MCTS for rectangle packing: why industrial optimization demands interpretable algorithms

The problem: “blind” optimization sacrifices reliability

When we tackle complex combinatorial problems in industry, such as 2D rectangle packing for logistics or raw material processing, the massive scale of data often renders exact algorithms unviable. To solve this, research has shifted toward approximation approaches, including Artificial Intelligence and Deep Learning models that offer high precision but often lack structural transparency.

An optimization algorithm cannot be genuinely Interpretability-focused or trustworthy if its decision-making logic is a black box. In industrial fields where inaccuracy is costly and human oversight is mandatory, relying on inscrutable optimization sacrifices the core requirement of Accountability. If a system generates a cutting pattern and a human operator needs to understand why certain pieces were prioritized, an opaque model offers no insight, rendering the decision-making process unauditable.

What do we propose in this work?

To bridge this gap, we published research introducing three approaches based on Monte Carlo Tree Search (MCTS), including its standalone application and its integration with metaheuristic algorithms and Deep Learning models to obtain approximated solutions that remain auditable.

In short, the paper demonstrates how MCTS builds the necessary foundation for industrial auditing through three core capabilities:

  • Inherent Interpretability: Unlike opaque black-box methods, the search tree structure of MCTS is inherently transparent. It allows engineers to trace exactly which decision paths (piece placements) were evaluated, compared, and discarded during the optimization process.
  • Knowledge Extraction: By making the algorithm’s exploration visible, the system goes beyond just providing a final solution; it allows for the extraction of tactical “rules of thumb” that can be used to train human operators or guide other heuristics.
  • Industrial-Grade Performance: The integration of the search tree with advanced learning methods allows us to match the quality of state-of-the-art methods while providing significant improvements in computation time, offering the required Observability for real-world industrial environments.

The connection to trustworthy algorithms

This work addresses two fundamental principles of trustworthy computing: the necessity of Interpretability by design and the requirement for computational Observability in high-stakes environments. We demonstrate that it is not necessary to sacrifice auditability to achieve high-performance approximations. By building the architecture upon transparent search structures, we provide engineers with the tools to inspect, extract, and challenge the machine’s mathematical reasoning.

Read the full research

If you want to dive deeper into the formulation of MCTS states and actions, the reinforcement learning architecture used, or how we implemented the adjustment space calculation, the full article has been published in the Journal of Heuristics.

👉 Read the full paper here (DOI: 10.1007/s10732-024-09525-2)