• School Mathematics
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• v.16 no.1
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• pp.19-37
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• 2014

This study investigated the degree of understanding pre-service teachers' random variable concept, based on the attention and the importance for developing pre-service teachers' ability on statistical reasoning in statistics education. To accomplish this, the subject of this study was 70 pre-service teachers belonged to three universities respectively. The teachers were given to 7 tasks on random variable and requested to solve them in 40 minutes. The tasks consisted of three contents in large; 1) one was on the definition of random variables, 2) the other was on the understanding of random variables in different/diverse conditions, and 3) another was on problem solving relevant to random variable concept. The findings are as follows. First, while 20% of pre-service teachers understood the definition of random variable correctly, most teachers could not distinguish between random variable and variable or probability. Second, there was a significant difference in understanding random variables in different/diverse conditions. Namely, the degree of understanding on the continuous random variable was superior to that of discrete random variable and also the degree of understanding on the equal distribution was superior to that of unequality distribution. Third, three types of problems relevant to random variable concept dealt with in this study were finding a sample space and an elementary event, and finding a probability value. In result, the teachers responded to the problem on finding a probability value most correctly and on the contrary to this, they had the mot difficulty in solving the problem on finding a sample space.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.241-247
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• 2005

Let ${\gamma}{\equiv}\left{{\gamma}_{ij}\right}(0{\leq}i+j{\leq}2n)$ be a collection of complex numbers with ${\gamma}_{00}>0$ and ${\gamma}_{ji}={\bar{\gamma}}_{ij}$. The truncated complex moment problem for ${\gamma}$ entails finding a positive Borel measure ${\mu}$ supported in the complex plane ${\mathbb{C}}$ such that ${\gamma}_{ij}={\int}{\bar{z}}^{i}z^jd{\mu}(z)(0{\leq}i+j{\leq}2n)$. We solve this truncated moment problem with data in a circle and discuss the behavior of data in an extended moment matrix.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.1
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• pp.19-30
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• 2013

Recently, the constrained index tracking problem, in which the task of trading a set of stocks is performed so as to closely follow an index value under some constraints, has often been considered as an important application domain for control theory. Because this problem can be conveniently viewed and formulated as an optimal decision-making problem in a highly uncertain and stochastic environment, approaches based on stochastic optimal control methods are particularly pertinent. Since stochastic optimal control problems cannot be solved exactly except in very simple cases, approximations are required in most practical problems to obtain good suboptimal policies. In this paper, we present a procedure for finding a suboptimal solution to the constrained index tracking problem based on approximate dynamic programming. Illustrative simulation results show that this procedure works well when applied to a set of real financial market data.

• Journal of the Korean Society of Marine Environment & Safety
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• v.6 no.1
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• pp.23-33
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• 2000

This paper is concerned with finding the global optimal solutions for the redundancy optimization problems in series-parallel systems related with system safety. This study transforms the difficult problem, which is classified as a nonlinear integer problem, into a 0/1 IP(Integer Programming) by using binary integer variables. And the global optimal solution to this problem can be easily obtained by applying GAMS (General Algebraic Modeling System) to the transformed 0/1 IP. From computational results, we notice that GA(Genetic Algorithm) to this problem, which is, to our knowledge, known as a best algorithm, is poor in many cases.

• Journal of Ocean Engineering and Technology
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• v.28 no.6
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• pp.560-565
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• 2014

In this study, the problem of trajectory optimization for underwater gliders considering depth constraints is discussed. Typically, underwater gliders are controlled to dive and climb in a saw-tooth pattern at constant gliding angles. This approach is effective and close to optimal for deep water applications. However, the optimal path deviates from the saw-tooth path in shallow water conditions. This study focuses on finding more efficient gliding paths that can minimize the traverse time in the horizontal plane when the water depth is limited. The trajectory optimization problem is formulated into a minimum time control problem with inequality path constraints and hydrodynamic drag effects. A numerical approach based on the pseudo-spectral method is adopted as a solution approach, and the simulation results are presented.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2006.11a
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• pp.573-576
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• 2006

This paper deals with multi-objective optimization problem of finding a set of well-distributed solutions close to the true Pareto optimal solutions. In this paper, we present a two-leveled symbiotic evolutionary algorithm to efficiently solve the problem. Most of the existing multi-objective evolutionary algorithms (MOEAs) operate one population that consists of individuals representing the complete solution to the problem. The proposed algorithm maintains several populations, each of which represents a partial solution to the entire problem, and has a structure with two levels. The parallel search and the structure are intended to improve the capability of searching diverse and good solutions. The performance of the proposed algorithm is compared with those of the existing algorithms in terms of convergence and diversity. The experimental results confirm the effectiveness of the proposed algorithm.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.35 no.1
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• pp.10-15
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• 2012

This paper considers an economic design problem of a tree-based network which is a kind of computer network. This problem can be modeling to be an objective function to minimize installation costs, on the constraints of spanning tree and maximum traffic capacity of sub tree. This problem is known to be NP-hard. To efficiently solve the problem, a tabu list coupled genetic algorithm approach is proposed. Two illustrative examples are used to explain and test the proposed approach. Experimental results show evidence that the proposed approach performs more efficiently for finding a good solution or near optimal solution in comparison with a genetic algorithm approach.

• International Journal of Reliability and Applications
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• v.12 no.2
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• pp.79-94
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• 2011

Redundancy-reliability allocation problems in multi-stage series-parallel systems are addressed in this study. Fuzzy programming techniques are proposed for finding satisfactory solutions. First, a multi-objective programming model is formulated for simultaneously maximizing system reliability and minimizing system total cost. Due to the nature of uncertainty in the problem, the fuzzy set theory and technique are used to convert the deterministic multi-objective programming model into a fuzzy nonlinear programming problem. A heuristic method is developed to get satisfactory solutions for the fuzzy nonlinear programming problem. A Pareto optimal solution is found with maximal degree of satisfaction from the interception area of fuzzy sets. A case study that is related to the electronic control unit installed on aircraft engine over-speed protection system is used to implement the developed approach. Results suggest that the developed fuzzy multi-objective programming model can effectively resolve the fuzzy and uncertain problem when design goals and constraints are not clearly confirmed at the initial conceptual design phase.

• Proceedings of the KIEE Conference
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• 1999.07c
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• pp.1123-1125
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• 1999

This paper proposes an optimization technique using Genetic Algorithm(GA) for service restoration in the distribution system. Restoration planning problem can be treated as a combinatorial optimization problem. So GA is appropriate to solve the service restoration problem in the distribution network. But searching capabilities of the GA can be enhanced by developing relevant repairing operation and modifying GA operations. In this paper, we aimed at finding appropriate open sectionalizing switch position for the restoration of distribution networks after disturbances using enhanced GA with repairing operation and modified mutation. Simulation results show that proposed method found the open sectionalizing switches with less out of service area and minimize transmission line losses and voltage drop.

• 제어로봇시스템학회:학술대회논문집
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• 1989.10a
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• pp.635-642
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• 1989

We formulated the multi-robot trajectory problem into a series of NLP problem, each of which is that of finding the optimal tip positions of the robots for the next time step. The NLP problem is composed of an objective function and three constraints, namely: a) Joint position limits, b) Joint velocity limits, and c) Collision-avoidance constraints. By solving a series of NLP problem, optimally coordinated trajectories can be determined without requiring any prior path information. This is a novel departure from the previous approach in which either all paths or at least one path is assumed to be given. Practical application of the developed method is for optimal synthesis of multiple robot trajectories in off-line. To test the validity and effectiveness of the method, numerical examples are illustrated.