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A heuristic for solving the irregular strip packing problem with quantum optimization

Paul-Amaury Matt, Marco Roth

TL;DR

A quantum-inspired heuristic is employed that decomposes the irregular strip packing problem into two sub-problems: ordering pieces via the traveling salesman problem and spatially arranging them in a rectangle packing problem, aiming to minimize waste and enhance material efficiency.

Abstract

We introduce a novel quantum computing heuristic for solving the irregular strip packing problem, a significant challenge in optimizing material usage across various industries. This problem involves arranging a set of irregular polygonal pieces within a fixed-height, rectangular container to minimize waste. Traditional methods heavily rely on manual optimization by specialists, highlighting the complexity and computational difficulty of achieving quasi-optimal layouts. The proposed algorithm employs a quantum-inspired heuristic that decomposes the strip packing problem into two sub-problems: ordering pieces via the traveling salesman problem and spatially arranging them in a rectangle packing problem. This strategy facilitates a novel application of quantum computing to industrial optimization, aiming to minimize waste and enhance material efficiency. Experimental evaluations using both classical and quantum computational methods demonstrate the algorithm's efficacy. We evaluate the algorithm's performance using the quantum approximate optimization algorithm and the quantum alternating operator ansatz, through simulations and real quantum computers, and compare it to classical approaches.

A heuristic for solving the irregular strip packing problem with quantum optimization

TL;DR

A quantum-inspired heuristic is employed that decomposes the irregular strip packing problem into two sub-problems: ordering pieces via the traveling salesman problem and spatially arranging them in a rectangle packing problem, aiming to minimize waste and enhance material efficiency.

Abstract

We introduce a novel quantum computing heuristic for solving the irregular strip packing problem, a significant challenge in optimizing material usage across various industries. This problem involves arranging a set of irregular polygonal pieces within a fixed-height, rectangular container to minimize waste. Traditional methods heavily rely on manual optimization by specialists, highlighting the complexity and computational difficulty of achieving quasi-optimal layouts. The proposed algorithm employs a quantum-inspired heuristic that decomposes the strip packing problem into two sub-problems: ordering pieces via the traveling salesman problem and spatially arranging them in a rectangle packing problem. This strategy facilitates a novel application of quantum computing to industrial optimization, aiming to minimize waste and enhance material efficiency. Experimental evaluations using both classical and quantum computational methods demonstrate the algorithm's efficacy. We evaluate the algorithm's performance using the quantum approximate optimization algorithm and the quantum alternating operator ansatz, through simulations and real quantum computers, and compare it to classical approaches.
Paper Structure (20 sections, 13 equations, 12 figures, 2 tables, 2 algorithms)

This paper contains 20 sections, 13 equations, 12 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. The irregular strip packing problem
  4. The Opus Incertum Algorithm
  5. Definitions and details
  6. Geometrical compatibility between pieces
  7. Generate groups of geometrically compatible pieces
  8. Ordering pieces in each cluster
  9. Packing the pieces of each cluster
  10. Partition filtering
  11. Rectangle packing
  12. Local optimization
  13. Global optimization
  14. The algorithm
  15. Experimental Results
  16. ...and 5 more sections

Figures (12)

  • Figure 1: (a) Set of eight pieces to pack. (b) Example of a hand-designed placement of the eight pieces.
  • Figure 2: The distance between two pieces and wasted area (grey). The axes and distances are given in arbitrary units.
  • Figure 3: Packing of pieces in clusters. Axes are given in arbitrary units.
  • Figure 4: Results for the example shown in Fig. \ref{['fig:pieces_DEMO1']}. (a) Rectangle packing for the . The rectangles packed are from left to right, bottom to top $R(\{0,1,2,3\})$, $R(\{4,5,6,7\})$. (b) Layout obtained with Opus Incertum. The container has a length of $L=1151.89$. The percentage of waste is $6.59\%$. The axes are given in arbitrary units.
  • Figure 5: Performance results for PUZZLE1, PUZZLE2 and PUZZLE3. Results from real quantum computer are obtained from IBM Ehningen.
  • ...and 7 more figures

Theorems & Definitions (3)

  • Definition 1: Distance and geometrical incompatibility/compatibility
  • Definition 2: Distance matrix
  • Definition 3: shortest Hamiltonian path