# Augmenting High-dimensional Nonlinear Optimization with Conditional GANs

arXiv: https://arxiv.org/abs/2103.04748 · HTML: https://mlsanity.com/paper/2103.04748/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 46 references that are in the map.
- First posted on arXiv 20 Feb 2021.

## Builds on (most cited first, 10 of 10)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Image De-raining Using a Conditional Generative Adversarial Network](https://mlsanity.com/paper/1701.05957/) (2017)
- [Adversarial Time-to-Event Modeling](https://mlsanity.com/paper/1804.03184/) (2018)
- [Evolutionary Multiobjective Optimization Driven by Generative Adversarial Networks (GANs)](https://mlsanity.com/paper/1910.04966/) (2019)
- [Distributionally Robust Chance Constrained Programming with Generative Adversarial Networks (GANs)](https://mlsanity.com/paper/2002.12486/) (2020)
- [Semi-supervised Text Regression with Conditional Generative Adversarial Networks](https://mlsanity.com/paper/1810.01165/) (2018)

## Built on by (most cited first, 1 of 1)

- [Generative Models in Decision Making: A Survey](https://mlsanity.com/paper/2502.17100/) (2025)

## Abstract (arXiv)

Many mathematical optimization algorithms fail to sufficiently explore the solution space of high-dimensional nonlinear optimization problems due to the curse of dimensionality. This paper proposes generative models as a complement to optimization algorithms to improve performance in problems with high dimensionality. To demonstrate this method, a conditional generative adversarial network (C-GAN) is used to augment the solutions produced by a genetic algorithm (GA) for a 311-dimensional nonconvex multi-objective mixed-integer nonlinear optimization. The C-GAN, composed of two networks with three fully connected hidden layers, is trained on solutions generated by GA, and then given sets of desired labels (i.e., objective function values), generates complementary solutions corresponding to those labels. Six experiments are conducted to evaluate the capabilities of the proposed method. The generated complementary solutions are compared to the original solutions in terms of optimality and diversity. The generative model generates solutions with objective functions up to 100% better, and with hypervolumes up to 100% higher, than the original solutions. These findings show that a C-GAN with even a simple training approach and architecture can, with a much shorter runtime, highly improve the diversity and optimality of solutions found by an optimization algorithm for a high-dimensional nonlinear optimization problem. [Link to GitHub repository: https://github.com/PouyaREZ/GAN_GA]