A practical approach for dealing with hard knapsack problems using general‐purpose integer programming software

IF 3.1 4区管理学 Q2 MANAGEMENT

International Transactions in Operational Research Pub Date : 2024-03-01 DOI:10.1111/itor.13449

Myung Soon Song, Pei Hua Lin, Yun Lu, Emre Shively‐Ertas, Francis J. Vasko

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引用次数: 0

Abstract

Several articles dealing with the generation of hard 0‐1 knapsack problems (KPs) have given rise to 13,940 KP instances being made available for empirical testing. These KPs are typically solved using algorithms specifically designed to solve hard KPs. The goal of this paper is to demonstrate that two general‐purpose integer programming software packages using default parameter settings and a standard PC can successfully be used to generate optimal or guaranteed near‐optimal solutions for these 13,940 KP instances. Over 97% of the 13,940 instances have solutions generated that are guaranteed to be within 0.01% of optimum in less than 1 minute and a practical strategy for dealing with the other 3% is presented. Additionally, 3240 of the most difficult KPs were generated based on 6 parameters. Statistical analyses for predicting which values for these six parameters result in difficult‐to‐solve KPs based on the software used will be discussed. These results will be of particular interest to operations research practitioners who need to efficiently solve hard KPs related to real‐world applications.

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使用通用整数编程软件处理难题的实用方法

有几篇文章论述了 0-1 棘褶问题（KPs）的生成问题，并提供了 13,940 个 KPs 实例供实证测试。这些 KPs 通常使用专门设计用于解决困难 KPs 的算法来解决。本文旨在证明，使用默认参数设置和标准个人电脑的两个通用整数编程软件包可以成功地为这 13940 个 KP 实例生成最优解或保证接近最优解。在这 13940 个实例中，有 97% 以上的解可以在 1 分钟内保证在最优解的 0.01% 以内，同时还介绍了处理其他 3% 实例的实用策略。此外，还根据 6 个参数生成了 3240 个最难的 KPs。将讨论根据所用软件预测这六个参数的哪些值会导致难以解决的 KP 的统计分析。这些结果对于需要高效解决与现实世界应用相关的高难度 KPs 的运筹学从业人员特别有意义。

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

International Transactions in Operational Research OPERATIONS RESEARCH & MANAGEMENT SCIENCE-

CiteScore

7.80

自引率

12.90%

发文量

146

审稿时长

>12 weeks

期刊介绍： International Transactions in Operational Research (ITOR) aims to advance the understanding and practice of Operational Research (OR) and Management Science internationally. Its scope includes: International problems, such as those of fisheries management, environmental issues, and global competitiveness International work done by major OR figures Studies of worldwide interest from nations with emerging OR communities National or regional OR work which has the potential for application in other nations Technical developments of international interest Specific organizational examples that can be applied in other countries National and international presentations of transnational interest Broadly relevant professional issues, such as those of ethics and practice Applications relevant to global industries, such as operations management, manufacturing, and logistics.