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Pattern based learning and optimisation through pricing for bin packing problem

Huayan Zhang, Ruibin Bai, Tie-Yan Liu, Jiawei Li, Bingchen Lin, Jianfeng Ren

TL;DR

This work makes a connection between data mining and the duality theory in operations research and proposes a novel scheme to efficiently identify patterns and dynamically quantify their values for each specific condition, showing that the proposed algorithm significantly outperforms the state-of-the-art methods.

Abstract

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.

Pattern based learning and optimisation through pricing for bin packing problem

TL;DR

This work makes a connection between data mining and the duality theory in operations research and proposes a novel scheme to efficiently identify patterns and dynamically quantify their values for each specific condition, showing that the proposed algorithm significantly outperforms the state-of-the-art methods.

Abstract

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.
Paper Structure (23 sections, 5 equations, 4 figures, 5 tables, 2 algorithms)

This paper contains 23 sections, 5 equations, 4 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Bin packing problem (BPP)
  4. Online bin packing problem
  5. Pricing and duality
  6. Literature review
  7. Proposed pattern based method
  8. Pattern based reformulation
  9. Framework overview
  10. Planning
  11. Plan-based packing
  12. Uncertainty handling
  13. Experimental results
  14. Algorithm configuration
  15. Experiments on different items' distributions
  16. ...and 8 more sections

Figures (4)

  • Figure 1: The general framework of CGPP. Left: main procedure loop of iteratively packing items. Right: two critical module of the algorithm. Red rhombuses: uncertainty handling mechanism.
  • Figure 2: Average bin filled rate with confidence interval
  • Figure 3: Average Bin Filled Rate for Periodic Weibull
  • Figure 4: Histogram of pattern quantity and their fill rates. Blue curve: fill rate of patterns measured by the second y-axis on the right.