• Journal of the Korean Operations Research and Management Science Society
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• v.14 no.2
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• pp.53-66
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• 1989

The Public Vehicle Routing Problem (PVRP) is to find the minimum total cost routes of M or less Public-Vehicles to traverse the required arcs(streets) at least once, and return to their starting depot on a directed network. In this paper, first, a mathematical model is formulated as minimal cost flow model with illegal subtour elimination constraints, and with the fixed cost and routing cost as an objective function. Second, an efficient branch and bound algorithm is developed to obtain an exact solution. A subproblem in this method is a minimal cost flow problem relaxing illegal subtour elimination constraints. The branching strategy is a variable dichotomy method according to the entering nonrequired arcs which are candidates to eneter into an illegal subtour. To accelerate the fathoming process, a tighter lower bound of a candidate subproblem is calculated by using a minimum reduced coast of the entering nonrequired arcs. Computational results based on randomly generated networks report that the developed algorithm is efficient.

• Journal of the Korean Operations Research and Management Science Society
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• v.16 no.2
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• pp.86-102
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• 1991

The purpose of this paper is to present a branch and bound algorithm for the hierarchical transportation network design problem in 2-level directed networks. This problem is to find the least cost of hierarchical transportation networks which consist of a primary path and a secondary path. The primary path is a simple path from a prespecified orgin node to a prespecified terminal node. All nodes must be either a transsipment node on the primary path or connected to that path via secondary arcs. This problem is formulated to a 0-1 inter programming problem with assignment and illegal subtour elimination equations as constaints. We show that the subproblem relaxing subtour elimination constraints is transformed to a linear programming problem by means of the totally unimodularity. Optimal solutions of this subproblem are polynoially obtained by the assignment algorithm and complementary slackness conditions. Therefore, the optimal value of this subproblme is used as a lower bound. When an optimal solution of the subproblem has an illegal subtour, a better disjoint rule is adopted as the branching strategy for reducing the number of branched problems. The computational comparison between the least bound rule and the depth first rule for the search strategy is given.

• Journal of Korean Institute of Industrial Engineers
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• v.33 no.2
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• pp.201-212
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• 2007

Genetic algorithms (GAs) are very useful methods for global search and have been applied to various optimization problems. They have two kinds of important search mechanisms, crossover and mutation. Because the performance of GAs depends on these operators, a large number of operators have been developed for improving the performance of GAs. Especially, many researchers have been more interested in a crossover operator than a mutation operator. The reason is that a crossover operator is a main search operator in GAs and it has a more effect on the search performance. So, we also focus on a crossover operator. In this paper we first investigate the drawback of various crossovers, especially subtour-based crossovers and then introduce a new crossover operator to avoid such drawback and to increase efficiency. Also we compare it with several crossover operators for symmetric traveling salesman problem (STSP) for showing the performance of the proposed crossover. Finally, we introduce an efficient simple hybrid genetic algorithm using the proposed operator and then the quality and efficiency of the obtained results are discussed.

• The Transactions of the Korea Information Processing Society
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• v.6 no.11
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• pp.3070-3076
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• 1999

Petri net is one of the effective modeling techniques which analyzes and designs concurrent and asynchronous systems. CPN is an extended Petri net which has color tokens. In this paper, we propose a new test case generation method using CPN. It transforms Estelle Specification into CPN, which is applicable to Design/CPN. It also generates UIO and subtour from OG and descriptor, which are resulted from Design/CPN. Using the proposed method, we can get more improved test coverage than existing methods. Therefore, more effective protocol conformance testing could be conducted. The test case generating method will be the basis of the automatic testing environmented.

• Journal of the Korean Operations Research and Management Science Society
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• v.12 no.1
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• pp.34-44
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• 1987

The general vehicle routing problem has been studied by many researchers such as Christofides, et al. and Laporte, et al., but only limited effort has been devoted to developing the optimal algorithms. The purpose of this paper is to develop a branch and bound algorithm which determines the optimal vechicle routes and the optimal number of vehicles concurrenetly for the asymmetrical vehicle routing problem. In order to enhance the efficiency, this algorithm emphasizes the followings ; First, an efficient primal-dual approach is developed to solve subproblems which are called the specialized transportation problem, formed by relaxing the illegal subtour constraints from the vehicle routing problem, second, an improved branching scheme is developed to reduce the number of candidate subproblems by adequate utilization of vehicle capacity restrictions.

• Journal of the Korean Operations Research and Management Science Society
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• v.39 no.1
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• pp.13-27
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• 2014

In this paper, we deal with a Steiner Ring Star (SRS) problem arising from the design of survivable telecommunication networks. We develop two mixed integer programming formulations for the SRS problem by implementing Miller-Tucker-Zemlin (MTZ) and Sarin-Sherali-Bhootra (SSB) subtour elimination constraints, and then apply the reformulation-linearization technique (RLT) to enhance the lower bound obtained by the LP relaxation. By exploiting the ring-star structure of underlying network, we devise some valid inequalities that tighten the LP relaxation. Computational results demonstrate the effectiveness of the proposed solution procedure.

• Proceedings of the Korea Information Processing Society Conference
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• 2000.10b
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• pp.1207-1210
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• 2000

프로토콜을 설계하고 이를 구현하면 IUT가 프로토콜 규격과 일치하는지를 검증하는 적합성 시험을 수행한다. 기존의 시험열 생성 방법은 오일러 경로에 의한 방법을 사용하였으나 이 방법은 전체 경로를 다 포함하지 못한다는 단점이 있다. 이 단점을 개선하여 TPT(Transition Possibility Tree)를 생성하여 확장된 테스트 커버리지를 갖는 서브투어 생성방법이 제안되었다. 이 논문에서 기존에 제안된 TPT 서브투어 생성 방법에서 시험열의 갯수가 많아진다는 단점을 보안하여 TPT 서브투어 생성 방법에서의 효과적인 시험열 선택 방법을 제안하였다. 제안 방법에 의해서 생성된 시험열도 완전한 시험 목적에 부합하지 않는다는 단점은 있으나 시험자가 선택해야 하는 시험열의 양을 최소화하는 데 그 의미가 있다.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.19 no.39
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• pp.9-18
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• 1996

Many algorithms have been developed for optimizing the asymmectric traveling salesman problem known as a representative NP-Complete problem. The most efficient ones of them are branch and bound algorithms based on the subtour elimination approach. To increase efficiency of the branch and bound algorithm. number of decision nodes should be decreased. For this the minimum bound that is more close at the optimal solution should be found or an effective bounding strategy should be used. If the optimal solution has been known, we may apply it usefully to branching. Because a good feasible solution should be found as soon as possible and have similar features of the optimal solution. By the way, the upper bound solution in branch and bound algorithm is most close at the optimal solution. Therefore, the upper bound solution can be used instead of the optimal solution and information of which can be applied to new branching criteria. As mentioned above, this paper will propose an effective branching rule using the information of the upper bound solution in the branch and bound algorithm. And superiority of the new branching rule will be shown by comparing with Bellmore-Malone's one and carpaneto-Toth's one that were already proposed.

• The KIPS Transactions:PartD
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• v.11D no.3
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• pp.649-658
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• 2004

An object-oriented system is organized by a set of interacting objects and the system behavior is represented by the cooperating interaction bet ween objects. The characteristics of object-oriented software. such as inheritance and polymorphism, increase the difficulty of the object-oriented software testing. At running time of a program, one call from a member function can bind to other member functions because of the dynamic characteristics such as concurrence, dynamic binding and interaction. Therefore, there need the research about considering the characteristics of object-oriented software and concurrently testing the interaction between objects. In this paper, we propose the techniques as follows. First, we construct a flattened state chart diagram by considering the inheritance and polymorphism. Next, we model the system with CPN(Colored Petri Net) that usually is applying the system modeling and simulation. Last, we propose a test case generation techniques for testing the interaction between objects in object-oriented software by applying a Design/CPN tool.