capprara等人的集合覆盖贪心启发式的理论证明。

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Torbjörn Larsson, Nils-Hassan Quttineh
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引用次数: 0

摘要

大规模集覆盖问题通常采用建设性贪婪启发式方法来解决,并且对这种启发式方法的各种贪婪准则的设计和评价进行了大量的研究。capprara等人(1999)提出的标准是基于相对于尚未实现的约束的减少成本,由此产生的贪婪启发式据报道优于基于原始成本或普通减少成本的启发式。我们通过从一般非凸优化问题的全局最优性条件推导出capprara等人提出的贪婪准则,给出了它的理论证明。结果表明,对于一个量的增量贡献,该准则实际上是贪婪的,该量在终止时与拉格朗日对偶界与所找到的可行解的目标值之间的偏差一致。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A theoretical justification of the set covering greedy heuristic of Caprara et al.

Large scale set covering problems have often been approached by constructive greedy heuristics, and much research has been devoted to the design and evaluation of various greedy criteria for such heuristics. A criterion proposed by Caprara et al. (1999) is based on reduced costs with respect to the yet unfulfilled constraints, and the resulting greedy heuristic is reported to be superior to those based on original costs or ordinary reduced costs.

We give a theoretical justification of the greedy criterion proposed by Caprara et al. by deriving it from a global optimality condition for general non-convex optimisation problems. It is shown that this criterion is in fact greedy with respect to incremental contributions to a quantity which at termination coincides with the deviation between a Lagrangian dual bound and the objective value of the feasible solution found.

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来源期刊
Discrete Optimization
Discrete Optimization 管理科学-应用数学
CiteScore
2.10
自引率
9.10%
发文量
30
审稿时长
>12 weeks
期刊介绍: Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.
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