Pavel Surynek, Vojtěch Bubník, Lukáš Matěna, Petr Kubiš

Object Packing and Scheduling for Sequential 3D Printing: A Linear Arithmetic Model and a CEGAR-Inspired Optimal Solver (Extended Abstract)

Introduction

Object packing and scheduling for sequential 3d printing: a linear arithmetic model and a cegar-inspired optimal solver (extended abstract). Optimize sequential 3D printing object packing and scheduling. A linear arithmetic model and CEGAR-inspired SMT solver prevent printer collisions for efficient production.

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, in sequential 3D printing, objects are completed one after another. In the sequential case, it is necessary to ensure that the moving parts of the printer do not collide with previously printed objects. We propose to express the problem of sequential printing as a linear arithmetic formula, which is then solved using a solver for satisfiability modulo theories (SMT) combined with counterexample guided abstraction refinement (CEGAR).

Review

This extended abstract presents a compelling and novel approach to a critical problem in advanced manufacturing: object packing and scheduling for sequential 3D printing. The distinct challenge of sequential printing, where collision avoidance with already completed objects is paramount, is clearly articulated, distinguishing it from traditional batch 3D printing. The authors propose to model this complex problem as a linear arithmetic formula, leveraging the power of satisfiability modulo theories (SMT) solvers in conjunction with a counterexample-guided abstraction refinement (CEGAR) strategy. This choice of methodology is theoretically sound and promises to deliver optimal solutions, which is a significant strength given the combinatorial nature of the problem. The key strength of this work lies in its ambitious and rigorous mathematical formulation. Expressing the problem as a linear arithmetic formula lays the groundwork for exact optimization, differentiating it from heuristic-based approaches that might sacrifice optimality for speed. The subsequent use of SMT and CEGAR is particularly well-suited for problems that combine logical constraints (like scheduling and sequencing) with numerical constraints (like geometric packing and collision detection). This combination represents a state-of-the-art technique for solving intricate combinatorial optimization problems and positions the work at the forefront of applying formal methods to manufacturing challenges. The focus on optimal solutions is highly desirable for industrial applications where maximizing throughput and minimizing material waste are crucial. As an extended abstract, the submission provides an excellent high-level overview, but a full paper would naturally require substantial additional detail and empirical validation. Key areas to elaborate upon include the precise formulation of the linear arithmetic model, particularly how geometric collision avoidance constraints are encoded efficiently. Crucially, comprehensive experimental results demonstrating the scalability and practical performance of the SMT/CEGAR solver on various problem instances (e.g., varying numbers of objects, geometries, and printer workspace sizes) will be essential. A discussion on the computational complexity and a comparison against any existing heuristics (or adaptations thereof) for sequential 3D printing would also significantly strengthen the contribution. While the promise of optimality is strong, understanding the trade-offs in solve time for realistic industrial scenarios will be vital for assessing its practical applicability.

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