The Internet of Things emphasizes the concept of objects connected with each other, which includes all kinds of wireless sensor networks. An important issue is to reduce the energy consumption in the sensor networks s...The Internet of Things emphasizes the concept of objects connected with each other, which includes all kinds of wireless sensor networks. An important issue is to reduce the energy consumption in the sensor networks since sensor nodes always have energy constraints. Deployment of thousands of wireless sensors in an appropriate pattern will simultaneously satisfy the application requirements and reduce the sensor network energy consumption. This article deployed a number of sensor nodes to record temperature data. The data was then used to predict the temperatures of some of the sensor node using linear programming. The predictions were able to reduce the node sampling rate and to optimize the node deployment to reduce the sensor energy consumption. This method can compensate for the temporarily disabled nodes. The main objective is to design the objective function and determine the constraint condition for the linear programming. The result based on real experiments shows that this method successfully predicts the values of unknown sensor nodes and optimizes the node deployment. The sensor network energy consumption is also reduced by the optimized node deployment.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
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
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
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
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
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
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
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
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
In this paper, we propose an interactive method for solving the multilevel linear programming problems based on the intuitionistic fuzzy set theory. Firstly, the membership function and the non-membership function are...In this paper, we propose an interactive method for solving the multilevel linear programming problems based on the intuitionistic fuzzy set theory. Firstly, the membership function and the non-membership function are introduced to describe the uncertainty of the decision makers. Secondly, a satisfactory solution is derived by updating the minimum satisfactory degrees with considerations of the overall satisfactory balance among all levels. In addition, the steps of the proposed method are given in this paper. Finally, numerical examples illustrate the feasibility of this method.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
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
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 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
In this article,the authors discuss the optimal conditions of the linear fractionalprogramming problem and prove that a locally optional solution is a globally optional solution and the locally optimal solution can be...In this article,the authors discuss the optimal conditions of the linear fractionalprogramming problem and prove that a locally optional solution is a globally optional solution and the locally optimal solution can be attained at a basic feasible solution withconstraint condition.展开更多
Planning and production optimization within multiple mines or several work sites （entities） mining systems by using fuzzy linear programming （LP） was studied. LP is the most commonly used operations research metho...Planning and production optimization within multiple mines or several work sites （entities） mining systems by using fuzzy linear programming （LP） was studied. LP is the most commonly used operations research methods in mining engineering. After the introductory review of properties and limitations of applying LP, short reviews of the general settings of deterministic and fuzzy LP models are presented. With the purpose of comparative analysis, the application of both LP models is presented using the example of the Bauxite Basin Niksic with five mines. After the assessment, LP is an efficient mathematical modeling tool in production planning and solving many other single-criteria optimization problems of mining engineering. After the comparison of advantages and deficiencies of both deterministic and fuzzy LP models, the conclusion presents benefits of the fuzzy LP model but is also stating that seeking the optimal plan of production means to accomplish the overall analysis that will encompass the LP model approaches.展开更多
In this paper we present a new method combining interior and exterior approaches to solve linear programming problems. With the assumption that a feasible interior solution to the input system is known, this algorithm...In this paper we present a new method combining interior and exterior approaches to solve linear programming problems. With the assumption that a feasible interior solution to the input system is known, this algorithm uses it and appropriate constraints of the system to construct a sequence of the so called station cones whose vertices tend very fast to the solution to be found. The computational experiments show that the number of iterations of the new algorithm is significantly smaller than that of the second phase of the simplex method. Additionally, when the number of variables and constraints of the problem increase, the number of iterations of the new algorithm increase in a slower manner than that of the simplex method.展开更多
基金supported in part by the National High-Tech Research and Development (863) Program of China(No. 2011AA010101)the National Natural Science Foundation of China (Nos. 61103197 and 61073009)+2 种基金the Science and Technology Key Project of Jilin Province(No. 2011ZDGG007)the Youth Foundation of Jilin Province of China (No. 201101035)the Fundamental Research Funds for the Central Universities of China(No. 200903179)
文摘The Internet of Things emphasizes the concept of objects connected with each other, which includes all kinds of wireless sensor networks. An important issue is to reduce the energy consumption in the sensor networks since sensor nodes always have energy constraints. Deployment of thousands of wireless sensors in an appropriate pattern will simultaneously satisfy the application requirements and reduce the sensor network energy consumption. This article deployed a number of sensor nodes to record temperature data. The data was then used to predict the temperatures of some of the sensor node using linear programming. The predictions were able to reduce the node sampling rate and to optimize the node deployment to reduce the sensor energy consumption. This method can compensate for the temporarily disabled nodes. The main objective is to design the objective function and determine the constraint condition for the linear programming. The result based on real experiments shows that this method successfully predicts the values of unknown sensor nodes and optimizes the node deployment. The sensor network energy consumption is also reduced by the optimized node deployment.
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 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 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(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.
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.
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(71471140,71171150,71103135)
文摘In this paper, we propose an interactive method for solving the multilevel linear programming problems based on the intuitionistic fuzzy set theory. Firstly, the membership function and the non-membership function are introduced to describe the uncertainty of the decision makers. Secondly, a satisfactory solution is derived by updating the minimum satisfactory degrees with considerations of the overall satisfactory balance among all levels. In addition, the steps of the proposed method are given in this paper. Finally, numerical examples illustrate the feasibility of this method.
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) ?
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.
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 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.
基金Supported by the Natural Science Foundation of Henan Province（0511012000 0511013600） Supported by the Science Foundation for Pure Research of Natural Science of the Education Department of Henan Province（200512950001）
文摘In this article,the authors discuss the optimal conditions of the linear fractionalprogramming problem and prove that a locally optional solution is a globally optional solution and the locally optimal solution can be attained at a basic feasible solution withconstraint condition.
文摘Planning and production optimization within multiple mines or several work sites （entities） mining systems by using fuzzy linear programming （LP） was studied. LP is the most commonly used operations research methods in mining engineering. After the introductory review of properties and limitations of applying LP, short reviews of the general settings of deterministic and fuzzy LP models are presented. With the purpose of comparative analysis, the application of both LP models is presented using the example of the Bauxite Basin Niksic with five mines. After the assessment, LP is an efficient mathematical modeling tool in production planning and solving many other single-criteria optimization problems of mining engineering. After the comparison of advantages and deficiencies of both deterministic and fuzzy LP models, the conclusion presents benefits of the fuzzy LP model but is also stating that seeking the optimal plan of production means to accomplish the overall analysis that will encompass the LP model approaches.
文摘In this paper we present a new method combining interior and exterior approaches to solve linear programming problems. With the assumption that a feasible interior solution to the input system is known, this algorithm uses it and appropriate constraints of the system to construct a sequence of the so called station cones whose vertices tend very fast to the solution to be found. The computational experiments show that the number of iterations of the new algorithm is significantly smaller than that of the second phase of the simplex method. Additionally, when the number of variables and constraints of the problem increase, the number of iterations of the new algorithm increase in a slower manner than that of the simplex method.
