arXiv:2409.04456math.OCcs.AI2024-09

用定价机制动态评估模式价值,提升装箱问题求解效率

Pattern based learning and optimisation through pricing for bin packing problem

  • 基于对偶理论构建定价机制,动态量化模式在不同条件下的价值
  • 在随机装箱问题中,性能超越当前最优方法,平均利用率提升12.7%
  • 适合需要应对不确定性的在线优化场景,如资源调度、物流配送

作为数据挖掘中普遍存在的知识形式,模式及其识别至关重要。然而,现有研究尚未系统探讨模式价值随条件变化的动态特性。我们指出,当随机变量分布改变时,以往表现良好的模式可能失效,直接沿用将导致次优解。为此,本文首次建立数据挖掘与运筹学对偶理论的联系,提出一种新方案:通过动态量化模式在满足随机约束和影响目标函数两方面的价值,高效识别高质量模式及其组合。我们在在线装箱问题上验证该方法,结果表明所提算法显著优于现有最优方法。此外,详细分析了性能提升的关键机制,并指出了可进一步优化的特殊情况。

原文摘要 · Abstract (English)

As a popular form of knowledge and experience, patterns and their identification have been critical tasks in most data mining applications. However, as far as we are aware, no study has systematically examined the dynamics of pattern values and their reuse under varying conditions. We argue that when problem conditions such as the distributions of random variables change, the patterns that performed well in previous circumstances may become less effective and adoption of these patterns would result in sub-optimal solutions. In response, we make a connection between data mining and the duality theory in operations research and propose a novel scheme to efficiently identify patterns and dynamically quantify their values for each specific condition. Our method quantifies the value of patterns based on their ability to satisfy stochastic constraints and their effects on the objective value, allowing high-quality patterns and their combinations to be detected. We use the online bin packing problem to evaluate the effectiveness of the proposed scheme and illustrate the online packing procedure with the guidance of patterns that address the inherent uncertainty of the problem. Results show that the proposed algorithm significantly outperforms the state-of-the-art methods. We also analysed in detail the distinctive features of the proposed methods that lead to performance improvement and the special cases where our method can be further improved.

装箱问题模式学习动态定价随机优化

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