Pattern based learning and optimisation through pricing for bin packing problem

TL;DR

This paper introduces a novel pattern-based learning and optimization scheme for the bin packing problem, dynamically assessing pattern values under changing conditions to improve solution quality.

Contribution

It connects data mining with duality theory to develop a method that identifies and evaluates patterns based on their effectiveness in stochastic constraints.

Findings

Significantly outperforms state-of-the-art methods

Effectively handles uncertainty in bin packing

Provides detailed analysis of pattern value dynamics

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.