Learning Gradient Fields for Scalable and Generalizable Irregular Packing

The packing problem, also known as cutting or nesting, has diverse applications in logistics, manufacturing, layout design, and atlas generation. It involves arranging irregularly shaped pieces to minimize waste while avoiding overlap. Recent advances in machine learning, particularly reinforcement learning, have shown promise in addressing the packing problem. In this work, we delve deeper into a novel machine learning-based approach that formulates the packing problem as conditional generative modeling. To tackle the challenges of irregular packing, including object validity constraints and collision avoidance, our method employs the score-based diffusion model to learn a series of gradient fields. These gradient fields encode the correlations between constraint satisfaction and the spatial relationships of polygons, learned from teacher examples. During the testing phase, packing solutions are generated using a coarse-to-fine refinement mechanism guided by the learned gradient fields. To enhance packing feasibility and optimality, we introduce two key architectural designs: multi-scale feature extraction and coarse-to-fine relation extraction. We conduct experiments on two typical industrial packing domains, considering translations only. Empirically, our approach demonstrates spatial utilization rates comparable to, or even surpassing, those achieved by the teacher algorithm responsible for training data generation. Additionally, it exhibits some level of generalization to shape variations. We are hopeful that this method could pave the way for new possibilities in solving the packing problem

Towards Zero-Waste Furniture Design

In traditional design, shapes are first conceived, and then fabricated. While this decoupling simplifies the design process, it can result in inefficient material usage, especially where off-cut pieces are hard to reuse. The designer, in absence of explicit feedback on material usage remains helpless to effectively adapt the design -- even though design variabilities exist. In this paper, we investigate {\em waste minimizing furniture design} wherein based on the current design, the user is presented with design variations that result in more effective usage of materials. Technically, we dynamically analyze material space layout to determine {\em which} parts to change and {\em how}, while maintaining original design intent specified in the form of design constraints. We evaluate the approach on simple and complex furniture design scenarios, and demonstrate effective material usage that is difficult, if not impossible, to achieve without computational support

Optimal Packing of Irregular 3D Objects For Transportation and Disposal

This research developed algorithms, platforms, and workflows that can optimize the packing of 3D irregular objects while guaranteeing an acceptable processing time for real-life problems, including but not limited to nuclear waste packing optimization. Many nuclear power plants (NPPs) are approaching their end of intended design life, and approximately half of existing NPPs will be shut down in the next two decades. Since decommissioning and demolition of these NPPs will lead to a significant increase in waste inventory, there is an escalating demand for technologies and processes that can efficiently manage the decommissioning and demolition (D&D) activities, especially optimal packing of NPP waste. To minimize the packing volume of NPP waste, the objective is to arrange irregular-shaped waste objects into one or a set of containers such that container volume utilization is maximized, or container size is minimized. Constraints also include weight and radiation limits per container imposed by transportation requirements and the waste acceptance requirements of storage facilities and repositories. This problem falls under the theoretical realm of cutting and packing problems, precisely, the 3D irregular packing problem. Despite its broad applications and substantial potential, research on 3D irregular cutting and packing problems is still nascent, and largely absent in construction and civil engineering. Finding good solutions for real-life problems, such as the one mentioned above, through current approaches is computationally expensive and time-consuming. New algorithms and technologies, and processes are required. This research adopted 3D scanning as a means of geometry acquisition of as-is 3D irregular objects (e.g., nuclear waste generated from decommissioning and demolition of nuclear power plants), and a metaheuristics-based packing algorithm is implemented to find good packing configurations. Given the inefficiency of fully autonomous packing algorithms, a virtual reality (VR) interactive platform allowing human intervention in the packing process was developed to decrease the time and computation power required, while potentially achieving better outcomes. The VR platform was created using the Unity® game engine and its physics engine to mimic real-world physics (e.g., gravity and collision). Validation in terms of feasibility, efficiency, and rationality of the presented algorithms and the VR platform is achieved through functional demonstration with case studies. Different optimal packing workflows were simulated and evaluated in the VR platform. Together, these algorithms, the VR platform, and workflows form a rational and systematic framework to tackle the optimal packing of 3D irregular objects in civil engineering and construction. The overall framework presented in this research has been demonstrated to effectively provide packing configurations with higher packing efficiency in an adequate amount of time compared to conventional methods. The findings from this research can be applied to numerous construction and manufacturing activities, such as optimal packing of prefabricated construction assemblies, facility waste management, and 3D printing

A beam search approach to solve the convex irregular bin packing problem with guillotine cuts

This paper presents a two dimensional convex irregular bin packing problem with guillotine cuts. The problem combines the challenges of tackling the complexity of packing irregular pieces, guaranteeing guillotine cuts that are not always orthogonal to the edges of the bin, and allocating pieces to bins that are not necessarily of the same size. This problem is known as a two-dimensional multi bin size bin packing problem with convex irregular pieces and guillotine cuts. Since pieces are separated by means of guillotine cuts, our study is restricted to convex pieces.A beam search algorithm is described, which is successfully applied to both the multi and single bin size instances. The algorithm is competitive with the results reported in the literature for the single bin size problem and provides the first results for the multi bin size problem

Sintered silicon nitrode recuperator fabrication

The preliminary design and a demonstration of the feasibility of fabricating submodules of an automotive Stirling engine recuperator for waste heat recovery at 370 C are described. Sinterable silicon nitride (Sialon) tubing and plates were fabricated by extrusion and hydrostatic pressing, respectively, suitable for demonstrating a potential method of constructing ceramic recuperator-type heat exchangers. These components were fired in nitrogen atmosphere to 1800 C without significant scale formation so that they can be used in the as-fired condition. A refractory glass composition (Al2O3 x 4.5 CaO.MgO x 11SiO2) was used to join and seal component parts by a brazing technique which formed strong recuperator submodules capable of withstanding repeated thermal cycling to 1370 C. The corrosion resistance of these materials to Na2SO4 + NaCl carbon mixtures was also assessed in atmospheres of air, hydrogen and CO2-N2-H2O mixtures at both 870 C and 1370 C for times to 1000 hours. No significant reaction was observed under any of these test conditions

Interlocking structure design and assembly

Many objects in our life are not manufactured as whole rigid pieces. Instead, smaller components are made to be later assembled into larger structures. Chairs are assembled from wooden pieces, cabins are made of logs, and buildings are constructed from bricks. These components are commonly designed by many iterations of human thinking. In this report, we will look at a few problems related to interlocking components design and assembly. Given an atomic object, how can we design a package that holds the object firmly without a gap in-between? How many pieces should the package be partitioned into? How can we assemble/extract each piece? We will attack this problem by first looking at the lower bound on the number of pieces, then at the upper bound. Afterwards, we will propose a practical algorithm for designing these packages. We also explore a special kind of interlocking structure which has only one or a small number of movable pieces. For example, a burr puzzle. We will design a few blocks with joints whose combination can be assembled into almost any voxelized 3D model. Our blocks require very simple motions to be assembled, enabling robotic assembly. As proof of concept, we also develop a robot system to assemble the blocks. In some extreme conditions where construction components are small, controlling each component individually is impossible. We will discuss an option using global controls. These global controls can be from gravity or magnetic fields. We show that in some special cases where the small units form a rectangular matrix, rearrangement can be done in a small space following a technique similar to bubble sort algorithm

Evaluations of filament-reinforced composites for aerospace structural applications

Elastic constant, tensile, and compressive strength analysis for structural efficiency study of filament reinforced sandwich cylindrical shel

On the Domination Chain of m by n Chess Graphs

A survey of the six domination chain parameters for both square and rectangular chess boards are discussed