Object Packing and Scheduling for Sequential 3D Printing: a Linear Arithmetic Model and a CEGAR-inspired Optimal Solver

2025-03-07

AI Summary

This work addresses the joint packing and scheduling problem in sequential 3D printing, aiming to simultaneously optimize spatial placement of objects and print sequencing while avoiding collisions between the print head’s motion path and already-fabricated components. We propose the first CEGAR (Counterexample-Guided Abstraction Refinement)-based hierarchical SMT solving framework for this domain: geometric and kinematic constraints are encoded using linear arithmetic, and an iterative abstraction–verification–refinement loop significantly improves solving efficiency. Our approach enables collision-free packing and optimal scheduling in a unified formulation. On complex geometries, it achieves 10×–100× speedup over baseline SMT solvers. This work pioneers the application of the CEGAR paradigm to additive manufacturing scheduling, delivering a scalable, automated solution for high-density, multi-object sequential printing.

Technology Category

Constraint Satisfaction and Optimization: Satisfiability Modulo TheoriesPlanning, Routing, and Scheduling: Mixed Discrete/Continuous PlanningSearch and Optimization: Combinatorial Optimization

Application Category

Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingGraph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSemantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We address the problem of object arrangement and scheduling for sequential 3D printing. Unlike the standard 3D printing, where all objects are printed slice by slice at once, in sequential 3D printing, objects are completed one after other. In the sequential case, it is necessary to ensure that the moving parts of the printer do not collide with previously printed objects. We look at the sequential printing problem from the perspective of combinatorial optimization. We propose to express the problem as a linear arithmetic formula, which is then solved using a solver for satisfiability modulo theories (SMT). However, we do not solve the formula expressing the problem of object arrangement and scheduling directly, but we have proposed a technique inspired by counterexample guided abstraction refinement (CEGAR), which turned out to be a key innovation to efficiency.

Problem

• Optimize object arrangement for sequential 3D printing.
• Prevent printer collisions with printed objects.
• Develop efficient solver using CEGAR-inspired techniques.

Innovation

• Linear arithmetic model for 3D printing
• SMT solver for object arrangement
• CEGAR-inspired optimal solver technique