Augmenting High-dimensional Nonlinear Optimization with Conditional GANs

TL;DR

This paper introduces a method that uses conditional GANs to enhance the diversity and optimality of solutions in high-dimensional nonlinear optimization problems, significantly outperforming traditional genetic algorithms.

Contribution

It demonstrates that a simple C-GAN can effectively augment genetic algorithms, improving solution quality and diversity in high-dimensional optimization tasks.

Findings

Generated solutions up to 100% better in objective functions

Hypervolumes of solutions up to 100% higher

Shorter runtime compared to traditional methods

Abstract

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]