• Korean Journal of Computational Design and Engineering
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• v.15 no.1
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• pp.24-32
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• 2010

This paper introduces a B-spline based branch & bound algorithm for global optimization. The branch & bound is a well-known algorithm paradigm for global optimization, of which key components are the subdivision scheme and the bound calculation scheme. For this, we consider the B-spline hypervolume to approximate an objective function defined in a design space. This model enables us to subdivide the design space, and to compute the upper & lower bound of each subspace where the bound calculation is based on the LHS sampling points. We also describe a search tree to represent the searching process for optimal solution, and explain iteration steps and some conditions necessary to carry out the algorithm. Finally, the performance of the proposed algorithm is examined on some test problems which would cover most difficulties faced in global optimization area. It shows that the proposed algorithm is complete algorithm not using heuristics, provides an approximate global solution within prescribed tolerances, and has the good possibility for large scale NP-hard optimization.

• Journal of Korea Multimedia Society
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• v.13 no.12
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• pp.1798-1804
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• 2010

TCP with AIMD mechanism, one of the most popular protocols in internet, can solve congestion control in wired networks. This protocol, however, is not efficient in wireless networks. This paper proposes a new mechanism namely General AIMD with Congestion Window Upper Bound in which congestion window is limited by an upper bound. By applying optimization theory, we find an optimal policy for congestion window upper bound to maximize network throughput.

• Proceedings of the KSME Conference
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• 2001.06a
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• pp.734-739
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• 2001

In this paper, an algorithm for stacking sequence optimization which deals with discrete ply angles is used for optimization of composite laminated plates. To handle discrete ply angles, the branch and bound method is modified. Numerical results show that the optimal stacking sequence is found with fewer evaluations of objective function than expected with the size of feasible region, which shows the algorithm can be effectively used for layup optimization of composite laminates..

• Proceedings of the KSME Conference
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• 2003.04a
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• pp.420-424
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• 2003

Stacking sequence optimization needs discrete programming techniques because ply angles are limited to a fixed set of angles such as $0^{\circ},\;{\pm}45^{\circ},\;90^{\circ}$. Two typical methods are genetic algorithm and branch and bound method. The goal of this paper is to compare the methods in the light of their efficiency and performance in handling the constraints and finding the global optimum. For numerical examples, maximization of buckling load is used as objective and optimization results from each method are compared.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.34 no.2
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• pp.191-201
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• 2010

This paper presents a new global optimization algorithm based on the branch-and-bound principle using Bspline approximation techniques. It describes the algorithmic components and details on their implementation. The key components include the subdivision of a design space into mutually disjoint subspaces and the bound calculation of the subspaces, which are all established by a real-valued B-spline volume model. The proposed approach was demonstrated with various test problems to reveal computational performances such as the solution accuracy, number of function evaluations, running time, memory usage, and algorithm convergence. The results showed that the proposed algorithm is complete without using heuristics and has a good possibility for application in large-scale NP-hard optimization.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2004.05a
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• pp.107-110
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• 2004

We present a unifying framework to establish a lower-bound on the number of semidefinite programming based, lift-and-project iterations (rank) for computing the convex hull of the feasible solutions of various combinatorial optimization problems. This framework is based on the maps which are commutative with the lift-and-project operators. Some special commutative maps were originally observed by $Lov{\acute{a}}sz$ and Schrijver, and have been used usually implicitly in the previous lowerbound analyses. In this paper, we formalize the lift-and-project commutative maps and propose a general framework for lower-bound analysis, in which we can recapture many of the previous lower-bound results on the lift-and-project ranks.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.391-397
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• 2019

In this paper, we give a simple proof of the improved Johnson bound for A(n, d), the maximum number of codewords in a binary code of length n and minimum distance d, given by Mounits, Etzion and Litsyn.

• Advances in Computational Design
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• v.1 no.2
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• pp.119-138
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• 2016

In this article, hybridization of enhanced colliding bodies optimization (ECBO) with upper bound strategy (UBS) that is called UECBO is proposed for optimum design of truss structures with frequency constraints. The distinct feature of the proposed algorithm is that it requires less computational time while preserving the good accuracy of the ECBO. Four truss structures with frequency limitations selected from the literature are studied to verify the viability of the algorithm. This type of problems is highly non-linear and non-convex. The numerical results show the successful performance of the UECBO algorithm in comparison to the CBO, ECBO and some other metaheuristic optimization methods.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.3
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• pp.369-380
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• 2001

Although extensive efforts have been devoted to the optimal design of composite laminated plates in recent years, some practical issues still need further research. Two of them are: the handling of the ply angle as either continuous or discrete; and that of the uncertainties in material properties, which were treated as continuous and ignored respectively in most researches in the past. In this paper, an algorithm for stacking sequence optimization which deals with discrete ply angles and that for thickness optimization which considers uncertainties in material properties are used for a two step optimization of composite laminated plates. In the stacking sequence optimization, the branch and bound method is modified to handle discrete variables; and in the thickness optimization, the convex modeling is used in calculating the failure criterion, given as constraint, to consider the uncertain material properties. Numerical results show that the optimal stacking sequence is found with fewer evaluations of objective function than expected with the size of feasible region taken into consideration; and the optimal thickness increases when the uncertainties of elastic moduli considered, which shows such uncertainties should not be ignored for safe and reliable designs.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.12
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• pp.4305-4323
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• 2014

In this paper, we investigate the degrees of freedom (DOF) of the Y channel consisting of three single-antenna users and a two-antenna common access relay, where each user intends to exchange independent messages with the other two users with the assistance of the relay. We show that the DOF of this particular scenario is 1.5. In order to prove this result, we firstly derive a DOF upper bound based on cut-set bound by allowing cooperation among users, which shows that the total DOF is upper bounded by 1.5. Then we propose a novel transmission scheme based on asymmetric signal space alignment (ASSA) to demonstrate the achievability of the upper bound. Theoretical evaluation and numerical results confirm that the upper bound can be achieved by utilizing ASSA, which also proves the optimality of the ASSA-based scheme in terms of DOF. Combining the upper bound and achievability, we conclude that the exact DOF is 1.5. Moreover, we present a novel iterative joint beamforming optimization (I-JBO) algorithm to further improve the sum rate. Numerical simulations have been provided to demonstrate the convergence speed and performance advantage of the I-JBO algorithm.