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Deep Insights into Automated Optimization with Large Language Models and Evolutionary Algorithms

He Yu, Jing Liu

TL;DR

A systematic review and thorough analysis of the LLM-EA paradigm can assist researchers in better understanding the current research and promoting the development of combining LLMs with EAs for automated optimization.

Abstract

Designing optimization approaches, whether heuristic or meta-heuristic, usually demands extensive manual intervention and has difficulty generalizing across diverse problem domains. The combination of Large Language Models (LLMs) and Evolutionary Algorithms (EAs) offers a promising new approach to overcome these limitations and make optimization more automated. In this setup, LLMs act as dynamic agents that can generate, refine, and interpret optimization strategies, while EAs efficiently explore complex solution spaces through evolutionary operators. Since this synergy enables a more efficient and creative search process, we first conduct an extensive review of recent research on the application of LLMs in optimization. We focus on LLMs' dual functionality as solution generators and algorithm designers. Then, we summarize the common and valuable designs in existing work and propose a novel LLM-EA paradigm for automated optimization. Furthermore, centered on this paradigm, we conduct an in-depth analysis of innovative methods for three key components: individual representation, variation operators, and fitness evaluation. We address challenges related to heuristic generation and solution exploration, especially from the LLM prompts' perspective. Our systematic review and thorough analysis of the paradigm can assist researchers in better understanding the current research and promoting the development of combining LLMs with EAs for automated optimization.

Deep Insights into Automated Optimization with Large Language Models and Evolutionary Algorithms

TL;DR

A systematic review and thorough analysis of the LLM-EA paradigm can assist researchers in better understanding the current research and promoting the development of combining LLMs with EAs for automated optimization.

Abstract

Designing optimization approaches, whether heuristic or meta-heuristic, usually demands extensive manual intervention and has difficulty generalizing across diverse problem domains. The combination of Large Language Models (LLMs) and Evolutionary Algorithms (EAs) offers a promising new approach to overcome these limitations and make optimization more automated. In this setup, LLMs act as dynamic agents that can generate, refine, and interpret optimization strategies, while EAs efficiently explore complex solution spaces through evolutionary operators. Since this synergy enables a more efficient and creative search process, we first conduct an extensive review of recent research on the application of LLMs in optimization. We focus on LLMs' dual functionality as solution generators and algorithm designers. Then, we summarize the common and valuable designs in existing work and propose a novel LLM-EA paradigm for automated optimization. Furthermore, centered on this paradigm, we conduct an in-depth analysis of innovative methods for three key components: individual representation, variation operators, and fitness evaluation. We address challenges related to heuristic generation and solution exploration, especially from the LLM prompts' perspective. Our systematic review and thorough analysis of the paradigm can assist researchers in better understanding the current research and promoting the development of combining LLMs with EAs for automated optimization.

Paper Structure

This paper contains 28 sections, 3 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Evolution of Heuristics for Automated Optimization
  3. Pre-Heuristic Approaches to Optimization
  4. Classical Heuristics
  5. Rise of Meta-Heuristics
  6. Hyper-Heuristics: Automating Heuristic Design
  7. Toward a New Era of Automated Optimization
  8. Fundamental Technologies in LLM and EA for Automated Optimization
  9. Overview of LLMs and EAs
  10. Understanding Prompts in LLMs
  11. Prompt techniques
  12. Prompt optimization
  13. EAs for Prompt Optimization
  14. Development of LLM-based Optimization and LLM-EA Automated Optimization Paradigm
  15. LLM-based Optimization
  16. ...and 13 more sections

Figures (4)

  • Figure 1: The major development of heuristics
  • Figure 2: The examples of prompting
  • Figure 3: (a) This is the variation prompt for the TSP. The problem description introduces the TSP and presents data for an instance of the problem. The example data provides several routes along with their respective lengths. The task instruction specifies the requirement to provide a route that is shorter than all the routes given in the example data. (b) This reflective prompt is aimed at refining or optimizing the task instruction for the TSP.
  • Figure 4: An individual representation of EoH liu2024eoh is provided, where the heuristic is expressed in both natural language and executable code. The natural language description explains how the heuristic calculates scores for each bin, considering factors such as remaining capacity, bin index, and penalties for large differences. The code snippet implements this logic. A fitness score of 0.0143 reflects the performance of the generated heuristic in the optimization task.