• 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.

• International Journal of Reliability and Applications
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• 제5권4호
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• pp.147-154
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• 2004

This work developed and algorithm for a set covering model when the reliability of covers is a concern. This model extended the usage of the set covering model.

• 한국컴퓨터정보학회논문지
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• 제20권9호
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• pp.21-29
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• 2015

The set partitioning problem is a well-known NP-hard combinatorial optimization problem, and it is formulated as an integer programming model. This paper proposes an Integer Programming-based Local Search for solving the set partitioning problem. The key point is to solve the set partitioning problem as the set covering problem. First, an initial solution is generated by a simple heuristic for the set covering problem, and then the solution is set as the current solution. Next, the following process is repeated. The original set covering problem is reduced based on the current solution, and the reduced problem is solved by Integer Programming which includes a specific element in the objective function to derive the solution for the set partitioning problem. Experimental results on a set of OR-Library instances show that the proposed algorithm outperforms pure integer programming as well as the existing heuristic algorithms both in solution quality and time.

• Management Science and Financial Engineering
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• 제18권2호
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• pp.13-17
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• 2012

Set covering has widely been accepted as a staple tool for feature selection in data mining. We present a generalized version of this classical combinatorial optimization model to make it better suited for the purpose and propose a surrogate relaxation-based procedure for its meta-heuristic solution. Mathematically and also numerically with experiments on 25 set covering instances, we demonstrate the utility of the proposed model and the proposed solution method.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.1-11
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• 2010

The conditional covering problem is an important variation of well studied set covering problem. In the set covering problem, the problem is to find a minimum cardinality vertex set which will cover all the given demand points. The conditional covering problem asks to find a minimum cardinality vertex set that will cover not only the given demand points but also one another. This problem is NP-complete for general graphs. In this paper, we present an efficient algorithm to solve the conditional covering problem on interval graphs with n vertices which runs in O(n)time.

• 대한교통학회지
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• 제17권2호
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• pp.137-147
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• 1999

지금까지 시내버스 노선계획에 관한 대다수의 연구는 개별노선에 대한 지엽적인 분석을 바탕으로 하고 있으나 본 연구에서는 각 노선의 개별적 고려가 아닌 네트워크 차원의 최적화를 위한 노선계획 방법론을 제시하였다. 본 연구에서 제시하는 방법론은 계획가적 관점에서 버스이용자를 포함한 모든 통행자는 최단경로로 통행하기를 희망한다는 기본 전제하에 각 기종점의 최단경로로 구성된 대안 노선망을 도출하고 matrix 형태의 집합개념을 도입한 Set Covering 이론을 적용하여 노선공급수준을 축소하였다. 또한 노선축소과정에서 지금까지 부수적 통행요소로 인식되어온 환승을 활용하여 통행수요를 만족하는 최소규모의 노선망을 도출하였다. 본 연구는 고정수요를 가정하는 기존 연구와 달리 통행자 행태를 반영한 최적 노선망을 도출하기 위하여 시내버스 노선망 대안에 대한 가변수요를 구현하였다. 따라서 본 연구를 통하여 자가용이용자와 버스이용자로 구성된 전체 네트워크의 통행비용을 최소화하며 서비스 제공규모를 최소화하는 최적 시내버스 노선망을 도출하였다. 연구결과 기존연구와 비교하여 서비스 공급수준을 축소할 뿐 아니라 통행자의 행태를 고려한 해를 도출함으로써 현실성을 제고하였다.

• 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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• 제15권2호
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• pp.97-104
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• 1990

The problem is a variation of the weighted set-covering problem (SCP) which requires the minimum-cost cover to be self-covering. It is shown that direct extension of the well-known greedy heuristic for SCP can have an arbitrarily large error in the worst case. It remains an open question whther these exists a greedy heuristic with a finite error bound.

• Kyungpook Mathematical Journal
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• 제57권4호
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• pp.701-709
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• 2017

In this paper, we introduce the minimum covering Randic energy of a graph. We compute minimum covering Randic energy of some standard graphs and establish upper and lower bounds for this energy. Also we disprove a conjecture on Randic energy which is proposed by S. Alikhani and N. Ghanbari, [2].