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Generative Optimization: A Perspective on AI-Enhanced Problem Solving in Engineering

Lyle Regenwetter, Cyril Picard, Amin Heyrani Nobari, Akash Srivastava, Faez Ahmed

TL;DR

This paper argues that optimization and GenAI are complementary in engineering problem-solving. It defines generative optimization as frameworks that couple GenAI components with explicit optimization to leverage data-driven generation and rigorous evaluation. The authors outline three main approaches: using GenAI to speed and generalize optimization, using optimization to improve GenAI's solution quality, and unifying modal requirements and representations across domains. They discuss concrete methods such as warm-starts, GenAI operators, latent-space optimization, training on optimized data, iterative retraining, inverse optimization, cross-modal translation, and multimodal representations, and highlight key challenges like constraint satisfaction, diversity, data requirements, and retraining costs. The perspective suggests significant near-term developments and practical impact for engineering design and digital manufacturing.

Abstract

The field of engineering is shaped by the tools and methods used to solve problems. Optimization is one such class of powerful, robust, and effective engineering tools proven over decades of use. Within just a few years, generative artificial intelligence (GenAI) has risen as another promising tool for general-purpose problem-solving. While optimization shines at precisely identifying highly-optimal solutions, GenAI excels at inferring problem requirements, bridging solution domains, handling mixed data modalities, and rapidly generating copious numbers of solutions. These differing attributes also make the two frameworks complementary. Hybrid `generative optimization' algorithms have gained traction across a few engineering applications and now comprise an emerging paradigm for engineering problem-solving. We expect significant developments in the near future around generative optimization, leading to changes in how engineers solve problems using computational tools. We offer our perspective on existing methods, areas of promise, and key research questions.

Generative Optimization: A Perspective on AI-Enhanced Problem Solving in Engineering

TL;DR

This paper argues that optimization and GenAI are complementary in engineering problem-solving. It defines generative optimization as frameworks that couple GenAI components with explicit optimization to leverage data-driven generation and rigorous evaluation. The authors outline three main approaches: using GenAI to speed and generalize optimization, using optimization to improve GenAI's solution quality, and unifying modal requirements and representations across domains. They discuss concrete methods such as warm-starts, GenAI operators, latent-space optimization, training on optimized data, iterative retraining, inverse optimization, cross-modal translation, and multimodal representations, and highlight key challenges like constraint satisfaction, diversity, data requirements, and retraining costs. The perspective suggests significant near-term developments and practical impact for engineering design and digital manufacturing.

Abstract

The field of engineering is shaped by the tools and methods used to solve problems. Optimization is one such class of powerful, robust, and effective engineering tools proven over decades of use. Within just a few years, generative artificial intelligence (GenAI) has risen as another promising tool for general-purpose problem-solving. While optimization shines at precisely identifying highly-optimal solutions, GenAI excels at inferring problem requirements, bridging solution domains, handling mixed data modalities, and rapidly generating copious numbers of solutions. These differing attributes also make the two frameworks complementary. Hybrid `generative optimization' algorithms have gained traction across a few engineering applications and now comprise an emerging paradigm for engineering problem-solving. We expect significant developments in the near future around generative optimization, leading to changes in how engineers solve problems using computational tools. We offer our perspective on existing methods, areas of promise, and key research questions.

Paper Structure

This paper contains 15 sections, 1 figure.

Table of Contents

  1. Introduction
  2. Discussion
  3. Mitigate Optimization's Cost and Complexity using GenAI
  4. Warm-Start Optimization
  5. GenAI Operator in Optimization
  6. Latent-Space Optimization
  7. Improve GenAI's Solution Quality using Optimization
  8. Training GenAI on Optimized Data
  9. Iterative Retraining
  10. Optimization-Based Training Objectives
  11. Unify Disparate Modalities in Requirements and Solutions
  12. Cross-Modal Optimization
  13. Inferring Requirements from Data
  14. Unifying Solution Representations
  15. Conclusion

Figures (1)

  • Figure 1: Overview figure showing different techniques to combine Generative AI and Optimization, along with pictograms of the example cases discussed in each section. These approaches are grouped into methods that seek to mitigate optimization's cost and complexity using GenAI, improve GenAI's solution quality using optimization, or unify disparate modalities in requirements and solutions.