• Journal of applied mathematics & informatics
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• v.33 no.3_4
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• pp.387-399
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• 2015

In this paper, a new smoothing approximation to the l₁ exact penalty function for constrained optimization problems (COP) is presented. It is shown that an optimal solution to the smoothing penalty optimization problem is an approximate optimal solution to the original optimization problem. Based on the smoothing penalty function, an algorithm is presented to solve COP, with its convergence under some conditions proved. Numerical examples illustrate that this algorithm is efficient in solving COP.

• Nuclear Engineering and Technology
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• v.56 no.2
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• pp.520-525
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• 2024

The optimization design problem of nuclear reactor radiation shield is a typical multi-objective optimization problem with almost 10 sub-objectives and the sub-objectives are always demanded to be under tolerable limits. In this paper, a design method combining multi-objective optimization algorithms with paralleling discrete ordinate transportation code is developed and applied to shield design of the Savannah nuclear reactor. Three approaches are studied for light-weighted and compact design of radiation shield. Comparing with directly optimization with 10 objectives and the single-objective optimization, the approach by setting sub-objectives representing weight and volume as optimization objectives while treating other sub-objectives as constraints has the best performance, which is more suitable to reactor shield design.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.1
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• pp.41-55
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• 2024

The nonconvex and nonsmooth optimization problem has been widely applicable in image processing and machine learning. In this paper, we propose an extension of the proximal iteratively reweighted ℓ₁ algorithm for nonconvex and nonsmooth minmization problem. We assume the co-coerciveness of a term of objective function instead of Lipschitz gradient condition, which is generalized property of Lipschitz continuity. We prove the global convergence of the proposed algorithm. Numerical results show that the proposed algorithm converges faster than original proximal iteratively reweighed algorithm and existing algorithms.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.63 no.9
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• pp.1266-1272
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• 2014

We define the mobile robot navigation problem as an optimization problem to minimize the cost function with the pose error between the goal position and the position of a mobile robot. Using Gauss-Newton method for the optimization, the optimal speeds of the left and right wheels can be found as the solution of the optimization problem. Especially, the rotational speed of wheels of a mobile robot can be directly related to the overall speed of a mobile robot using the Jacobian derived from the kinematic model. When the robot detects the obstacle using sensors, the sub-goal switching method is adopted for the efficient obstacle avoidance during the navigation. The performance was evaluated using the simulation and the simulation results show the validity of the proposed method.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.10
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• pp.1597-1604
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• 2001

Alternative computational scheme is presented fur reliability based optimal design using a modified advanced first order second moment (AFOSH) method. Both design variables and design parameters are considered as random variables about their nominal values. Each probability constraint is transformed into a sub -optimization problem and then is resolved with the modified Hasofer- Lind-Rackwitz-Fiessler (HL-RF) method for computational efficiency and convergence. A method of design sensitivity analysis for probability constraint is presented and tested through simple examples. The suggested method is examined by solving several examples and the results are compared with those of other methods.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 2004.04a
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• pp.143-150
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• 2004

An optimum design problem for endosseous implant in dentistry is studied to find best implant design. An optimum design problem is formulated to reduce stresses arising at the cortical as well as cancellous bones, in which sufficient design parameters are chosen for design definition that encompasses major implants in popular use. Optimization at once (OAO) with the large number of design variables, however, causes too costly solution or even failure to converge. A concept of multilevel optimization (MLO) is employed to this end, which is to group the design variables of similar nature, solve the sub-problem of smaller size for each group in sequence, and this is iterated until convergence. Each sub-problem is solved based on the response surface method (RSM) due to its efficiency for small sized problem.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.7
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• pp.940-947
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• 2004

In this paper, an optimum design problem for endosseous implant in dentistry is studied to find best implant design. An optimum design problem is formulated to reduce stresses arising at the cortical as well as cancellous bones, in which sufficient design parameters are chosen for design definition that encompasses major implants in popular use. Optimization at once (OAO) with the large number of design variables, however, causes too costly solution or even failure to converge. A concept of multilevel optimization (MLO) is employed to this end, which is to group the design variables of similar nature, solve the sub-problem of smaller size for each group in sequence, and this is iterated until convergence. Each sub-problem is solved based on the response surface method (RSM) due to its efficiency for small sized problem.

• Computers and Concrete
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• v.26 no.1
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• pp.1-10
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• 2020

In this paper, a procedure for automated optimized design of reinforced concrete frames has been presented. The procedure consists of formulation and solution of the design problem in the form of an optimization problem. The minimization of total cost of R/C frame has been taken as the objective of optimization problem. In this research, consistent approximation method is applied to explicitly formulate constraints and objective function in terms of the design variables. In the presented method, the primary optimization problem is replaced with a sequence of explicit sub-problems. Each sub-problem is efficiently solved using the Sequential Quadratic Programming (SQP) method. The proposed method is demonstrated through a four-story frame and an eight-story frame, and the optimum results are compared with those in the available literature. It is shown that the proposed method can be easily applied to obtain rational, reliable, economical and practical designs for Reinforced Concrete Moment Resisting Frames (RCMRFs) while it is converged after a few analyses.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.7 no.2
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• pp.288-307
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• 2013

This paper formulates resource allocation for decode-and-forward (DF) relay assisted multi-cell orthogonal frequency division multiple (OFDM) networks as an optimization problem taking into account of inter-cell interference and users fairness. To maximize the transmit rate of system we propose a joint interference coordination, subcarrier and power allocation algorithm. To reduce the complexity, this semi-distributed algorithm divides the primal optimization into three sub-optimization problems, which transforms the mixed binary nonlinear programming problem (BNLP) into standard convex optimization problems. The first layer optimization problem is used to get the optimal subcarrier distribution index. The second is to solve the problem that how to allocate power optimally in a certain subcarrier distribution order. Based on the concept of equivalent channel gain (ECG) we transform the max-min function into standard closed expression. Subsequently, with the aid of dual decomposition, water-filling theorem and iterative power allocation algorithm the optimal solution of the original problem can be got with acceptable complexity. The third sub-problem considers dynamic co-channel interference caused by adjacent cells and redistributes resources to achieve the goal of maximizing system throughput. Finally, simulation results are provided to corroborate the proposed algorithm.

• Journal of Institute of Control, Robotics and Systems
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• v.11 no.2
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• pp.144-151
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• 2005

We propose an optimization method to reduce the assembly time of chip mounters. Feeder arrangement and assembly sequence are determined considering the multiple feeder assignment. The problem is divided into two sub-problems: feeder arrangement problem and assembly sequence problem. We present mathematical model for each sub-problem. The clustering algorithm and assignment algorithm are applied to solve the feeder arrangement problem. The assignment algorithm and connection algorithm are applied to solve the assembly sequence problem. Simulation results are then presented to verity the usefulness of the proposed method.