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Large Language Model Aided Multi-objective Evolutionary Algorithm: a Low-cost Adaptive Approach

Wanyi Liu, Long Chen, Zhenzhou Tang

TL;DR

The paper tackles the challenge of slow convergence and manual tuning in multi-objective evolutionary algorithms by introducing a low-cost, adaptive framework that integrates a Large Language Model with MOEAs. It uses an auxiliary evaluation function and automated prompt construction to selectively engage the LLM, and a hybrid mechanism to combine LLM guidance with traditional MOEA operations, minimizing interaction costs. Empirical results on ZDT and UF benchmarks show that the LLM-assisted MOEA can accelerate convergence and improve Pareto front coverage compared to strong baselines. The framework is designed to be generalizable across MOEAs and reduces reliance on expert tuning, enabling broader applicability in practical, real-world optimization tasks.

Abstract

Multi-objective optimization is a common problem in practical applications, and multi-objective evolutionary algorithm (MOEA) is considered as one of the effective methods to solve these problems. However, their randomness sometimes prevents algorithms from rapidly converging to global optimization, and the design of their genetic operators often requires complicated manual tuning. To overcome this challenge, this study proposes a new framework that combines a large language model (LLM) with traditional evolutionary algorithms to enhance the algorithm's search capability and generalization performance.In our framework, we employ adaptive and hybrid mechanisms to integrate the LLM with the MOEA, thereby accelerating algorithmic convergence. Specifically, we leverage an auxiliary evaluation function and automated prompt construction within the adaptive mechanism to flexibly adjust the utilization of the LLM, generating high-quality solutions that are further refined and optimized through genetic operators.Concurrently, the hybrid mechanism aims to minimize interaction costs with the LLM as much as possible.

Large Language Model Aided Multi-objective Evolutionary Algorithm: a Low-cost Adaptive Approach

TL;DR

The paper tackles the challenge of slow convergence and manual tuning in multi-objective evolutionary algorithms by introducing a low-cost, adaptive framework that integrates a Large Language Model with MOEAs. It uses an auxiliary evaluation function and automated prompt construction to selectively engage the LLM, and a hybrid mechanism to combine LLM guidance with traditional MOEA operations, minimizing interaction costs. Empirical results on ZDT and UF benchmarks show that the LLM-assisted MOEA can accelerate convergence and improve Pareto front coverage compared to strong baselines. The framework is designed to be generalizable across MOEAs and reduces reliance on expert tuning, enabling broader applicability in practical, real-world optimization tasks.

Abstract

Multi-objective optimization is a common problem in practical applications, and multi-objective evolutionary algorithm (MOEA) is considered as one of the effective methods to solve these problems. However, their randomness sometimes prevents algorithms from rapidly converging to global optimization, and the design of their genetic operators often requires complicated manual tuning. To overcome this challenge, this study proposes a new framework that combines a large language model (LLM) with traditional evolutionary algorithms to enhance the algorithm's search capability and generalization performance.In our framework, we employ adaptive and hybrid mechanisms to integrate the LLM with the MOEA, thereby accelerating algorithmic convergence. Specifically, we leverage an auxiliary evaluation function and automated prompt construction within the adaptive mechanism to flexibly adjust the utilization of the LLM, generating high-quality solutions that are further refined and optimized through genetic operators.Concurrently, the hybrid mechanism aims to minimize interaction costs with the LLM as much as possible.
Paper Structure (18 sections, 8 equations, 4 figures, 4 tables, 1 algorithm)

This paper contains 18 sections, 8 equations, 4 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. MOEA using the LLM
  4. Problem Formulation
  5. LLM for MOEA
  6. Framework
  7. LLM as a black-box optimizer
  8. Prompts the desired individual for selection
  9. Prompt engineering
  10. Error handling
  11. Experiment
  12. Test instances
  13. Baseline algorithms
  14. Experimental Settings
  15. Results
  16. ...and 3 more sections

Figures (4)

  • Figure 1: The LLM-assisted MOEA framework integrates LLMs as a black-box optimization operator. The LLM generates high-quality solution sets through prompts, accelerating the algorithm's convergence while also increasing the solution diversity. Prompt engineering is used to facilitate contextual learning for LLM.
  • Figure 2: HV values obtained by different multi-objective optimization algorithms.
  • Figure 3: Each algorithm is based on the PF surface of the ZDT1 instance: (a) NSGA-II, (b) NSGA-II-ARSBX, (c) NSGA-III, and (d) NSGA-II-LLM.
  • Figure 7: (a) The number of tokens required by each decision threshold for a single run, and (b) the average IGD comparison of UF instances..