# MO-PaDGAN: Reparameterizing Engineering Designs for Augmented Multi-objective Optimization

arXiv: https://arxiv.org/abs/2009.07110 · HTML: https://mlsanity.com/paper/2009.07110/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2020.

## Built on by (most cited first, 21 of 21)

- [Deep Generative Models in Engineering Design: A Review](https://mlsanity.com/paper/2110.10863/) (2021)
- [CreativeGAN: Editing Generative Adversarial Networks for Creative Design Synthesis](https://mlsanity.com/paper/2103.06242/) (2021)
- [Beyond Statistical Similarity: Rethinking Metrics for Deep Generative Models in Engineering Design](https://mlsanity.com/paper/2302.02913/) (2023)
- [Deep Learning in Deterministic Computational Mechanics](https://mlsanity.com/paper/2309.15421/) (2023)
- [IH-GAN: A Conditional Generative Model for Implicit Surface-Based Inverse Design of Cellular Structures](https://mlsanity.com/paper/2103.02588/) (2021)
- [ShipHullGAN: A generic parametric modeller for ship hull design using deep convolutional generative model](https://mlsanity.com/paper/2305.00210/) (2023)
- [Constraining Generative Models for Engineering Design with Negative Data](https://mlsanity.com/paper/2306.15166/) (2023)
- [Deep Generative Model for Efficient 3D Airfoil Parameterization and Generation](https://mlsanity.com/paper/2101.02744/) (2021)
- [GAN-DUF: Hierarchical Deep Generative Models for Design Under Free-Form Geometric Uncertainty](https://mlsanity.com/paper/2202.10558/) (2022)
- [Design Target Achievement Index: A Differentiable Metric to Enhance Deep Generative Models in Multi-Objective Inverse Design](https://mlsanity.com/paper/2205.03005/) (2022)
- [Learning to design without prior data: Discovering generalizable design strategies using deep learning and tree search](https://mlsanity.com/paper/2211.15068/) (2022)
- [Generative VS non-Generative Models in Engineering Shape Optimization](https://mlsanity.com/paper/2402.08540/) (2024)
- [Towards Goal, Feasibility, and Diversity-Oriented Deep Generative Models in Design](https://mlsanity.com/paper/2206.07170/) (2022)
- [Nonlinear denoising score matching for enhanced learning of structured distributions](https://mlsanity.com/paper/2405.15625/) (2024)
- [Exploring the Potentials and Challenges of Deep Generative Models in Product Design Conception](https://mlsanity.com/paper/2407.11104/) (2024)
- [Generative Thermal Design Through Boundary Representation and Multi-Agent Cooperative Environment](https://mlsanity.com/paper/2208.07952/) (2022)
- [GFocal: A Global-Focal Neural Operator for Solving PDEs on Arbitrary Geometries](https://mlsanity.com/paper/2508.04463/) (2025)
- [Deep Generative Models for Geometric Design Under Uncertainty](https://mlsanity.com/paper/2112.08919/) (2021)
- [Large-Batch, Iteration-Efficient Neural Bayesian Design Optimization](https://mlsanity.com/paper/2306.01095/) (2023)
- [Conformal Predictions Enhanced Expert-guided Meshing with Graph Neural Networks](https://mlsanity.com/paper/2308.07358/) (2023)
- [Masked Conditioning for Deep Generative Models](https://mlsanity.com/paper/2505.16725/) (2025)

## Abstract (arXiv)

Multi-objective optimization is key to solving many Engineering Design problems, where design parameters are optimized for several performance indicators. However, optimization results are highly dependent on how the designs are parameterized. Researchers have shown that deep generative models can learn compact design representations, providing a new way of parameterizing designs to achieve faster convergence and improved optimization performance. Despite their success in capturing complex distributions, existing generative models face three challenges when used for design problems: 1) generated designs have limited design space coverage, 2) the generator ignores design performance, and 3)~the new parameterization is unable to represent designs beyond training data. To address these challenges, we propose MO-PaDGAN, which adds a Determinantal Point Processes based loss function to the generative adversarial network to simultaneously model diversity and (multi-variate) performance. MO-PaDGAN can thus improve the performances and coverage of generated designs, and even generate designs with performances exceeding those from training data. When using MO-PaDGAN as a new parameterization in multi-objective optimization, we can discover much better Pareto fronts even though the training data do not cover those Pareto fronts. In a real-world multi-objective airfoil design example, we demonstrate that MO-PaDGAN achieves, on average, an over 180% improvement in the hypervolume indicator when compared to the vanilla GAN or other state-of-the-art parameterization methods.