• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1993년도 한국자동제어학술회의논문집(국내학술편); Seoul National University, Seoul; 20-22 Oct. 1993
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• pp.1095-1098
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• 1993

This paper presents linear programming neural networks for job-shop scheduling. The starting times of tasks and constraints are formulated as the linear programming problem. A modified Hopfield neural network is proposed for solving job-shop scheduling.

• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.121-144
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• 2005

In this paper, we propose unconstrained and constrained posynomial Geometric Programming (GP) problem with negative or positive integral degree of difficulty. Conventional GP approach has been modified to solve some special type of GP problems. In specific case, when the degree of difficulty is negative, the normality and the orthogonality conditions of the dual program give a system of linear equations. No general solution vector exists for this system of linear equations. But an approximate solution can be determined by the least square and also max-min method. Here, modified form of geometric programming method has been demonstrated and for that purpose necessary theorems have been derived. Finally, these are illustrated by numerical examples and applications.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제6권3호
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• pp.232-239
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• 2006

This paper is for applying interactive fuzzy linear programming for the problem of product mix planning, which is one of the aggregate planning problem. We developed a modified algorithm, which has two-phase approach for interactive fuzzy linear programming to get a better solution. Adding two-phase method, we expect to obtain not only the highest membership degree, but also a better utilization of each constrained resource.

• 한국경영과학회지
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• 제17권1호
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• pp.3-16
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• 1992

We present a modified Tank and Hopfield's neural network model for solving Linear Programming problems. We have found the fact that the Tank and Hopfield's neural circuit for solving Linear Programming problems has some difficulties in guaranteeing convergence, and obtaining both the primal and dual optimum solutions from the output of the circuit. We have identified the exact conditions in which the circuit stops at an interior point of the feasible region, and therefore fails to converge. Also, proper scaling of the problem parameters is required, in order to obtain a feasible solution from the circuit. Even after one was successful in getting a primal optimum solution, the output of the circuit must be processed further to obtain a dual optimum solution. The modified model being proposed in the paper is designed to overcome such difficulties. We describe the modified model and summarize our computational experiment.

• Journal of applied mathematics & informatics
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• 제9권2호
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• pp.717-730
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• 2002

In this paper we use measure theory to solve a wide range of the nonlinear programming problems. First, we transform a nonlinear programming problem to a classical optimal control problem with no restriction on states and controls. The new problem is modified into one consisting of the minimization of a special linear functional over a set of Radon measures; then we obtain an optimal measure corresponding to functional problem which is then approximated by a finite combination of atomic measures and the problem converted approximately to a finite-dimensional linear programming. Then by the solution of the linear programming problem we obtain the approximate optimal control and then, by the solution of the latter problem we obtain an approximate solution for the original problem. Furthermore, we obtain the path from the initial point to the admissible solution.

• 산업경영시스템학회지
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• 제12권20호
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• pp.97-104
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• 1989

본 연구는 계층구조를 갖는 시스템의 각 목적함수들에 퍼지(FUZZY)집합 개념을 적용한 이단계 선형계획 모형을 다목적계획법으로 다루었다. 선형멤버쉽 함수를 이용하여 전형적인 Bi-level Linear Programming Problem(BLPP)으로 변형시켰으며, 기존의 BLPP 해법을 이용한 변형된 해법을 주시하고 예제를 통한 계산결과를 제시하였다. 퍼지이단계선형계층 (FBLPP)은 BLPP보다 실제환경을 자연스럽게 묘사할 수 있다. FBLPP는 각 의사결정자가 다목적함수를 갖는 다목적 이단계수리계획 모형의 유효해를 구하는데 이용할 수 있다.

• 대한전기학회:학술대회논문집
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• 대한전기학회 1993년도 하계학술대회 논문집 A
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• pp.221-223
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• 1993

The Hopfield model is defined as an adaptive dynamic system. In this paper we propose a modified neural network which is capable of solving linear programming problems and a set of linear equations. The model is directly implemented from the given system, and solves the problem without calculating the inverse of the matrices. We get the better stability results by the addition of scaling property and by using the nonlinearities in the linear programming neural networks.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2001년도 하계학술대회 논문집 A
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• pp.190-193
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• 2001

This paper presents a linear programming based Optimal Reactive Power Dispatch (ORPD) problem using modified sensitivity method. The proposed model minimizes the real power losses and improves the voltage profiles in the system with consideration of voltage and reactive power constraints. The method employs modified sensitivity relationships of power systems to establish both the objective function for minimizing the system losses and the system performance sensitivities relating dependent and control variables. The proposed algorithm has been evaluated with the IEEE 6-bus and IEEE 30-bus systems.

• Journal of applied mathematics & informatics
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• 제25권1_2호
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• pp.231-244
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• 2007

In this paper, we use measure theory for considering asymptotically stable of an autonomous system [1] of first order nonlinear ordinary differential equations(ODE's). First, we define a nonlinear infinite-horizon optimal control problem related to the ODE. Then, by a suitable change of variable, we transform the problem to a finite-horizon nonlinear optimal control problem. Then, the problem is modified into one consisting of the minimization of a linear functional over a set of positive Radon measures. The optimal measure is approximated by a finite combination of atomic measures and the problem converted to a finite-dimensional linear programming problem. The solution to this linear programming problem is used to find a piecewise-constant control, and by using the approximated control signals, we obtain the approximate trajectories and the error functional related to it. Finally the approximated trajectories and error functional is used to for considering asymptotically stable of the original problem.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.97-113
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• 2004

In this paper we shall study moving boundary problems, and we introduce an approach for solving a wide range of them by using calculus of variations and optimization. First, we transform the problem equivalently into an optimal control problem by defining an objective function and artificial control functions. By using measure theory, the new problem is modified into one consisting of the minimization of a linear functional over a set of Radon measures; then we obtain an optimal measure which is then approximated by a finite combination of atomic measures and the problem converted to an infinite-dimensional linear programming. We approximate the infinite linear programming to a finite-dimensional linear programming. Then by using the solution of the latter problem we obtain an approximate solution for moving boundary function on specific time. Furthermore, we show the path of moving boundary from initial state to final state.