• Nonlinear Functional Analysis and Applications
• /
• v.26 no.4
• /
• pp.811-837
• /
• 2021

In this paper, we propose a new conjugate gradient method for solving unconstrained optimization models. By using exact and strong Wolfe line searches, the proposed method possesses the sufficient descent condition and global convergence properties. Numerical results show that the proposed method is efficient at small, medium, and large dimensions for the given test functions. In addition, the proposed method was applied to solve practical application problems in portfolio selection.

• Journal of applied mathematics & informatics
• /
• v.20 no.1_2
• /
• pp.239-254
• /
• 2006

An efficient descent method for unconstrained optimization problems is line search method in which the step size is required to choose at each iteration after a descent direction is determined. There are many ways to choose the step sizes, such as the exact line search, Armijo line search, Goldstein line search, and Wolfe line search, etc. In this paper we propose a new inexact line search for a general descent method and establish some global convergence properties. This new line search has many advantages comparing with other similar inexact line searches. Moreover, we analyze the global convergence and local convergence rate of some special descent methods with the new line search. Preliminary numerical results show that the new line search is available and efficient in practical computation.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.27 no.11
• /
• pp.1809-1814
• /
• 2003

Differential evolution (DE) algorithm is presented and applied to global optimization in this research. DE suggested initially fur the solution to Chebychev polynomial fitting problem is similar to genetic algorithm(GA) including crossover, mutation and selection process. However, differential evolution algorithm is simpler than GA because it uses a vector concept in populating process. And DE turns out to be converged faster than CA, since it employs the difference information as pseudo-sensitivity In this paper, a trial vector and its control parameters of DE are examined and unconstrained optimization problems of highly nonlinear multimodal functions are demonstrated. To illustrate the efficiency of DE, convergence rates and robustness of global optimization algorithms are compared with those of simple GA.

• Journal of applied mathematics & informatics
• /
• v.5 no.3
• /
• pp.701-716
• /
• 1998

In this paper we develop algorithms in programming lan-guage SCHEME for implementation of the main first order gradient techniques for unconstrained optimization. Implementation of the de-scent techniques which use non-optimal descent steps as well as imple-mentation of the optimal descent techniques are described. Also we investigate implementation of the global problem called optimization along a line. Developed programs are effective and simpler with re-spect to the corresponding in the procedural programming languages. Several numerical examples are reported.

• Journal of applied mathematics & informatics
• /
• v.34 no.1_2
• /
• pp.157-165
• /
• 2016

In this paper, we develop a new hybridization conjugate gradient method for solving the unconstrained optimization problem. Under mild assumptions, we get the sufficient descent property of the given method. The global convergence of the given method is also presented under the Wolfe-type line search and the general Wolfe line search. The numerical results show that the method is also efficient.

• Proceedings of the KSME Conference
• /
• 2000.04a
• /
• pp.725-730
• /
• 2000

Genetic algorithms based on the theory of natural selection, have been applied to many different fields, and have proven to be relatively robust means to search for global optimum and handle discontinuous or even discrete data. Genetic algorithms are widely used for unconstrained optimization problems. However, their application to constrained optimization problems remains unsettled. The most prevalent technique for coping with infeasible solutions is to penalize a population member for constraint violation. But, the weighting of a penalty for a particular problem constraint is usually determined in the heuristic way. Therefore this paper proposes, the effective technique for handling constraints, the ranking penalty method and hybrid genetic algorithms. And this paper proposes dynamic mutation tate to maintain the diversity in population. The effectiveness of the proposed algorithm is tested on several test problems and results are discussed.

• Journal of Institute of Control, Robotics and Systems
• /
• v.6 no.4
• /
• pp.268-275
• /
• 2000

The increasing technological demands of today call for complex systems, which in turn involve a series of optimization problems with some equality or inequality constraints. In this paper, we presents a real-coded genetic algorithm(RCGA) as an optimization tool which is implemented by three genetic operators based on real coding representation. Through a lot of simulation works, the optimum settings of its control parameters are obtained on the basis of global off-line robustness for use in off-line applications. Two optimization problems are Presented to illustrate the usefulness of the RCGA. In case of a constrained problem, a penalty strategy is incorporated to transform the constrained problem into an unconstrained problem by penalizing infeasible solutions.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• v.22 no.4
• /
• pp.811-825
• /
• 1998

An approximate line search is presented for dynamic response optimization with Augmented Lagrange Multiplier(ALM) method. This study empolys the approximate a augmented Lagrangian, which can improve the efficiency of the ALM method, while maintaining the global convergence of the ALM method. Although the approximate augmented Lagragian is composed of only the linearized cost and constraint functions, the quality of this approximation should be good since an approximate penalty term is found to have almost second-order accuracy near the optimum. Typical unconstrained optimization algorithms such as quasi-Newton and conjugate gradient methods are directly used to find exact search directions and a golden section method followed by a cubic polynomial approximation is empolyed for approximate line search since the approximate augmented Lagrangian is a nonlinear function of design variable vector. The numberical performance of the proposed approach is investigated by solving three typical dynamic response optimization problems and comparing the results with those in the literature. This comparison shows that the suggested approach is robust and efficient.

• Journal of Power Electronics
• /
• v.4 no.3
• /
• pp.127-137
• /
• 2004

This paper introduces a hybrid induction motor control using a genetically optimized pseudo-on-line method. Optimization results from the use of a look-up table based on genetic algorithms to find the global optimum of an unconstrained optimization problem. The approach to induction motor control includes a pseudo-on-line procedure that optimally estimates parameters of a fuzzy PID (FPID) controller. The proposed hybrid genetic fuzzy PID (GFPID) controller is applied to speed control of a 3-phase induction motor and its computer simulation is carried out. Simulation results show that the proposed controller performs better than conventional FPID and PID controllers. The contribution of this paper is the introduction of a high performance hybrid form of induction motor control that makes on-line and real-time control of the drive system possible.

• Steel and Composite Structures
• /
• v.21 no.3
• /
• pp.605-628
• /
• 2016

The energy absorption characteristics of diamond core sandwich cylindrical columns under axial crushing process depend greatly on the amount of material which participates in the plastic deformation. Both the single-objective and multi-objective optimizations are performed for columns under axial crushing load with core thickness and helix pitch of the honeycomb core as design variables. Models are optimized by multi-objective particle swarm optimization (MOPSO) algorithm to achieve maximum specific energy absorption (SEA) capacity and minimum peak crushing force (PCF). Results show that optimization improves the energy absorption characteristics with constrained and unconstrained peak crashing load. Also, it is concluded that the aluminum tube has a better energy absorption capability rather than steel tube at a certain peak crushing force. The results justify that the interaction effects between the honeycomb and column walls greatly improve the energy absorption efficiency. A ranking technique for order preference (TOPSIS) is then used to sort the non-dominated solutions by the preference of decision makers. That is, a multi-criteria decision which consists of MOPSO and TOPSIS is presented to find out a compromise solution for decision makers. Furthermore, local and global sensitivity analyses are performed to assess the effect of design variable values on the SEA and PCF functions in design domain. Based on the sensitivity analysis results, it is concluded that for both models, the helix pitch of the honeycomb core has greater effect on the sensitivity of SEA, while, the core thickness has greater effect on the sensitivity of PCF.