A probabilistic heuristic for a computationally difficult set covering problem

Feo, Thomas A.; Resende, Maurício G. C.

doi:10.1016/0167-6377(89)90002-3

Cited by 853 publications

(365 citation statements)

References 6 publications

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“…However, given the size of the numerical instances, exact resolution was impossible within a reasonable period of time. Our second stage involved the development of a heuristic method derived from the GRASP (Greedy Randomized Adaptative Search Procedure) metaheuristic [6]. Several general algorithms, which can solve any SPP, were developed.…”

Section: Introductionmentioning

confidence: 99%

GRASP for set packing problems

Delorme

Gandibleux

Rodríguez³

2004

European Journal of Operational Research

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The principles of the Greedy Randomized Adaptative Search Procedure (GRASP) metaheuristic are instantiated for the set packing problem. We investigated several construction phases, and evaluated improvements based on advanced strategies. These improvements include a self-tuning procedure (using reactive GRASP), an intensification procedure (using path relinking) and a procedure involving the diversification of the selection (using a learning process). Two sets of various numerical instances were used to perform the computational experiments. The first set contains randomly generated instances, while the second includes instances relating to real problems in railway planning. No metaheuristic has previously been applied to this combinatorial problem. Consequently, we have discussed GRASPÕs performances both in relation to lower/upper bounds and to the results obtained with Cplex when such results are available. Our analysis, based on the average performances observed, shows the impact of the suggested strategies, and indicates the configuration that produces the best results.

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Section: Introductionmentioning

confidence: 99%

GRASP for set packing problems

Delorme

Gandibleux

Rodríguez³

2004

European Journal of Operational Research

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“…The set cover problem has been well studied and a number of exact and approximate methods exist for it, including the exact branch-and-bound algorithms [27,28], greedy algorithms [15,29], LP relaxation [30], Lagrangian relaxation [31][32][33], and genetic algorithms [34,35]. For a detailed analysis of many of these, we refer readers to the recent survey by Caprara et.…”

Section: Algorithms For the Minimal Sirna Cover Problemmentioning

confidence: 99%

“…We modify the branch-and-bound algorithm to include biological constraint. Inspired by the randomized greedy algorithms [29,37], we propose a probabilistic greedy algorithm for selecting minimal siRNA covers efficiently.…”

Section: Algorithms For the Minimal Sirna Cover Problemmentioning

confidence: 99%

“…The probabilistic greedy algorithm shares some common aspects with the randomized greedy algorithm [29], but it differs in some important ways. The randomized greedy algorithm [29] iteratively selects to the cover an siRNA completely randomly from a subset of unselected siRNAs, while our approach selects each siRNA randomly but according to a selection probability distribution.…”

Section: Probabilistic Greedy Algorithmmentioning

confidence: 99%

“…The randomized greedy algorithm [29] iteratively selects to the cover an siRNA completely randomly from a subset of unselected siRNAs, while our approach selects each siRNA randomly but according to a selection probability distribution. Let f (s) be the number of genes which an siRNA s covers, and h(g) be the number of siRNAs which cover a particular gene g. By analyzing the covering relationship matrix (such as the one in Figure 3), we found two important features which imply whether an siRNA is a good pick: f (s) and min g∈g(s) h(g).…”

Section: Probabilistic Greedy Algorithmmentioning

confidence: 99%

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Efficient RNAi-based gene family knockdown via set cover optimization

Zhao

Fanning

Lane

2005

Artificial Intelligence in Medicine

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RNA interference (RNAi) is a recently discovered genetic immune system with widespread therapeutic and genomic applications. In this paper, we address the problem of selecting an efficient set of initiator molecules (siRNAs) for RNAi-based gene family knockdown experiments. Our goal is to select a minimal set of siRNAs that (a) cover a targeted gene family or a specified subset of it, (b) do not cover any untargeted genes, and (c) are individually highly effective at inducing knockdown. We show that the problem of minimizing the number of siRNAs required to knock down a family of genes is NP-Hard via a reduction to the set cover problem. We also give a formal statement of a generalization of the basic problem that incorporates additional biological constraints and optimality criteria. We modify the classical branch-and-bound algorithm to include some of these biological criteria. We find that, in many typical cases, these constraints reduce the search space enough that we are able to compute exact minimal siRNA covers within reasonable time. For larger cases, we propose a probabilistic greedy algorithm for finding minimal siRNA covers efficiently. Our computational results on real biological data show that the probabilistic greedy algorithm produces siRNA covers as good as the branch-andbound algorithm in most cases. Both algorithms return minimal siRNA covers with high predicted probability that the selected siRNAs will be effective at inducing knockdown. We also examine the role of "off-target" interactions -the constraint of avoiding covering untargeted genes can, in some cases, substantially increase the complexity of the resulting solution. Overall, however, we find that in many common cases, our approach significantly reduces the number of siRNAs required in gene family knockdown experiments, as compared to knocking down genes independently.

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Greedy Algorithms

Moshkov

2015

Wiley Encyclopedia of Electrical and Electronics Engineering

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Greedy algorithms seek to find optimal solutions by making locally optimal steps. They form a class of usually simple (simple from the point of view of both description and time complexity) algorithms which often return optimal solutions or have good enough accuracy. This article presents representative greedy algorithms returning optimal solutions, such as Dijkstra's, Prim's, Huffman's, and Kruskal's algorithms. In addition, matroids, greedy algorithms for NP‐hard problems, the set cover problem as well as randomized greedy algorithms and greedy approaches for continuous models are also discussed.

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A probabilistic heuristic for a computationally difficult set covering problem

Cited by 853 publications

References 6 publications

GRASP for set packing problems

GRASP for set packing problems

Efficient RNAi-based gene family knockdown via set cover optimization

Greedy Algorithms

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