Solving hard bi-objective knapsack problems using deep reinforcement learning

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Hadi Charkhgard , Hanieh Rastegar Moghaddam , Ali Eshragh , Sasan Mahmoudinazlou , Kimia Keshanian
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引用次数: 0

Abstract

We study a class of bi-objective integer programs known as bi-objective knapsack problems (BOKPs). Our research focuses on the development of innovative exact and approximate solution methods for BOKPs by synergizing algorithmic concepts from two distinct domains: multi-objective integer programming and (deep) reinforcement learning. While novel reinforcement learning techniques have been applied successfully to single-objective integer programming in recent years, a corresponding body of work is yet to be explored in the field of multi-objective integer programming. This study is an effort to bridge this existing gap in the literature. Through a computational study, we demonstrate that although it is feasible to develop exact reinforcement learning-based methods for solving BOKPs, they come with significant computational costs. Consequently, we recommend an alternative research direction: approximating the entire nondominated frontier using deep reinforcement learning-based methods. We introduce two such methods, which extend classical methods from the multi-objective integer programming literature, and illustrate their ability to rapidly produce high-quality approximations.
利用深度强化学习解决双目标背包问题
我们研究了一类双目标整数规划,称为双目标背包问题。我们的研究重点是通过协同来自两个不同领域的算法概念来开发BOKPs的创新精确和近似解方法:多目标整数规划和(深度)强化学习。虽然近年来新的强化学习技术已经成功地应用于单目标整数规划,但在多目标整数规划领域,相应的工作还有待探索。这项研究是为了弥补文献中存在的这一差距。通过计算研究,我们证明,尽管开发精确的基于强化学习的方法来解决BOKPs是可行的,但它们具有显着的计算成本。因此,我们推荐另一个研究方向:使用基于深度强化学习的方法逼近整个非支配边界。我们介绍了两种这样的方法,它们扩展了多目标整数规划文献中的经典方法,并说明了它们快速产生高质量逼近的能力。
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
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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