• School Mathematics
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• v.19 no.3
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• pp.481-494
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• 2017

Tasks of multiple solutions have been said to be suitable for the cultivation of mathematical creativity. However, studies on the fact that multiple solutions presented by students are useful or meaningful, and students' thoughts while finding multiple solutions are very short. In this study, we set goals to confirm the qualitative differences among the multiple solutions presented by the students and, if present, from the viewpoint of mathematical creativity. For this reason, after presenting the set of tasks of the two versions to eight mathematically gifted students of the second-grade middle school, we analyzed qualitative differences that appeared among the solutions. In the study, there was a difference among the solution presented first and the solutions presented later, and qualitatively substantial differences in terms of flexibility and creativity. In this regard, it was concluded that the need to account for such qualitative differences in designing and applying multiple solutions should be considered.

• Journal of Korean Society of Transportation
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• v.20 no.6
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• pp.99-113
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• 2002

The multi-class traffic assignment problem is the most typical one of the multi-solution traffic assignment problems and, recently formulation of the models and the solution algorithm have been received a great deal of attention. The useful solution algorithm, however, has not been proposed while formulation of the multi-class traffic assignment could be performed by adopting the variational inequality problem or the fixed point problem. In this research, we developed a hybrid solution algorithm which combines GA algorithm, diagonal algorithm and clustering algorithm for the multi-class traffic assignment formulated as a variational inequality Problem. GA algorithm and clustering algorithm are introduced for the wide area and small cost. We also performed an experiment with toy network(2 link) and tested the characteristics of the suggested algorithm.

• Journal of the Korea Convergence Society
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• v.10 no.11
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• pp.71-77
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• 2019

This paper defines a multi-selection knapsack problem and presents an algorithm for seeking its optimal solution. Multi-selection means that all members of the particular group be selected or excluded. Our branch-and-bound algorithm introduces a simplex containing the feasible region of the original problem to exploit the fact that the most tightly underestimating function on the simplex is linear. In bounding operation, the subproblem defined over the candidate simplex is minimized. During the branching process the candidate simplex is splitted into two one-less dimensional subsimplices by being projected onto two hyperplanes. The approach of this paper can be applied to solving the global minimization problems under various types of the knapsack constraints.

• Education of Primary School Mathematics
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• v.27 no.4
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• pp.435-462
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• 2024

This study aims to derive educational implications for fostering mathematical creativity in elementary students. To achieve this, proportional distribution problems were presented as multiple-solution tasks, and students' problem-solving processes were analyzed from the perspective of mathematical creativity. The study involved 100 sixth-grade elementary students who were given proportional distribution problems as multiple-solution tasks to analyze their problem-solving methods. The students were grouped based on teacher variables, and the groups were assessed in terms of fluency, originality, and flexibility in mathematical creativity. The characteristics of the collective solution spaces were identified by comparing the frequency of various problem-solving strategies and representation types. The study found that teachers significantly influence mathematical creativity within collective solution spaces. Depending on the teacher, differences in fluency and originality were observed. Collective solution spaces with less reliance on formulaic approaches and higher use of diverse representations scored higher in creativity. Conversely, heavy reliance on symbolic representations was associated with lower creativity. These findings highlight the importance of encouraging various problem-solving strategies and representations within collective solution spaces to foster creativity. The study confirms that teachers play a crucial role in fostering mathematical creativity. Differences in creativity between groups based on teacher variables indicate that teachers impact students' problem-solving approaches. Additionally, relying solely on symbolic representations does not naturally lead to mathematical creativity, underscoring the need to provide students with opportunities to explore diverse mathematical representations. Creating an educational environment that encourages students to experiment with various strategies and representations is essential for nurturing their creativity.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.42 no.6
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• pp.445-452
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• 2014

This paper discusses the multifrontal direct solution method with out of core storage for large scale structural analysis in a limited computing resource. Large scale structural analysis requires huge amount of memory space and computation, so out of core solution method is needed in limited computing resource. In this research, out of core multifrontal solution algorithm which utilize the small size of physical memory and minimize the amount of access of low speed out of core storage is introduced. Three ideas, which are stack space in lower trianglar part of square factorization matrix, inverse stack data structure and selective data caching and recovery by data block size, are proposed.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.7B
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• pp.1220-1228
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• 1999

In this paper, we deal with an important network design problem in providing multimedia telecommunication services. The problem is to find an optimal gateway location and fiber routing, while minimizing the total cost. The cost elements are the installation cost of add-drop multiplexer and fiber cables. We have developed effective heuristic procedures for the problem. The performance of the developed heuristic shows promising computational results.

• Journal of the Korea Society of Computer and Information
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• v.10 no.5 s.37
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• pp.179-186
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• 2005

This paper describes a genetic algorithm and compares three crossover operators for Rural Postman Problem with Time Windows (RPPTW). The RPPTW which is a multiobjective optimization problem, is an extension of Rural Postman Problem(RPP) in which some service places (located at edge) require service time windows that consist of earliest time and latest time. Hence, RPM is a m띤tieect optimization Problem that has minimal routing cost being serviced within the given time at each service Place. To solve the RPPTW which is a multiobjective optimization problem, we obtain a Pareto-optimal set that the superiority of each objective can not be compared. This Paper performs experiments using three crossovers for 12 randomly generated test problems and compares the results. The crossovers using in this Paper are Partially Matched Exchange(PMX) Order Exchange(OX), and Modified Order Exchange(MOX) which is proposed in this paper. For each test problem, the results show the efficacy of MOX method for RPPTW.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.602-605
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• 1996

가상경로의 개념은 ATM망의 효율적인 전송체게임이 이미 여러 연구에 의하여 밝혀져 있다[1,2,7,9,10]. 본 논문에서는 등가대역의 개념을 이용하여 가상경로가 가질 수 있는 QoS를 다양하게 고려한 새로운 가상경로 설정모형(MVCAP)과 해법을 제사하였다. 모형 MVCAP은 (1) 가상경로의 설정에 따르는 용량비용(capacity cost)과 제어비용(control cost)간의 trade-off을 반영하였으며 (2) 가상경로의 QoS를 다양하게 고려하여 통계적 다중화 효과를 충분히 반영하도록 하였고 (3) 가상경로의 설정방법들인 분리설정법(segregation method)와 통합설정법(integration method)을 동시에 고려한 모형을 수립하였으며 (4) 등가대역식의 선형근사를 이용하여 목적함수를 단조 감소시키는 발견적 해법을 제시하였다. 소형문제에 대한 실험결과, 본 논문의 모형은 가상경로의 설정을 실시간 안에 이룰 수 있는 가능성을 열어 보였다.

• Journal of the Korean Operations Research and Management Science Society
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• v.32 no.2
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• pp.89-97
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• 2007

We study the maximum integer multiflow problem and the minimum multicut problem in a ring network. Both problems in a general network are known to be NP-hard. In this paper, we develop polynomial time algorithms to solve the problems. We also prove that even In a ring network, maximum multiflow is not always integral, which implies that the amount of maximum integer flow does not always reach the minimum capacity of multicut.

• Journal of the Korean Operations Research and Management Science Society
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• v.17 no.1
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• pp.31-41
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• 1992

An extension of generalized linear multiple choice knapsack problem [1] is presented and an algorithm of order 0([n .n$_{max}$]$_{2}$) is developed by exploiting its extended properties, where n and n$_{max}$ denote the total number of variables and the cardinality of the largest multiple choice set, respectively. A numerical example is presented and computational aspects are discussed.sed.