• 한국국방경영분석학회지
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• 제8권1호
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• pp.53-70
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• 1982

This thesis develops a more realistic and applicable new set covering model that is adjusted and supplied by the existing set covering models, and induces an algorithm for solving the new set covering model, and applies the new model and the algorithm to an actual set covering problems. The new set covering model introduces a probabilistic covering aistance ($0{\eqslantless}p{\eqslantless}1$)or time($0{\eqslantless}p{\eqslantless}1$) instead of a deterministic covering distance(0 or 1) or time (0 or 1) of the existing set covering model. The existing set covering model has not considered the merit of the overcover of customers. But this new set covering model leads a concept of this overcover to a concept of the parallel system reliability. The algorithm has been programmed on the UNIVAC 9030 for solving large-scale covering problems. An application of the new set covering model is presented in order to determine the locations of the air surveillance radars as a set covering problem for a case-study.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제4권2호
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• pp.137-144
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• 1997

In this paper we consider covering problems in spherical geometry. Let $cov_q{S_1}^n$ be the smallest radius of q equal metric balls that cover n-dimensional unit sphere ${S_1}^n$. We show that $cov_q{S_1}^n\;=\;\frac{\pi}{2}\;for\;2\leq\;q\leq\;n+1$ and $\pi-arccos(\frac{-1}{n+1})$ for q = n ＋ 2. The configuration of centers of balls realizing $cov_q{S_1}^n$ are established, simultaneously. Moreover, some properties of $cov_{q}$X for the compact metric space X, in general, are proved.

• 한국경영과학회지
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• 제27권4호
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• pp.87-109
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• 2002

A satisfiability problem in propositional logic is the problem of checking for the existence of a set of truth values of atomic prepositions that renders an input propositional formula true. This paper describes an empirical investigation of a particular integer programming approach, using the set covering model, to solve satisfiability problems. Our satisfiability engine, SETSAT, is a fully integrated, linear programming based, branch and bound method using various symbolic routines for the reduction of the logic formulas. SETSAT has been implemented in the integer programming shell MINTO which, in turn, uses the CPLEX linear programming system. The logic processing routines were written in C and integrated into the MINTO functions. The experiments were conducted on a benchmark set of satisfiability problems that were compiled at the University of Ulm in Germany. The computational results indicate that our approach is competitive with the state of the art.

• 산업공학
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• 제12권1호
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• pp.94-101
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• 1999

The set covering(SC) problem is the problem of covering all the rows of an $m{\times}n$ matrix of ones and zeros by a subset of columns with a minimal cost. It has many practical applications of modeling of real world problems. The SC problem has been proven to be NP-complete and many algorithms have been presented to solve the SC problem. In this paper we present hybrid simulated annealing(HSA) algorithm based on the Simulated Annealing(SA) for the SC problem. The HSA is an algorithm which combines SA with a crossover operation in a genetic algorithm and a local search method. Our experimental results show that the HSA obtains better results than SA does.

• 한국경영과학회지
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• 제19권1호
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• pp.189-199
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• 1994

This paper considers the covering network design problem (CNDP). In the CNDP, an undirected graph is given where nodes correspond to potential facility sites and arcs to potential links connecting facilities. The objective of the CNDP is to identify the least cost connected subgraph whose nodes cover the given demand points. The problem difines a demand point to be covered if some node in the selected graph is present within an appropriate distance from the demand point. We present an integer programming formulation for the problem and develop a dual-based solution procedure. The computational results for randomly generated test problems are also shown.

• 경영과학
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• 제26권3호
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• pp.1-9
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• 2009

In this paper, we present mathematical models for the ring covering problems arising in the design of multi-ring WDM networks. Also, we present efficient algorithms to solve the suggested models. By the computational experiment, our model can solve the medium-sized networks efficiently and shows better performance than the existing heuristic method. Although we propose an efficient method for the column generation procedure, branching rule that does not destroy the column generation structure is unsolved. Further research is required to develop an effective branching rule.

• 한국항행학회논문지
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• 제15권5호
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• pp.781-788
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• 2011

Sphere-packing problem은 주어진 공간에 가능한 한 많은 구(sphere)를 채울 수 있는 배열을 찾는 문제이고 covering problem은 이에 쌍대적인 최적화의 문제로 코딩이론에 적용된다. 본 논문에서는 이진 코드이론에서의 가중치(weight)와 해밍거리(Hamming distance)에 대한 개념을 부울 대수(Boolean algebra)의 개념으로 일반화한다. 부울 대수에서의 가중치와 이를 이용하여 거리함수를 정의하고, 이들의 기본적인 성질들을 밝힌다. 또한, 부울 대수에서의 sphere-packing bound와 Gilbert-Varshamov bound의 정리를 증명한다.

• 한국컴퓨터정보학회논문지
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• 제19권10호
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• pp.13-21
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• 2014

집합 커버링 문제는 대표적인 조합 최적화 문제들 중 하나로서 n개의 열로부터 일부를 선택하여 m개의 행을 커버하되 비용을 최소화하는 문제로 정의된다. 본 논문에서는 집합 커버링 문제를 해결하기 위한 정수 계획법 기반 지역 탐색의 적용 방안을 제시하고 있다. 정수계획법 기반 지역 탐색은 이웃해를 탐색하여 현재해를 반복적으로 개선하는 지역 탐색 기법의 일종으로서 이웃해를 생성하기 위한 알고리즘으로 정수계획법을 사용한다. 본 논문에서 제시한 기법의 효과를 검증하기 위해 OR-Library의 테스트 데이터를 대상으로 실험을 수행하였다. 실험 결과, 모든 테스트 데이터에 있어서 정수계획법 기반 지역 탐색을 통해 지금까지 알려진 가장 좋은 해를 탐색할 수 있었다. 특히 4개의 테스트 데이터에 대해서는 지금까지 알려진 가장 좋은 해보다 더 좋은 해를 도출할 수 있음을 확인할 수 있었다.

• 산업경영시스템학회지
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• 제9권13호
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• pp.79-86
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• 1986

This paper presents a heuristic algorithm for a crew scheduling problem with dead head flights. This paper modifies and improves saving method for finding the Multiple Salesman tours in the graph. The results show that the computing time from this algorithm is implemented very much than those from general crew scheduling algorithms by set covering models.

• 대한수학회보
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• 제39권2호
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• pp.347-357
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• 2002

In this paper, we study the concepts of isocompactness and cl-isocompactness. We generalize a pure space defined by Arhangelskii and get some results on initially K-compact spaces. We also consider open problems related to isocompactness and cl-isocompactness.