• Journal of Korean Institute of Industrial Engineers
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• v.17 no.2
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• pp.131-142
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• 1991

The concept of criterion function is proposed as a framework for comparing the geometric and computational characteristics of various nonlinear programming approaches to linear programming such as the method of centers, Karmakar's algorithm and the gravitational method. Also, we discuss various computational issues involved in obtaining an efficient parallel implementation of these methods. Clearly, the most time consuming part in solving a linear programming problem is the direction finding procedure, where we obtain an improving direction. In most cases, finding an improving direction is equivalent to solving a simple optimization problem defined at the current feasible solution. Again, this simple optimization problem can be seen as a least squares problem, and the computational effort in solving the least squares problem is, in fact, same as the effort as in solving a system of linear equations. Hence, getting a solution to a system of linear equations fast is very important in solving a linear programming problem efficiently. For solving system of linear equations on parallel computing machines, an iterative method seems more adequate than direct methods. Therefore, we propose one possible strategy for getting an efficient parallel implementation of an iterative method for solving a system of equations and present the summary of computational experiment performed on transputer based parallel computing board installed on IBM PC.

• Journal of Information Technology Application
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• v.3 no.3
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• pp.25-40
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• 2001

This paper deals with the problem of generating optimal polynomials using Genetic Programming(GP). The polynomial should approximate nonlinear response surfaces. Also, there should be a consideration regarding the size of the polynomial, It is not desirable if the polynomial is too large. To build small or medium size of polynomials that enable to model nonlinear response surfaces, we use the low order Tailor series in the function set of GP, and put the constrain on generating GP tree during the evolving process in order to prevent GP trees from becoming too large size of polynomials. Also, GAGPT(Group of Additive Genetic Programming Trees) is adopted to help achieving such purpose. Two examples are given to demonstrate our method.

• Journal of the Korea Society of Computer and Information
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• v.14 no.2
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• pp.27-35
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• 2009

Integer programming is a very effective technique for searching optimal solution of combinatorial optimization problems. However, its applicability is limited to linear models. In this paper, I propose an effective method for solving a nonlinear optimization problem by integrating the powerful search performance of integer programming and the flexibility of neighborhood search algorithms. In the first phase, integer programming is executed with subproblem which can be represented as a linear form from the given problem. In the second phase, a neighborhood search algorithm is executed with the whole problem by taking the result of the first phase as the initial solution. Through the experimental results using a nonlinear maximal covering problem, I confirmed that such a simple integration method can produce far better solutions than a neighborhood search algorithm alone. It is estimated that the success is primarily due to the powerful performance of integer programming.

• Journal of Biosystems Engineering
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• v.8 no.2
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• pp.69-85
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• 1983

Nonlinear Goal Programming(NGP)이 Multiple Objective Decision Making(MODM) 문제(問題)를 적정화(適正化)할 수 있는 방법(方法)으로 소개(紹介)가 되었다. 그리고 6 가지의 벼 조제(調製) 및 저장시설(貯藏施設)을 분석(分析)한 후, NGP에 의(依)하여 적정시설설계(適正施設設計)를 하기 위하여 Model Systems를 개발(開發)하고 그에 의(依)하여 MODM의 수학적(數學的) 모형(模型)을 개발(開發)하였다.

• Structural Engineering and Mechanics
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• v.7 no.5
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• pp.485-502
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• 1999

Using the continuous Hopfield network model as the basis to solve the general crisp and fuzzy constrained optimization problem is presented and examined. The model lies in its transformation to a parallel algorithm which distributes the work of numerical optimization to several simultaneously computing processors. The method is applied to different structural engineering design problems that demonstrate this usefulness, satisfaction or potential. The computing algorithm has been given and discussed for a designer who can program it without difficulty.

• IE interfaces
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• v.1 no.1
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• pp.17-26
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• 1988

This paper describes a nonlinear goal programming approach to the optimal composition of composite solid propellant taking multiple characteristics into consideration synchronously. The nonlinear goal programming model with response functions, restrictions and the optimal value of each characteristic is developed using Scheffe's "Experiments with mixtures" and preference weighting system. Objective functions are described based on process, performance and assurance characteristics. The systematic approach to optimal composition in this study is proved efficient through a CTPB-AL-AP propellant which is one of composite solid propellant systems.

• Journal of the Korean Operations Research and Management Science Society
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• v.34 no.4
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• pp.153-163
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• 2009

Unlike the mean-variance approach, the stochastic dominance approach is to form a portfolio that stochastically dominates a predetermined benchmark portfolio such as KOSPI. This study is to search a set of portfolio weights for the first-order stochastic dominance with maximum expected return by managing the constraint set and the objective function separately. A nonlinear programming algorithm was developed and tested with promising results against Korean stock market data sets.

• Journal of Biosystems Engineering
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• v.9 no.1
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• pp.46-52
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• 1984

MODM(Multiple Objective Decision Making) 문제(問題)로서의 벼 건조(乾燥) 및 저장시설(貯藏施設)의 설계문제(設計問題)에 NGP(Nonlinear Goal Programming)를 이용(利用)하여 어떻게 적정화(適正化)할 수 있는가를 예제(例題)를 통하여 제시(提示)한 후, $1,762m^2$의 수확량(收穫量)에 대한 6가지의 벼 건조(乾燥) 및 저장시설(貯藏施設)에 대한 각각의 적정(適正)시스템을 제시(提示)하였다.

• Journal of the Korean Operations Research and Management Science Society
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• v.7 no.1
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• pp.11-16
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• 1982

A method is described for the solution of a linearly constrained program with parametric nonlinear objective function. The algorithm proposed in this paper may be regarded as an extension of the simplex method for parametric linear programming. Namely, it specifies the basis at each stage such that feasibility ana optimality of the original problem are satisfied by the optimal solution of the reduced parametric problem involving only nonbasic variables. It is shown that under appropriate assumptions the algorithm is finite. Parametric procedures are also indicated for solving each reduced parametric problem by maintaining the Kuhn-Tucker conditions as the parameter value varies.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10b
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• pp.474-477
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• 1996

In this paper, a numerical method is developed to solve the 2 dimensional missile/target persuit-evasion game. The numerical solver for the problem is composed of two parts: parametrization of the kinematic equations of motion using collocation and optimization of the parametrized minimax problem using a nonlinear programming. A numerical example is solved to verify the performance of the proposed numerical scheme.