• Journal of the military operations research society of Korea
• /
• v.11 no.2
• /
• pp.53-63
• /
• 1985

This paper presents a multi-costraint optimization model for redundant system reliability. The optimization model is usually formulated as a nonlinear integer programming (NIP) problem. This paper reformulates the NIP problem into a linear integer programming (LIP) problem. Then an efficient 'Branch and Straddle' algorithm is proposed to solve the LIP problem. The efficiency of this algorithm stems from the simultaneous handling of multiple variables, unlike in ordinary branch and bound algorithms. A numerical example is given to illustrate this algorithm.

• Journal of applied mathematics & informatics
• /
• v.20 no.1_2
• /
• pp.391-399
• /
• 2006

In order to solve the optimization problem of designing the trajectory of three-dimensional horizontal well, we establish a multi-phase, nonlinear, stochastic dynamic system of the trajectory of horizontal well. We take the precision of hitting target and the total length of the trajectory as the performance index. By the integration of the state equation, this model can be transformed into a nonlinear stochastic programming. We discuss here the necessary conditions under which a local solution exists and depends in a continuous way on the parameter (perturbation). According to the properties we propose a revised Hooke-Jeeves algorithm and work out corresponding software to calculate the local solution of the nonlinear stochastic programming and the expectancy of the performance index. The numerical results illustrate the validity of the proposed model and algorithm.

• Journal of Korean Society for Quality Management
• /
• v.9 no.2
• /
• pp.31-36
• /
• 1981

This paper deals with the reliability optimization of parallel - in - series system subject to several linear constraints. The model of nonlinear constrained optimization is transformed to a saddle point problem by using Lagrange multipliers. Then Newton - Raphson method is used to solve the resulting problem and these step - by - step solution procedures are programmed in Basic Level II of micro - computer TRS-80. An example which has two linear constraints is solved and the results are analyzed.

• Structural Engineering and Mechanics
• /
• v.6 no.8
• /
• pp.857-870
• /
• 1998

This paper deals with a special class of inverse problems in discrete structural plasticity involving the identification of elastic limits and hardening moduli on the basis of information on displacements. The governing equations lead naturally to a special and challenging optimization problem known as a Mathematical Program with Equilibrium Constraints (MPEC), a key feature of which is the orthogonality of two sign-constrained vectors or so-called "complementarity" condition. We investigate numerically the application of two simple algorithms, both based on the use of the general purpose nonlinear programming code CONOPT accessed via the GAMS modeling language, for solving the suitably reformulated problem. Application is illustrated by means of two numerical examples.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.50 no.4
• /
• pp.180-187
• /
• 2001

This paper proposes an efficient evolutionary programming algorithm for solving a generation expansion planning(GEP) problem known as a highly-nonlinear dynamic problem. Evolutionary programming(EP) is an optimization algorithm based on the simulated evolution (mutation, competition and selection). In this paper, new algorithm is presented to enhance the efficiency of the EP algorithm for solving the GEP problem. By a domain mapping procedure, yearly cumulative capacity vectors are transformed into one dummy vector, whose change can yield a kind of trend in the cost value. To validate the proposed approach, this algorithm is tested on two cases of expansion planning problems. Simulation results show that the proposed algorithm can provide successful results within a resonable computational time compared with conventional EP and dynamic programming.

• Journal of applied mathematics & informatics
• /
• v.27 no.1_2
• /
• pp.123-137
• /
• 2009

A multiobjective variational problem involving higher order derivatives is considered and Fritz-John and Karush-Kuhn-Tucker type optimality conditions for this problem are derived. As an application of Karush-Kuhn-Tucker optimality conditions, Wolfe type dual to this variational problem is constructed and various duality results are validated under generalized invexity. Some special cases are mentioned and it is also pointed out that our results can be considered as a dynamic generalization of the already existing results in nonlinear programming.

• Journal of the Korean Society of Safety
• /
• v.12 no.1
• /
• pp.122-128
• /
• 1997

A new approach, called "two-phase approach", has been proposed In this study. Using this approach to solve MONLP(multiobjective nonlinear programming problem), the solution process is divied into two phase. In the first phase, the min-operator is used to aggregate the membership degree of fuzzy goals and constraints. In the second phase, the $\gamma$-operator is used to test and find an efficient solution in the sense of nondominated. It has been shown that no matter what the solution of the problem is unique or not, an efficient solution can be always obtained at the second phase. The proposed approach can be applied to industrial safety problem with multiobjective problems. On the basis of proposed approach, an illustrative numerical example is presented.presented.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2007.11a
• /
• pp.556-559
• /
• 2007

The notion of linearity is fundamental in science and engineering. Much of system and control theory is based on the analysis of linear system, which does not care whether it is nonlinear and complex. The dynamic programming is one of concerned technology when users are interested in choosing best choice from system operation for nonlinear or dynamic system‘s performance and control problem. In this paper, we will introduce the dynamic programming which is based on discrete system. When the discrete system is constructed with discrete state, transfer between states, and the event to induct transfer, the discrete system can describe the system operation as dynamic situation or symbolically at the logical point of view. We will introduce technologies which are related with controllable of Controlled Markov Chain as shown example of simple game. The dynamic programming will be able to apply to optimal control part which has adaptable performance in the discrete system.

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

• Journal of applied mathematics & informatics
• /
• v.26 no.1_2
• /
• pp.75-106
• /
• 2008

In this paper, we derive necessary optimality conditions for a continuous programming problem in which both objective and constraint functions contain support functions and is, therefore, nondifferentiable. It is shown that under generalized invexity of functionals, Karush-Kuhn-Tucker type optimality conditions for the continuous programming problem are also sufficient. Using these optimality conditions, we construct dual problems of both Wolfe and Mond-Weir types and validate appropriate duality theorems under invexity and generalized invexity. A mixed type dual is also proposed and duality results are validated under generalized invexity. A special case which often occurs in mathematical programming is that in which the support function is the square root of a positive semidefinite quadratic form. Further, it is also pointed out that our results can be considered as dynamic generalizations of those of (static) nonlinear programming with support functions recently incorporated in the literature.