilevel linear programming, which consists of the objective functions of the upper level and lower level, is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this pr... Bilevel linear programming, which consists of the objective functions of the upper level and lower level, is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this problem. Of all the algorithms, the ge- netic algorithm is an alternative to conventional approaches to find the solution of the bilevel linear programming. In this paper, we describe an adaptive genetic algorithm for solving the bilevel linear programming problem to overcome the difficulty of determining the probabilities of crossover and mutation. In addition, some techniques are adopted not only to deal with the difficulty that most of the chromosomes maybe infeasible in solving constrained optimization problem with genetic algorithm but also to improve the efficiency of the algorithm. The performance of this proposed algorithm is illustrated by the examples from references. 展开更多
关键词 bilevel linear programming genetic algorithm fitness value adaptive operator probabilities crossover and mutation
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Smoothing Newton Algorithm for Linear Programming over Symmetric Cones 认领 引用 被引量：3
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作者 刘晓红 倪铁 《Transactions of Tianjin University》 EI CAS 2009年第3期216-221,共6页
By using the theory of Euclidean Jordan algebras,based on a new class of smoothing functions,the QiSun-Zhou's smoothing Newton algorithm is extended to solve linear programming over symmetric cones(SCLP).The algor... By using the theory of Euclidean Jordan algebras,based on a new class of smoothing functions,the QiSun-Zhou's smoothing Newton algorithm is extended to solve linear programming over symmetric cones(SCLP).The algorithm is globally convergent under suitable assumptions. 展开更多
关键词 linear programming symmetric cone Euclidean Jordan algebra smoothing algorithm
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Discrete differential evolution algorithm for integer linear bilevel programming problems 认领 引用 被引量：1
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作者 Hong Li Li Zhang Yongchang Jiao 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2016年第4期912-919,共8页
A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forc... A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods. 展开更多
关键词 discrete linear bilevel programming problem discrete differential evolution constraint handling method branch and bound algorithm
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Polynomial Complexity Bounds of Mehrotra-type Predictor-corrector Algorithms for Linear Programming over Symmetric Cones 认领 引用
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作者 刘长河 尚有林 李振国 《Chinese Quarterly Journal of Mathematics》 2015年第4期475-494,共20页
We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the s... We establish polynomial complexity corrector algorithms for linear programming over bounds of the Mehrotra-type predictor- symmetric cones. We first slightly modify the maximum step size in the predictor step of the safeguard based Mehrotra-type algorithm for linear programming, that was proposed by Salahi et al. Then, using the machinery of Euclidean Jordan algebras, we extend the modified algorithm to symmetric cones. Based on the Nesterov-Todd direction, we obtain O（r log ε1） iteration complexity bound of this algorithm, where r is the rank of the Jordan algebras and ε is the required precision. We also present a new variant of Mehrotra-type algorithm using a new adaptive updating scheme of centering parameter and show that this algorithm enjoys the same order of complexity bound as the safeguard algorithm. We illustrate the numerical behaviour of the methods on some small examples. 展开更多
关键词 linear programming symmetric cone Euclidean Jordan algebra interior-point methods Mehrotra-type algorithm polynomial complexity
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An Exact Virtual Network Embedding Algorithm Based on Integer Linear Programming for Virtual Network Request with Location Constraint 认领 引用 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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Primal-Dual Interior-Point Algorithms with Dynamic Step-Size Based on Kernel Functions for Linear Programming 认领 引用 被引量：3
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作者 钱忠根 白延琴 《Journal of Shanghai University(English Edition)》 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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An Improved Affine-Scaling Interior Point Algorithm for Linear Programming 认领 引用 被引量：1
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作者 Douglas Kwasi Boah Stephen Boakye Twum 《Journal of Applied Mathematics and Physics》 2019年第10期2531-2536,共6页
In this paper, an Improved Affine-Scaling Interior Point Algorithm for Linear Programming has been proposed. Computational results of selected practical problems affirming the proposed algorithm have been provided. Th... In this paper, an Improved Affine-Scaling Interior Point Algorithm for Linear Programming has been proposed. Computational results of selected practical problems affirming the proposed algorithm have been provided. The proposed algorithm is accurate, faster and therefore reduces the number of iterations required to obtain an optimal solution of a given Linear Programming problem as compared to the already existing Affine-Scaling Interior Point Algorithm. The algorithm can be very useful for development of faster software packages for solving linear programming problems using the interior-point methods. 展开更多
关键词 Interior-Point Methods Affine-Scaling Interior Point Algorithm Optimal Solution Linear Programming Initial Feasible Trial Solution
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A Primal-Dual Infeasible-Interior-Point Algorithm for Multiple Objective Linear Programming Problems 认领 引用
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作者 HUANG Hui FEI Pu-sheng YUAN Yuan 《Wuhan University Journal of Natural Sciences》 EI CAS 2005年第2期351-354,共4页
A primal-dual infeasible interior point algorithm for multiple objective linear programming(MOLP)problems was presented.In contrast to the current MOLP algorithm.moving through the interior of polytope but not confini... A primal-dual infeasible interior point algorithm for multiple objective linear programming(MOLP)problems was presented.In contrast to the current MOLP algorithm.moving through the interior of polytope but not confining the iterates within the feasible region in our proposed algorithm result in a solution approach that is quite different and less sensitive to problem size,so providing the potential to dramatically improve the practical computation effectiveness. 展开更多
关键词 multiple objective linear programming primal dual infeasible interior point algorithm
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A new heuristic algorithm for general integer linear programming problems 认领 引用 被引量：1
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作者 高培旺 《Journal of Chongqing University》 2006年第3期170-174,共5页
A new heuristic algorithm is proposed for solving general integer linear programming problems. In the algorithm, the objective function hyperplane is used as a cutting plane, and then by introducing a special set of a... A new heuristic algorithm is proposed for solving general integer linear programming problems. In the algorithm, the objective function hyperplane is used as a cutting plane, and then by introducing a special set of assistant sets, an efficient heuristic search for the solution to the integer linear program is carried out in the sets on the objective function hyperplane. A simple numerical example shows that the algorithm is efficient for some problems, and therefore, of practical interest. 展开更多
关键词 integer linear programming objective function hyperplane cutting plane heuristic algorithm
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A Glorious Literature on Linear Goal Programming Algorithms 认领 引用 被引量：1
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作者 Ukamaka Cynthia Orumie Daniel Ebong 《American Journal of Operations Research》 2014年第2期59-71,共13页
In the last several years, there has been a marked improvement in the development of new algorithms for solving Linear Goal programming (LGP). This paper presents a survey of current methods for LGP.
关键词 Linear Goal Programming Algorithms Current Methods
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A Primal-Dual Simplex Algorithm for Solving Linear Programming Problems with Symmetric Trapezoidal Fuzzy Numbers 认领 引用 被引量：2
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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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An online value iteration method for stochastic linear quadratic control with multiplicative noise 认领 引用
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作者 Shumei Li Bing-Chang Wang Baoqiang Zhang 《Control Theory and Technology》 EI CSCD 2026年第3期451-461,共11页
This paper proposes a model-free online value iteration(VI)algorithm for solving stochastic linear quadratic control problems with ergodic cost functions,where the diffusion term in the dynamics equation is influenced... This paper proposes a model-free online value iteration(VI)algorithm for solving stochastic linear quadratic control problems with ergodic cost functions,where the diffusion term in the dynamics equation is influenced by both the state and control variables.First,we propose an offline VI algorithm based on the idea of stochastic approximation.However,this algorithm requires prior knowledge of the system parameters,which are not always readily available.To overcome this limitation,we then develop a(partially)model-free online learning algorithm based on VI.This algorithm only requires a single system trajectory and does not need the initial control to be stabilizing.By exploiting the growth rate of Itô’s integrals to handle the stochastic term generated by multiplicative noise,we provide a rigorous proof of the algorithm’s convergence.Finally,a simulation example is presented to validate the convergence of the proposed algorithms. 展开更多
关键词 Stochastic linear quadratic problem Model-free Value iteration algorithm Ergodic control Robust dynamic programming
Solving the Binary Linear Programming Model in Polynomial Time 认领 引用 被引量：1
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作者 Elias Munapo 《American Journal of Operations Research》 2016年第1期1-7,共7页
The paper presents a technique for solving the binary linear programming model in polynomial time. The general binary linear programming problem is transformed into a convex quadratic programming problem. The convex q... The paper presents a technique for solving the binary linear programming model in polynomial time. The general binary linear programming problem is transformed into a convex quadratic programming problem. The convex quadratic programming problem is then solved by interior point algorithms. This settles one of the open problems of whether P = NP or not. The worst case complexity of interior point algorithms for the convex quadratic problem is polynomial. It can also be shown that every liner integer problem can be converted into binary linear problem. 展开更多
关键词 NP-Complete Binary Linear Programming Convex Function Convex Quadratic Programming Problem Interior Point Algorithm and Polynomial Time
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Improved Balas and Mazzola Linearization for Quadratic 0-1 Programs with Application in a New CuttingPlane Algorithm 认领 引用 被引量：1
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作者 Wajeb Gharibi 《International Journal of Communications, Network and System Sciences》 2012年第4期208-212,共5页
Balas and Mazzola linearization (BML) is widely used in devising cutting plane algorithms for quadratic 0-1 programs. In this article, we improve BML by first strengthening the primal formulation of BML and then consi... Balas and Mazzola linearization (BML) is widely used in devising cutting plane algorithms for quadratic 0-1 programs. In this article, we improve BML by first strengthening the primal formulation of BML and then considering the dual formulation. Additionally, a new cutting plane algorithm is proposed. 展开更多
关键词 Quadratic Program Integer Program Linearization Cutting Plane Algorithm
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Determining Efficient Solutions of Multi-Objective Linear Fractional Programming Problems and Application 认领 引用
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作者 Farhana Akond Pramy Md. Ainul Islam 《Open Journal of Optimization》 2017年第4期164-175,共12页
In this paper, a modified method to find the efficient solutions of multi-objective linear fractional programming (MOLFP) problems is presented. While some of the previously proposed methods provide only one efficient... In this paper, a modified method to find the efficient solutions of multi-objective linear fractional programming (MOLFP) problems is presented. While some of the previously proposed methods provide only one efficient solution to the MOLFP problem, this modified method provides multiple efficient solutions to the problem. As a result, it provides the decision makers flexibility to choose a better option from alternatives according to their financial position and their level of satisfaction of objectives. A numerical example is provided to illustrate the modified method and also a real life oriented production problem is modeled and solved. 展开更多
关键词 Linear Programming (LP) Linear Fractional Programming (LFP) Multi-Objective Linear Programming (MOLP) Multi-Objective Linear Fractional Programming (MOLFP)
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Application of Linear Programming for Optimal Investments in Software Company 认领 引用
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作者 Abdulrahman O. Mustafa Mohamad Alamin Housam Sayegh Saim Rasheed 《Open Journal of Applied Sciences》 2021年第10期1092-1101,共10页
We apply the simplex algorithm which is a branch of linear programming to efficiently determine the allocation of resources required to operate a company in the software development field. The main aim of applying thi... We apply the simplex algorithm which is a branch of linear programming to efficiently determine the allocation of resources required to operate a company in the software development field. The main aim of applying this technique is to maximize the profit of a company under certain limitations. This can be done using the trial-and-error approach. However, this tedious process can be replaced by user-level tools such as Excel which are based on linear programming that will give more accurate results. Small software companies cannot afford to hire a high number of senior programmers to produce the required level of quality and to keep up with the demand for adding new features. On the other hand, lowering the quality of the product will reduce the number of customers and decrease profit. Another aspect is maximizing the utilization of hosting servers which are required for providing the services to customers since the cost of buying servers and maintaining them is extremely high. The simplex algorithm in linear programming will take the specified constraints into account to compute the optimal allocation of the available resources to maximize profit and limit the cost. This paper will present a model that uses the simplex algorithm with a set of constraints to determine how many projects of each type a company should take in one period of time. 展开更多
关键词 Linear Programming Simplex Algorithm Operational Costs
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A Complex Algorithm for Solving a Kind of Stochastic Programming 认领 引用
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作者 Yunpeng Luo Xinshun Ma 《Journal of Applied Mathematics and Physics》 2020年第6期1016-1030,共15页
Considering that the probability distribution of random variables in stochastic programming usually has incomplete information due to a perfect sample data in many real applications, this paper discusses a class of tw... Considering that the probability distribution of random variables in stochastic programming usually has incomplete information due to a perfect sample data in many real applications, this paper discusses a class of two-stage stochastic programming problems modeling with maximum minimum expectation compensation criterion (MaxEMin) under the probability distribution having linear partial information (LPI). In view of the nondifferentiability of this kind of stochastic programming modeling, an improved complex algorithm is designed and analyzed. This algorithm can effectively solve the nondifferentiable stochastic programming problem under LPI through the variable polyhedron iteration. The calculation and discussion of numerical examples show the effectiveness of the proposed algorithm. 展开更多
关键词 Stochastic Programming with Recourse Probability Distribution with Linear Partial Information Maximized Minimum Expectation Complex Algorithm
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A hybrid algorithm based on ILP and genetic algorithm for time-aware test case prioritization 认领 引用 被引量：1
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作者 Sun Jiaze Wang Gang 《Journal of Southeast University(English Edition)》 EI CAS 2018年第1期28-35,共8页
To solve the problem of time-awarc test case prioritization,a hybrid algorithm composed of integer linear programming and the genetic algorithm(ILP-GA)is proposed.First,the test case suite which cm maximize the number... To solve the problem of time-awarc test case prioritization,a hybrid algorithm composed of integer linear programming and the genetic algorithm(ILP-GA)is proposed.First,the test case suite which cm maximize the number of covered program entities a d satisfy time constraints is selected by integer linea progamming.Secondly,the individual is encoded according to the cover matrices of entities,and the coverage rate of program entities is used as the fitness function and the genetic algorithm is used to prioritize the selected test cases.Five typical open source projects are selected as benchmark programs.Branch and method are selected as program entities,and time constraint percentages a e 25%and 75%.The experimental results show that the ILP-GA convergence has faster speed and better stability than ILP-additional and IP-total in most cases,which contributes to the detection of software defects as early as possible and reduces the software testing costs. 展开更多
关键词 test case prioritization integer linear programming(I LP) genetic algorithm time constraint
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