Portfolio of Solving Strategies in CEGAR-based Object Packing and Scheduling for Sequential 3D Printing

2026-03-12

AI Summary

This work addresses the inefficiency in sequential 3D printing caused by suboptimal placement and scheduling of complex objects, which leads to excessive build-plate waste. To tackle this issue, the authors propose Portfolio-CEGAR-SEQ, a novel framework that integrates multiple high-level placement strategies—such as corner alignment and height-based scheduling—in parallel within the CEGAR-SEQ algorithm. Leveraging the Counterexample-Guided Abstraction Refinement (CEGAR) mechanism, the approach models placement and scheduling constraints using linear arithmetic formulas and exploits multi-core CPUs for parallel solving. Compared to the original CEGAR-SEQ, Portfolio-CEGAR-SEQ significantly improves computational efficiency and reduces the number of required build plates in batch printing tasks, thereby overcoming the limitations inherent in single-strategy approaches like center-only placement.

Technology Category

Planning, Routing, and Scheduling: Replanning and Plan RepairConstraint Satisfaction and Optimization: Distributed CSP/OptimizationSearch and Optimization: Combinatorial Optimization

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingSystems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments

Abstract

Computing power that used to be available only in supercomputers decades ago especially their parallelism is currently available in standard personal computer CPUs even in CPUs for mobile telephones. We show how to effectively utilize the computing power of modern multi-core personal computer CPU to solve the complex combinatorial problem of object arrangement and scheduling for sequential 3D printing. We achieved this by parallelizing the existing CEGAR-SEQ algorithm that solves the sequential object arrangement and scheduling by expressing it as a linear arithmetic formula which is then solved by a technique inspired by counterexample guided abstraction refinement (CEGAR). The original CEGAR-SEQ algorithm uses an object arrangement strategy that places objects towards the center of the printing plate. We propose alternative object arrangement strategies such as placing objects towards a corner of the printing plate and scheduling objects according to their height. Our parallelization is done at the high-level where we execute the CEGAR-SEQ algorithm in parallel with a portfolio of object arrangement strategies, an algorithm is called Porfolio-CEGAR-SEQ. Our experimental evaluation indicates that Porfolio-CEGAR-SEQ outperforms the original CEGAR-SEQ. When a batch of objects for multiple printing plates is scheduled, Portfolio-CEGAR-SEQ often uses fewer printing plates than CEGAR-SEQ.

Problem

• object packing
• scheduling
• sequential 3D printing
• combinatorial optimization
• CEGAR

Innovation

• CEGAR
• parallelization
• object packing
• scheduling
• 3D printing