• Journal of the Korean Institute of Intelligent Systems
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• v.13 no.4
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• pp.439-447
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• 2003

This paper proposes a proportional-integral-derivative (PID) evaluation method for enhancing performance of genetic algorithms. In PID evaluation, the fitness of individuals is evaluated by not only the fitness derived from an evaluation function, but also the parents fitness of each individual and the minimum and maximum fitness from initial generation to previous generation. This evaluation decreases the probability that the genetic algorithms fall into a premature convergence phenomenon and results in enhancing the performance of genetic algorithms. We experimented our evaluation method with typical numerical function optimization problems. It was found from extensive experiments that out evaluation method can increase the performance of genetic algorithms greatly. This evaluation method can be easily applied to the other types of genetic algorithms for improving their performance.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.1
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• pp.1-21
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• 2015

This paper presents two algorithms based on the Jamshidian equation which is from the Black-Scholes partial differential equation. The first algorithm is for American call options and the second one is for American put options. They compute numerically free boundary and then option price, iteratively, because the free boundary and the option price are coupled implicitly. By the upwind finite-difference scheme, we discretize the Jamshidian equation with respect to asset variable s and set up a linear system whose solution is an approximation to the option value. Using the property that the coefficient matrix of this linear system is an M-matrix, we prove several theorems in order to formulate a bisection method, which generates a sequence of intervals converging to the fixed interval containing the free boundary value with error bound h. These algorithms have the accuracy of O(k + h), where k and h are step sizes of variables t and s, respectively. We prove that they are unconditionally stable. We applied our algorithms for a series of numerical experiments and compared them with other algorithms. Our algorithms are efficient and applicable to options with such constraints as r > d, $r{\leq}d$, long-time or short-time maturity T.

• Structural Engineering and Mechanics
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• v.66 no.3
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• pp.399-409
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• 2018

This paper demonstrates the potential application of machine learning algorithms for approximate prediction of the load and deflection capacities of the novel type of Laced Steel Concrete-Composite (LSCC) beams proposed by Anandavalli et al. (Engineering Structures 2012). Initially, global and local responses measured on LSCC beam specimen in an experiment are used to validate nonlinear FE model of the LSCC beams. The data for the machine learning algorithms is then generated using validated FE model for a range of values of the identified sensitive parameters. The performance of four well-known machine learning algorithms, viz., Support Vector Regression (SVR), Minimax Probability Machine Regression (MPMR), Relevance Vector Machine (RVM) and Multigene Genetic Programing (MGGP) for the approximate estimation of the load and deflection capacities are compared in terms of well-defined error indices. Through relative comparison of the estimated values, it is demonstrated that the algorithms explored in the present study provide a good alternative to expensive experimental testing and sophisticated numerical simulation of the response of LSCC beams. The load carrying and displacement capacity of the LSCC was predicted well by MGGP and MPMR, respectively.

• ETRI Journal
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• v.15 no.3
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• pp.47-59
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• 1994

A capacity expansion planning problem with buy-or-lease decisions is considered. Demands for capacity are deterministic and are given period-dependently at each period. Capacity additions occur by buying or leasing a capacity, and leased capacity at any period is reconverted to original source after a fixed length of periods, say, lease period. All cost functions (buying, leasing and idle costs) are assumed to be concave. And shortages of capacity and disposals are not considered. The properties of an optimal solution are characterized. This is then used in a tree search algorithm for the optimal solution and other two algorithms for a near-optimal solution are added. And these algorithms are illustrated with numerical examples.

• 제어로봇시스템학회:학술대회논문집
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• 1991.10b
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• pp.1617-1622
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• 1991

Plane sweep is a general method in computational geometry. There are many efficient theoretical algorithms designed using plane sweep technique. However, their practical implementations are still suffering from the topological inconsistencies resulting from the numerical errors in geometric computations with finite-precision arithmetic. In this paper, we suggest new implementation techniques for the plane sweep algorithms to resolve the topological inconsistencies and construct the planar object boundaries from given input curve segments.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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• pp.238-242
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• 2005

This paper considers a routing problem on a RPR(Resilient Packet Ring). The RPR is one of the ring-type data telecommunication network. Our major problem is to find an optimal routing algorithm for a given data traffic on the network under no splitting the traffic service, where the maximum load of a link is minimized. This paper characterizes the Minmax problem and develops two heuristic algorithms. By using the numerical comparison, we show that our heuristic algorithm is valuable for efficient routing the data traffic on a RPR.

• Korean Journal of Mathematics
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• v.13 no.1
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• pp.113-122
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• 2005

We consider the iterative schemes for the large sparse linear system to solve partial differential equations. Using spectral radius of iteration matrices, the optimal relaxation parameters and good parameters can be obtained. With those parameters we compare the effectiveness of the SOR and SSOR algorithms. Applying Crank-Nicolson approximation, we observe the error distribution according to domain decomposition. The number of processors due to domain decomposition affects time and error. Numerical experiments show that effectiveness of SOR and SSOR can be reversed as time size varies, which is not the usual case. Finally, these phenomena suggest conjectures about equilibrium time grid for SOR and SSOR.

• Journal of the Korean Society of Safety
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• v.13 no.4
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• pp.240-247
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• 1998

This paper proposed a method for solving the nonlinear integer programing problem to get easily the best compromise solution while holding a nonlinear property by using the genetic algorithms. Also, this paper reported that the optimization problem of systems reliability as was solved by using the preposed method, and the numerical comparison experiments between the 0-1 LP/0-1 NP formulations were demonstrated, and from the quantitative evaluation the efficiency of the proposed method was demonstrated.

• Journal of the Korean Mathematical Society
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• v.47 no.4
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• pp.767-788
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• 2010

In this paper, we propose two limited memory BFGS algorithms with a nonmonotone line search technique for unconstrained optimization problems. The global convergence of the given methods will be established under suitable conditions. Numerical results show that the presented algorithms are more competitive than the normal BFGS method.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.959-973
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• 2001

We shall discuss one of some techniques needed to analyze algorithms. It is called a big-O function technique. The measures of efficiency of an algorithm have two cases. One is the time used by a computer to solve the problem using this algorithm when the input values are of a specified size. The other one is the amount of computer memory required to implement the algorithm when the input values are of a specified size. Mainly, we will restrict our attention to time complexity. To figure out the Time Complexity in nonlinear problems of Numerical Analysis seems to be almost impossible.