A cut-and-branch algorithm for the Quadratic Knapsack Problem

IF 0.9 4区数学 Q3 MATHEMATICS, APPLIED

Discrete Optimization Pub Date : 2022-05-01 DOI:10.1016/j.disopt.2020.100579

Franklin Djeumou Fomeni , Konstantinos Kaparis , Adam N. Letchford

引用次数: 15

Abstract

The Quadratic Knapsack Problem (QKP) is a well-known $NP$ -hard combinatorial optimisation problem, with many practical applications. We present a ‘cut-and-branch’ algorithm for the QKP, in which a cutting-plane phase is followed by a branch-and-bound phase. The cutting-plane phase is more sophisticated than the existing ones in the literature, incorporating several classes of cutting planes, two primal heuristics, and several rules for eliminating variables and constraints. Computational results show that the algorithm is competitive.

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二次型背包问题的割枝算法

二次背包问题(Quadratic backpack Problem, QKP)是一个著名的NP-hard组合优化问题，具有许多实际应用。我们提出了一种QKP的“切割和分支”算法，其中切割平面阶段之后是分支和定界阶段。切割平面阶段比现有文献中更复杂，包含几种切割平面，两个原始启发式和一些消除变量和约束的规则。计算结果表明，该算法具有一定的竞争力。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Optimization 管理科学-应用数学

CiteScore

2.10

自引率

9.10%

发文量

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.