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The Set Covering Problem Revisited: An Empirical Study of the Value of Dual Information
"... This paper investigates the role of dual information on the performances of heuristics designed for solving the set covering problem. After solving the linear programming relaxation of the problem, the dual information is used to obtain the two main approaches proposed here: (i) The size of the orig ..."
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This paper investigates the role of dual information on the performances of heuristics designed for solving the set covering problem. After solving the linear programming relaxation of the problem, the dual information is used to obtain the two main approaches proposed here: (i) The size of the original problem is reduced and then the resulting model is solved with exact methods. We demonstrate the effectiveness of this approach on a rich set of benchmark instances compiled from the literature. We conclude that set covering problems of various characteristics and sizes may reliably be solved to near optimality without resorting to custom solution methods. (ii) The dual information is embedded into an existing heuristic. This approach is demonstrated on a wellknown local search based heuristic that was reported to obtain the most successful results on the set covering problem to this day. Our results demonstrate that the use of dual information significantly improves the efficacy of the heuristic both in terms of solution time and accuracy.
Heuristic SetCoveringBased Postprocessing for Improving the QuineMcCluskey Method
"... Abstract—Finding the minimal logical functions has important applications in the design of logical circuits. This task is solved by many different methods but, frequently, they are not suitable for a computer implementation. We briefly summarise the wellknown QuineMcCluskey method, which gives a u ..."
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Abstract—Finding the minimal logical functions has important applications in the design of logical circuits. This task is solved by many different methods but, frequently, they are not suitable for a computer implementation. We briefly summarise the wellknown QuineMcCluskey method, which gives a unique procedure of computing and thus can be simply implemented, but, even for simple examples, does not guarantee an optimal solution. Since the Petrick extension of the QuineMcCluskey method does not give a generally usable method for finding an optimum for logical functions with a high number of values, we focus on interpretation of the result of the QuineMcCluskey method and show that it represents a set covering problem that, unfortunately, is an NPhard combinatorial problem. Therefore it must be solved by heuristic or approximation methods. We propose an approach based on genetic algorithms and show suitable parameter settings. Keywords—Boolean algebra, Karnaugh map, QuineMcCluskey method, set covering problem, genetic algorithm.
A WeightingBased Local Search Heuristic Algorithm for the Set Covering Problem
"... Abstract—The Set Covering Problem (SCP) is NPhard and has many applications. In this paper, we introduce a heuristic algorithm for SCPs based on weighting. In our algorithm, a local search framework is proposed to perturb the candidate solution under the best objective value found during the search ..."
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Abstract—The Set Covering Problem (SCP) is NPhard and has many applications. In this paper, we introduce a heuristic algorithm for SCPs based on weighting. In our algorithm, a local search framework is proposed to perturb the candidate solution under the best objective value found during the search, a weighting scheme and several search strategies are adopted to help escape from local optima and make the search more divergent. The effectiveness of our algorithm is evaluated on a set of instances from the ORLibrary and Steiner triple systems. The experimental results show that it is very competitive, for it is able to find all the optima or best known results with very small runtimes on nonunicost instances from the ORLibrary and outperforms two excellent solvers we have found in literature on the unicost instances from Steiner triple systems. Furthermore, it is conceptually simple and only needs one parameter to indicate the stopping criterion. This is a preview version of the paper [1] (see page 8 for the reference). Read the full piece in the proceedings. I.
Abstract—The Minimum Set Cover Problem has many prac
"... tical applications in various research areas. This problem belongs to the class of NPhard theoretical problems. Several approximation algorithms have been proposed to find approximate solutions to this problem and research is still going on to optimize the solution. This paper studies the existing ..."
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tical applications in various research areas. This problem belongs to the class of NPhard theoretical problems. Several approximation algorithms have been proposed to find approximate solutions to this problem and research is still going on to optimize the solution. This paper studies the existing algorithms of minimum set cover problem and proposes a heuristic approach to solve the problem using modified hill climbing algorithm. The effectiveness of the approach is tested on set cover problem instances from ORLibrary. The experimental results show the effectiveness of our proposed approach.
Big Step Greedy Heuristic for Maximum Coverage Problem
"... This paper proposes a greedy heuristic called Big step greedy heuristic and investigates its application to compute approximate solution for maximum coverage problem. Greedy algorithms construct the solution in multiple steps, the classical greedy algorithm for maximum coverage problem, in each step ..."
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This paper proposes a greedy heuristic called Big step greedy heuristic and investigates its application to compute approximate solution for maximum coverage problem. Greedy algorithms construct the solution in multiple steps, the classical greedy algorithm for maximum coverage problem, in each step selects one set that contains the greatest number of uncovered elements. The Big step greedy heuristic, in each step selects p (1 < = p < = k) sets such that the union of selected p sets contains the greatest number of uncovered elements by evaluating all the possible pcombinations of given sets. When p=k Big step greedy algorithm behaves like an exact algorithm that computes optimal solution by evaluating all possible kcombinations of the given sets. When p=1 it behaves like the classical greedy algorithm. The Big step greedy heuristic can be combined with local search methods to compute better approximate solution.
A CLONALGbased Approach for the Set Covering Problem
, 2014
"... In this paper, we propose a CLONALGbased simple heuristic, which is one of the most popular artificial immune system (AIS) models, for the nonunicost set covering problem (SCP). In addition, we have modified our heuristic to solve the unicost SCP. It is well known that SCP is an NPhard problem ..."
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In this paper, we propose a CLONALGbased simple heuristic, which is one of the most popular artificial immune system (AIS) models, for the nonunicost set covering problem (SCP). In addition, we have modified our heuristic to solve the unicost SCP. It is well known that SCP is an NPhard problem that can model several real world situations such as crew scheduling in airlines, facility location problem, production planning in industry etc. In real cases, the problem instances can reach huge sizes, making the use of exact algorithms impractical. So, for finding practically efficient approaches for solving SCP, different kind of heuristic approaches have been applied in the literature. To the best of our knowledge, our work here is the first attempt to solve SCP using Artificial Immune System. We have evaluated the performance of our algorithm on a number of benchmark nonunicost instances. Computational results have shown that it is capable of producing highquality solutions for nonunicost SCP. We have also performed some experiments on unicost instances that suggest that our heuristic also performs well on unicost SCP.
International Journal of Computational Intelligence 4;2 2008 Heuristic SetCoveringBased Postprocessing for Improving the QuineMcCluskey Method
"... Abstract—Finding the minimal logical functions has important applications in the design of logical circuits. This task is solved by many different methods but, frequently, they are not suitable for a computer implementation. We briefly summarise the wellknown QuineMcCluskey method, which gives a u ..."
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Abstract—Finding the minimal logical functions has important applications in the design of logical circuits. This task is solved by many different methods but, frequently, they are not suitable for a computer implementation. We briefly summarise the wellknown QuineMcCluskey method, which gives a unique procedure of computing and thus can be simply implemented, but, even for simple examples, does not guarantee an optimal solution. Since the Petrick extension of the QuineMcCluskey method does not give a generally usable method for finding an optimum for logical functions with a high number of values, we focus on interpretation of the result of the QuineMcCluskey method and show that it represents a set covering problem that, unfortunately, is an NPhard combinatorial problem. Therefore it must be solved by heuristic or approximation methods. We propose an approach based on genetic algorithms and show suitable parameter settings. Keywords—Boolean algebra, Karnaugh map, QuineMcCluskey method, set covering problem, genetic algorithm.
Heuristic SetCoveringBased Postprocessing for Improving the QuineMcCluskey Method
"... Abstract—Finding the minimal logical functions has important applications in the design of logical circuits. This task is solved by many different methods but, frequently, they are not suitable for a computer implementation. We briefly summarise the wellknown QuineMcCluskey method, which gives a u ..."
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Abstract—Finding the minimal logical functions has important applications in the design of logical circuits. This task is solved by many different methods but, frequently, they are not suitable for a computer implementation. We briefly summarise the wellknown QuineMcCluskey method, which gives a unique procedure of computing and thus can be simply implemented, but, even for simple examples, does not guarantee an optimal solution. Since the Petrick extension of the QuineMcCluskey method does not give a generally usable method for finding an optimum for logical functions with a high number of values, we focus on interpretation of the result of the QuineMcCluskey method and show that it represents a set covering problem that, unfortunately, is an NPhard combinatorial problem. Therefore it must be solved by heuristic or approximation methods. We propose an approach based on genetic algorithms and show suitable parameter settings. Keywords—Boolean algebra, Karnaugh map, QuineMcCluskey method, set covering problem, genetic algorithm.