• Journal of the military operations research society of Korea
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• v.8 no.1
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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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• v.5 no.4
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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.

• Journal of the Korea Society of Computer and Information
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• v.20 no.9
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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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• v.18 no.2
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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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• v.28 no.1_2
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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.

• Journal of Korean Society of Transportation
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• v.17 no.2
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• pp.137-147
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• 1999

This paper studies on the optimal bus network design in the framework of the set covering theory. The theory enables to cover passenger's loading and alighting areas as the set, and maximize the covering set as much as possible. In other words, it calculates the minimal set of the bus routes for covering whole bus passengers demand. After the optimal set of the bus routes is generated by the set covering theory, multimodal traffic equilibrium assignment is used for evaluating the generated set in terms of passenger's mode and route choice behavior. Whilst most previous works on it have been based on analyzing a specific route in a limited area, this study seeks to optimize the whole bus network.

• Journal of the Korean Operations Research and Management Science Society
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• v.27 no.4
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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.

• IE interfaces
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• v.12 no.1
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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.

• Journal of the Korean Operations Research and Management Science Society
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• v.15 no.2
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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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• v.57 no.4
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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].