Generative design techniques such as topology optimisation can produce lightweight structures that significantly reduce emissions in aerospace and automotive applications. However, a gap exists between computationally generated designs and manufacturable parts: while topology optimisation produces optimal shapes for 3D printing or single-piece machining, industrial manufacturing relies on assemblies of standard components using processes like welding, stamping, and cutting. This paper formalises the problem of approximating topology-optimised designs using of-the-shelf parts and conventional manufacturing processes as a configuration problem. We define this problem as finding high-performing configurations of parts from industrial catalogues, modified by available processes, that minimise cost and weight while maximising geometric similarity to the target design. The key challenges include managing discrete part catalogues, representing complex 3D geometries, navigating solution spaces that grow exponentially, and handling mixed discrete-continuous optimisation variables. By framing generative design approximation as a configuration problem, we aim to bridge the gap between computational design tools and the reality of industrial manufacturing.
The aerospace and automotive industries are both significant contributors to climate change. Aerospace
contributes 2.5 % [
The following industry cases illustrate the gap between the objectives of topology optimisation and
industrial use. In 2016, Airbus unveiled a prototype "bionic partition". Created using generative design,
the 3D printed design was 50 % lighter [
The benefits of generative design cannot be realised when it is limited to a small subset of manufacturing processes available. Automating the manual approximation of a generated design to use of-the-shelf parts and processes would bridge the gap between available tools and industry use. This would properly integrate generative design into engineers’ toolboxes as one way to lightweight parts and reduce emissions. To this end, we present the approximation process as a configuration problem.
In this section, we present a generalised form of the problem and provide illustrative examples. The Manufacturing Problem
• a target shape generated using topology optimisation • a library of parts • a set of processes that can modify instances of parts in the library • one or more optimisation criteria • a target production volume
• Nodes are manufacturing processes with parameters • Leaf nodes are processes adding parts from a part library • Edges are the flow of parts • Root is the final assembly process, which outputs the completed product
• The tree is connected (single root), • there are no intersecting parts, • all joints/connections are physically realisable, • each process node has compatible incoming edges, • and the parameters of each process node are feasible.
Finding valid configurations is not suficient. Many will be manufacturable but perform poorly against a given objective. Functional evaluations, such as Finite Element Analysis (FEA) and real-world testing are required in safety-critical industries such as aerospace and automotive. However, they are expensive (in terms of compute, time and resources). For searching through valid configurations, or training a system to generate them in a data-driven approach, a proxy is required. A configuration can be evaluated based on its geometric similarity to a target form generated using Topology Optimization. This can be done by instantiating 3D models of the stock material and applying the modifications of the processes in the tree. The resulting shape can be compared to the target using the Hausdorf distance (the maximum distance between any point on one shape and its nearest point on the other shape). Generally, this approach can be thought of as using a continuous representation and gradient descent to find a design, then approxmating that design with discrete operations. Using a shape-based metric also ofers flexibility. A user of a configuration generator could provide the output of available generative design and topology optimisation tools, or model a freeform shape by hand. A drawback to this approach is that small changes in geometry can lead to large changes in deflection or peak stress. As such, if such a system were being used in the aerospace or automotive industries, configurations suggested by the tool of interest to a designer would be evaluated using functional evaluations such as FEA.
Many valid configurations will approximate the target shape, but may not be optimal in terms of cost or production volume. As such, a cost objective must also be applied. This can be achieved by assigning a cost to each part in the library and summing the costs of the parts used in the configuration. Each process can be costed by assigning a set-up cost and an operation cost. The set-up cost is incurred once if the process is used in a configuration, and the operation cost is incurred for every instance of a process node in a configuration. 2.4. Data
The SELTO dataset [
First, the number of possible configurations grows exponentially with the size of the component library, the process library, the number of nodes added to a configuration, and the number of design variables. Industrial part catalogues contain thousands of components. This is often referred to as the curse of dimensionality.
Second, the challenge of representing a configuration. The parts and processes can be represented as trees as described in Section 2.1. However, the configuration also represents a 3D shape. It is necessary to generate and check the 3D shape for self-intersection. A configuration that appears valid based on the tree structure may still be invalid due to a self-intersection. Consider a bar that has been bent 270 degrees. Potential 3D representations include Signed Distance Functions (SDFs) or Boundary Representations (B-reps).
Finally, the problem combines discrete and continuous variables, for example, tubing comes in fixed diameters but can be cut to any length, and sheet materials have standard thicknesses but arbitrary cut shapes. The number of variables also varies depending on the configuration. A bend will have a diferent number of parameters than a cut.
In this section, we describe related problems and the ongoing research into them. We aim to diferentiate this problem, as well as explain the inspiration for the research avenues detailed in the next section.
Mittal and Frayman [
Researchers have modified density-based methods (such as SIMP [
Circuit topology synthesis shares the goal of configuring a library of parts. Typically, the circuit is represented as a graph, with parts as nodes and connections as edges (e.g. [23]). Gao et al. [24] argued that this representation is ambiguous, as parts have pins with diferent functionalities. They proposed adding pins as an additional node type to the graph, allowing for explicit pin-to-pin connections. They also demonstrated the efectiveness of converting the graph to a set of sequences using Eulerian walks and applying a Transformer [25] in a system they dubbed AnalogGenie.
Program synthesis is the search for a program that generates a desired output. In the context of 3D modelling, the output is commonly a target shape. Before the popularisation of Large Language Models (LLMs), Domain Specific Languages (DSLs) were used to constrain the search space to a tractable size. Jones et al. [26] proposed a DSL called ShapeAssembly. They trained a hierarchical Variational Autoencoder (VAE) on ShapeAssembly programs reverse engineered from assemblies in PartNet [27]. They could then generate new programs, and thus assemblies, by sampling from the latent space of programs. Ellis et al. [28] proposed DreamCoder, that could expand its own DSL through a process of self-improvement.
A limitation of DSLs is that they constrain what can be expressed. We note that this may actually be a useful property in the context of ensuring manufacturability. However, to overcome this, researchers have recently favoured using LLMs to generate programs in Turing-complete languages, for example, Python. Notable work related to geometry generation includes CAD-CODER, which takes an image of a part and produces a parametric Computer-Aided Design (CAD) model [29]. The approach makes use of a Vision Language Model (VLM) to generate Python code that generates the model. While such approaches demonstrate the potential to convert generatively designed parts into parametric CAD models, they do not fully address the manufacturing problem presented in this paper, as CAD models are not necessarily manufacturable.
We identify two broad categories of approaches for addressing the configuration problem presented in this paper. The first involves searching for a configuration directly, which we term an output-centric approach. The second focuses on searching for a program that generates a configuration, which we refer to as a program-centric approach.
For output-centric approaches, several promising directions emerge. Graph generation techniques offer a way to generate configurations directly. Transformer-based models show promise, as demonstrated in AnalogGenie [24].
The configuration described in Section 2.1 can be viewed as the Abstract Syntax Tree (AST) of a program. One program-centric approach is to use an LLM to write the program using a supplied library of functions. Another approach is to generate a program that searches for a configuration. Both approaches can be further enhanced by employing evolutionary algorithms on the output programs, feeding high-performing programs back into the model for iteration.
Jonathan Raines acknowledges funding from the UKRI for a Centre for Doctoral Training studentship in Interactive Artificial Intelligence at the University of Bristol. (EP/S022937/1)
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