• Journal of the Korea Convergence Society
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• v.6 no.5
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• pp.227-232
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• 2015

The fuzzy linear programming(FLP) is the useful approach to many real world problems under uncertainty. This paper deals with a FLP whose objective value is fuzzy. And the right hand sides of convergent equality constraints are fuzzy numbers. We assume that the membership function of the objective value is piecewise linear and those of the right hand side are trapezoidal. Each of these trapezoidal functions can be algebraically replaced with three linear functions. Then the FLP problem is transformed into the Zimmermann's symmetric model. The fuzzy solution based on the max-min rule can be obtained by solving the crisp linear programming problem derived from the symmetric model. A numerical example has illustrated our approach. The application of our approach to the inconsistent linear system can enable generate us to get define the useful and flexible inexact solutions within acceptable tolerance. Further research is required to generalize the membership function.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.9
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• pp.2800-2811
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• 1996

The deformation of a structure shall be called homologous, if a given geometrical relation holds, for a given number of structural points, before, during, and after the deformation. Some researchers have utilized the idea on structural design with finite element method. The approaches use the decomposition of the FEM equation or equality of eqality equations to obtain homologous deformation. However, weight reduction and response constraints such as stress, displacement or natural frequency cannot be considered by those theories. An optimization method solving the above problems is suggested to gain homologous deformation. Homology constraints can be considered under multiple loadindg conditions as well as a single loading condition. Homology index is defined for the multiple loading conditions Examples are solved to present the performances of the method.

• Kyungpook Mathematical Journal
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• v.58 no.2
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• pp.333-346
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• 2018

An approximation scheme utilizing Bezier curves is considered for solving time-delayed optimal control problems with terminal inequality constraints. First, the problem is transformed, using a $P{\acute{a}}de$ approximation, to one without a time-delayed argument. Terminal inequality constraints, if they exist, are converted to equality constraints. A computational method based on Bezier curves in the time domain is then proposed for solving the obtained non-delay optimal control problem. Numerical examples are introduced to verify the efficiency and accuracy of the proposed technique. The findings demonstrate that the proposed method is accurate and easy to implement.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.50 no.9
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• pp.406-410
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• 2001

This paper develops an efficient evolutionary programming based algorithm for solving the environmentally constrained economic dispatch problem in thermal power system. The proposed algorithm can deal with the power balance constraints and the emission constraints which are equality and inequality constraints, respectively. Numerical results show that the proposed algorithm can provide superior solutions within reasonable time through its application to a test system.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.15 no.11 s.104
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• pp.1255-1261
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• 2005

The dynamic contact model of a beam that contacts to a rigid wall in a reactor core was studied. The gap between the beam and contact wall results in dynamic contact accompanying inequality constraints. The inequality constraints can be relieved to an equality constraint problem by introducing a convex Penalty function. In this work, a beam with contact condition is formulated using quasi-convex penalty function and numerically solved. General coordinate solution is adopted to raise computational efficiency. Also nonlinearity is examined In the beam contacting to a rigid wall.

• Journal of the Korean Society of Safety
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• v.30 no.3
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• pp.32-37
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• 2015

In the fields of plant layout optimization, the main goal is to minimize the construction cost including pipelines as satisfying all constraints such as safety and operating issues. However, what is the lacking of considerations in previous researches is to consider proper safety and maintenance spaces for a complex plant. Based on the mathematical programming, MILP(Mixed Integer Linear Programming) problems including various constraints can be formulated to find the optimal solution which is to achieve the best economic benefits. The objective function of this problem is the sum of piping cost, pumping cost and area cost. In general, many conventional optimization solvers are used to find a MILP problem. However, it is really hard to solve this problem due to complex inequality and equality constraints, since it is impossible to use the derivatives of objective functions and constraints. To resolve this problem, the PSO (Particle Swarm Optimization), which is one of the representative sampling approaches and does not need to use derivatives of equations, is employed to find the optimal solution considering various complex constraints in this study. The EO (Ethylene Oxide) plant is tested to verify the efficacy of the proposed method.

• 전기의세계
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• v.30 no.6
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• pp.375-385
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• 1981

New algorithms are derived for nonlinear programming problems which are characterized by their large variables and equality and inequality constraints. The algorithms are based upon the introduction of the Dependent-Variable-Elimination method, Independent-Variable-Reduction method, Optimally-Ordered-Triangular-Factorization method, Equality-Inequality-Sequential-Satisfaction method, etc. For a case study problem relating to the optimal determination of load flow in a 10-bus, 13-line sample power system, several approaches are undertaken, such as SUMT, Lagrange's Multiplier method, sequential applications of linear and quadratic programming method. For applying the linear programming method, the conventional simplex algorithm is modified to the large-system-oriented one by the introduction of the Two-Phase method and Variable-Upper-Bounding method, thus resulting in remarkable savings in memory requirements and computing time. The case study shows the validity and effectivity of the algorithms presented herein.

• Journal of Mechanical Science and Technology
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• v.20 no.5
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• pp.612-620
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• 2006

This paper proposes an optimal trajectory generation method for biped robots for walking up-and-down stairs using a Real-Coded Genetic Algorithm (RCGA). The RCGA is most effective in minimizing the total consumption energy of a multi-dof biped robot. Each joint angle trajectory is defined as a 4-th order polynomial of which the coefficients are chromosomes or design variables to approximate the walking gait. Constraints are divided into equalities and inequalities. First, equality constraints consist of initial conditions and repeatability conditions with respect to each joint angle and angular velocity at the start and end of a stride period. Next, inequality constraints include collision prevention conditions of a swing leg, singular prevention conditions, and stability conditions. The effectiveness of the proposed optimal trajectory is shown in computer simulations with a 6-dof biped robot model that consists of seven links in the sagittal plane. The optimal trajectory is more efficient than that generated by the Modified Gravity-Compensated Inverted Pendulum Mode (MGCIPM). And various trajectories generated by the proposed GA method are analyzed from the viewpoint of the consumption energy: walking on even ground, ascending stairs, and descending stairs.

• Journal of Institute of Control, Robotics and Systems
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• v.21 no.6
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• pp.560-564
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• 2015

This paper presents a design method of a static output feedback controller for continuous T-S fuzzy systems via parallel distributed compensation (PDC). The existence condition of a set of static output feedback gains is represented in terms of linear matrix inequalities (LMIs). The sufficient condition presented here does not need any transformation matrices and equality constraints and is less conservative than the previous results seen in [20].

• Communications for Statistical Applications and Methods
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• v.5 no.3
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• pp.581-589
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• 1998

An algorithm is proposed for the $L_1$-estimation with linear equality and inequality constraints in linear regression model. The algorithm employs a linear scaling transformation to obtain the optimal solution of linear programming type problem. And a special scheme is used to maintain the feasibility of the updated solution at each iteration. The convergence of the proposed algorithm is proved. In addition, the updating and orthogonal decomposition techniques are employed to improve the computational efficiency and numerical stability.