This paper aims to find unit cost of a product for firms. It establishes a linear cost model to find unit cost. Linear goal programs assume a direct relationship between independent variable and dependent variable. De...This paper aims to find unit cost of a product for firms. It establishes a linear cost model to find unit cost. Linear goal programs assume a direct relationship between independent variable and dependent variable. Dependent variable of linear model is unit cost. Independent variables are cost accounting variables. They are supply cost, labor cost, and administration cost. This study assumes a direct relationship between supply-labor-administration costs and unit cost. Therefore, it establishes a linear cost model. The major research question of this study is to apply linear goal programming to cost accounting. The goal of this linear program is to find unit cost of product. This study uses quantitative method and human capital method. The main research result is linear costing model itself.展开更多
In this paper, we investigate a smoothing-type algorithm for solving the symmetric cone linear program （（SCLP） for short） by making use of an augmented system of its optimality conditions. The algorithm only needs...In this paper, we investigate a smoothing-type algorithm for solving the symmetric cone linear program （（SCLP） for short） by making use of an augmented system of its optimality conditions. The algorithm only needs to solve one system of linear equations and to perform one line search at each iteration. It is proved that the algorithm is globally convergent without assuming any prior knowledge of feasibility/infeasibility of the problem. In particular, the algorithm may correctly detect solvability of （SCLP）. Furthermore, if （SCLP） has a solution, then the algorithm will generate a solution of （SCLP）, and if the problem is strongly infeasible, the algorithm will correctly detect infeasibility of （SCLP）.展开更多
This is a brief report on our recent work in network piecewise linear programming (NPLP),and it consists of two parts. In the first park, we describe a generator for NPLP problems which is derived from the classical n...This is a brief report on our recent work in network piecewise linear programming (NPLP),and it consists of two parts. In the first park, we describe a generator for NPLP problems which is derived from the classical network linear program generator NETGEN. The generator creates networks of the same topological structures as NETGEN, but each arc is associated with a convex piecewise linear cost. The purpose of this program is to provide a set of standard test problems which can be used to compare the performance of various algorithms for NPLP. In the second part,we introduce a network simplex method that directly solves a network piecewise linear program without reformulating it as a network linear program of higher dimension. Forty benchmark NPLP problems are solved by this method and a reformulation method. The computational results are in favor of the direct method and show that solving an NPLP problem is not much harder than solving a network linear program of the same dimension.展开更多
Linear programming(LP)decoding is a classic decoding method for linear block codes,and has attracted recent researches because its potential in joint channel processing.However,for polar codes,LP decoders has long bee...Linear programming(LP)decoding is a classic decoding method for linear block codes,and has attracted recent researches because its potential in joint channel processing.However,for polar codes,LP decoders has long been outperformed by CRCaided successive cancellation list(CA-SCL)decoders.To increase the competitiveness of 5G NR LP polar decoding,it is possible to gain performance improvements by exploiting the cyclic redundancy check(CRC)setup.In this paper,we propose a combined scheme of reduced sparsified factor graph-sparsified CRC(RSFG-SCRC)and augmented generator matrix-CRC(AGM-CRC),for polytope generation in adaptive linear programming(ALP)decoder for 5G polar codes.Augmented generator matrix(AGM)polytope and improved maximum cycle strategy-auxiliary node pairs 4(MCS-ANP-4)algorithm are proposed,to make efficient use of CRC constraints and minimize the constraint size for the decoder.Numerical simulations show that adaptive linear programming decoders with our proposed RSFG-SCRC and AGM-CRC polytopes can achieve significantly better block error rate(BLER)performance than a benchmark CA-SCL-8 decoder especially in harsh low-to-medium SNR regions.展开更多
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
In this paper, we study linear static Stac kelberg problems with multiple leaders-followers in which each decision maker wi thin his group may or may not cooperate. An exact penalty function method is dev eloped. The ...In this paper, we study linear static Stac kelberg problems with multiple leaders-followers in which each decision maker wi thin his group may or may not cooperate. An exact penalty function method is dev eloped. The duality gaps of the followers’ problems are appended to the leaders’ objective function with a penalty. The structure leads to the decomposition of the composite problem into a series of linear programmings leading to an efficie nt algorithm. We prove that local optimality is reached for an exact penalty fun ction and illustrate the method with three examples. The model in this paper ext ends the stackelberg leader-follower model.展开更多
To conduct marine surveys,multiple unmanned surface vessels(Multi-USV)with different capabilities perform collaborative mapping in multiple designated areas.This paper proposes a task allocation algorithm based on int...To conduct marine surveys,multiple unmanned surface vessels(Multi-USV)with different capabilities perform collaborative mapping in multiple designated areas.This paper proposes a task allocation algorithm based on integer linear programming(ILP)with flow balance constraints,ensuring the fair and efficient distribution of sub-areas among USVs and maintaining strong connectivity of assigned regions.In the established gridmap,a search-based path planning algorithm is performed on the sub-areas according to the allocation scheme.It uses the greedy algorithm and the A*algorithm to achieve complete coverage of the barrier-free area and obtain an efficient trajectory of each USV.The greedy algorithm enables fast local traversal of unvisited grids,while the A*algorithm ensures navigation to escape from deadlock areas and maintains global path continuity.The comparison of task allocation results proves that the task allocation algorithm based on ILP improves the mapping efficiency and task distribution fairness.The proposed allocation method and result analysis provide a certain reference for the practical application ofMulti-USV to perform survey tasks collaboratively.展开更多
Byproduct gas is an important secondary energy in iron and steel industry, and its optimization is vital to cost reduction. With the development of iron and steel industry to be more eco-friendly, it is necessary to c...Byproduct gas is an important secondary energy in iron and steel industry, and its optimization is vital to cost reduction. With the development of iron and steel industry to be more eco-friendly, it is necessary to construct an integrated optimized system, taking economics, energy consumption and environment into consideration. Therefore, the environmental cost caused by pollutants discharge should be factored in total cost when optimizing byproduct gas distribution. A green mixed integer linear programming （MILP） model for the optimization of byproduct gases was established to reduce total cost, including both operation cost and environmental cost. The operation cost included penalty for gas deviation, costs of fuel and water consumption, holder booster trip penalty, and so forth; while the environmental cost consisted of penalties for both direct and indirect pollutants discharge. Case study showed that the proposed model brought an optimum solution and 2.2% of the total cost could be reduced compared with previous one.展开更多
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
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
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
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
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
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
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
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
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
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
The objective of this paper is to deal with a kind of fuzzy linear programming problem based on interval\|valued fuzzy sets(IVFLP)through the medium of procedure that turns IVFLP into parametric linear programming via...The objective of this paper is to deal with a kind of fuzzy linear programming problem based on interval\|valued fuzzy sets(IVFLP)through the medium of procedure that turns IVFLP into parametric linear programming via the mathematical programming.Some useful results for the benefit of solving IVFLP are expounded and proved,developed and discussed.Furthermore,that the proposed techniques in this paper allow the decision\|maker to assign a different degree of importance can provide a useful way to efficiently help the decision\|maker make their decisions.展开更多
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
文摘This paper aims to find unit cost of a product for firms. It establishes a linear cost model to find unit cost. Linear goal programs assume a direct relationship between independent variable and dependent variable. Dependent variable of linear model is unit cost. Independent variables are cost accounting variables. They are supply cost, labor cost, and administration cost. This study assumes a direct relationship between supply-labor-administration costs and unit cost. Therefore, it establishes a linear cost model. The major research question of this study is to apply linear goal programming to cost accounting. The goal of this linear program is to find unit cost of product. This study uses quantitative method and human capital method. The main research result is linear costing model itself.
基金Supported by the National Natural Science Foundation of China(No.11171252,11301375 and 71301118)Research Fund for the Doctoral Program of Higher Education of China(No.20120032120076)Tianjin Planning Program of Philosophy and Social Science(No.TJTJ11-004)
文摘In this paper, we investigate a smoothing-type algorithm for solving the symmetric cone linear program （（SCLP） for short） by making use of an augmented system of its optimality conditions. The algorithm only needs to solve one system of linear equations and to perform one line search at each iteration. It is proved that the algorithm is globally convergent without assuming any prior knowledge of feasibility/infeasibility of the problem. In particular, the algorithm may correctly detect solvability of （SCLP）. Furthermore, if （SCLP） has a solution, then the algorithm will generate a solution of （SCLP）, and if the problem is strongly infeasible, the algorithm will correctly detect infeasibility of （SCLP）.
文摘This is a brief report on our recent work in network piecewise linear programming (NPLP),and it consists of two parts. In the first park, we describe a generator for NPLP problems which is derived from the classical network linear program generator NETGEN. The generator creates networks of the same topological structures as NETGEN, but each arc is associated with a convex piecewise linear cost. The purpose of this program is to provide a set of standard test problems which can be used to compare the performance of various algorithms for NPLP. In the second part,we introduce a network simplex method that directly solves a network piecewise linear program without reformulating it as a network linear program of higher dimension. Forty benchmark NPLP problems are solved by this method and a reformulation method. The computational results are in favor of the direct method and show that solving an NPLP problem is not much harder than solving a network linear program of the same dimension.
基金supported by China Postdoctoral Science Foundation(No.2020M670469)National Key Research and Development Program of China(No.2019YFB1803303,No.2020YFB1806702).
文摘Linear programming(LP)decoding is a classic decoding method for linear block codes,and has attracted recent researches because its potential in joint channel processing.However,for polar codes,LP decoders has long been outperformed by CRCaided successive cancellation list(CA-SCL)decoders.To increase the competitiveness of 5G NR LP polar decoding,it is possible to gain performance improvements by exploiting the cyclic redundancy check(CRC)setup.In this paper,we propose a combined scheme of reduced sparsified factor graph-sparsified CRC(RSFG-SCRC)and augmented generator matrix-CRC(AGM-CRC),for polytope generation in adaptive linear programming(ALP)decoder for 5G polar codes.Augmented generator matrix(AGM)polytope and improved maximum cycle strategy-auxiliary node pairs 4(MCS-ANP-4)algorithm are proposed,to make efficient use of CRC constraints and minimize the constraint size for the decoder.Numerical simulations show that adaptive linear programming decoders with our proposed RSFG-SCRC and AGM-CRC polytopes can achieve significantly better block error rate(BLER)performance than a benchmark CA-SCL-8 decoder especially in harsh low-to-medium SNR regions.
文摘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.
文摘In this paper, we study linear static Stac kelberg problems with multiple leaders-followers in which each decision maker wi thin his group may or may not cooperate. An exact penalty function method is dev eloped. The duality gaps of the followers’ problems are appended to the leaders’ objective function with a penalty. The structure leads to the decomposition of the composite problem into a series of linear programmings leading to an efficie nt algorithm. We prove that local optimality is reached for an exact penalty fun ction and illustrate the method with three examples. The model in this paper ext ends the stackelberg leader-follower model.
基金supported in part by the International Science and Technology Project of Guangzhou Development District under Grant 2023GH08the Science and Technology Development Fund,MSAR,under Grants 0029/2022/AGJ and 0029/2023/RIA1the Program of Guangdong under Grant 2023A0505020003.
文摘To conduct marine surveys,multiple unmanned surface vessels(Multi-USV)with different capabilities perform collaborative mapping in multiple designated areas.This paper proposes a task allocation algorithm based on integer linear programming(ILP)with flow balance constraints,ensuring the fair and efficient distribution of sub-areas among USVs and maintaining strong connectivity of assigned regions.In the established gridmap,a search-based path planning algorithm is performed on the sub-areas according to the allocation scheme.It uses the greedy algorithm and the A*algorithm to achieve complete coverage of the barrier-free area and obtain an efficient trajectory of each USV.The greedy algorithm enables fast local traversal of unvisited grids,while the A*algorithm ensures navigation to escape from deadlock areas and maintains global path continuity.The comparison of task allocation results proves that the task allocation algorithm based on ILP improves the mapping efficiency and task distribution fairness.The proposed allocation method and result analysis provide a certain reference for the practical application ofMulti-USV to perform survey tasks collaboratively.
基金Sponsored by Beijing Social Science Foundation of China(14JGC110)Social Science Research Common Program of Beijing Municipal Commission of Education of China(SM201510038011)CUEB Foundation of China(2014XJG005)
文摘Byproduct gas is an important secondary energy in iron and steel industry, and its optimization is vital to cost reduction. With the development of iron and steel industry to be more eco-friendly, it is necessary to construct an integrated optimized system, taking economics, energy consumption and environment into consideration. Therefore, the environmental cost caused by pollutants discharge should be factored in total cost when optimizing byproduct gas distribution. A green mixed integer linear programming （MILP） model for the optimization of byproduct gases was established to reduce total cost, including both operation cost and environmental cost. The operation cost included penalty for gas deviation, costs of fuel and water consumption, holder booster trip penalty, and so forth; while the environmental cost consisted of penalties for both direct and indirect pollutants discharge. Case study showed that the proposed model brought an optimum solution and 2.2% of the total cost could be reduced compared with previous one.
基金supported by the Fundamental Research Funds for the Central Universities(K50511700004)the Natural Science Basic Research Plan in Shaanxi Province of China(2013JM1022)
文摘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.
基金supported by the National Basic Research Program of China(973 Program)under Grant 2013CB329005
文摘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%.
基金Project supported by Dutch Organization for Scientific Research(Grant No .613 .000 .010)
文摘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.
基金supported by the NSFC(U1536206,61232016,U1405254,61373133,61502242,71401176)BK20150925the PAPD fund
文摘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.
基金Supported by the National Natural Science Foundation of China(11971433)First Class Discipline of Zhe-jiang-A(Zhejiang Gongshang University-Statistics,1020JYN4120004G-091),Graduate Scientic Research and Innovation Foundation of Zhejiang Gongshang University.
文摘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.
基金Supported by Liu Hui Centre for Applied Mathematics,Nankai University and Tianjin University
文摘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.
基金supported by the National Natural Science Foundation of China (70771025)the Fundamental Research Funds for the Central Universities of Hohai University (2009B04514)Humanities and Social Sciences Foundations of Ministry of Education of China(10YJA630067)
文摘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.
文摘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.
基金supported by the National Natural Science Foundation of China(70771080)the Special Fund for Basic Scientific Research of Central Colleges+2 种基金China University of Geosciences(Wuhan) (CUG090113)the Research Foundation for Outstanding Young TeachersChina University of Geosciences(Wuhan)(CUGQNW0801)
文摘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.
文摘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.
基金Supported by the National Natural Science Foundation of China(79670060)Sichuan Youth Sci-ence and Technology Foundation.
文摘The objective of this paper is to deal with a kind of fuzzy linear programming problem based on interval\|valued fuzzy sets(IVFLP)through the medium of procedure that turns IVFLP into parametric linear programming via the mathematical programming.Some useful results for the benefit of solving IVFLP are expounded and proved,developed and discussed.Furthermore,that the proposed techniques in this paper allow the decision\|maker to assign a different degree of importance can provide a useful way to efficiently help the decision\|maker make their decisions.
基金Supported by the National Natural Science Foundation of China
文摘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) ?
