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Fully Automated Generation of Combinatorial Optimisation Systems Using Large Language Models

Daniel Karapetyan

TL;DR

The paper investigates fully automated generation of combinatorial optimisation systems (OSs) using large language models (LLMs) to eliminate the need for human expert software development. It proposes FAOGs that interpret natural-language problem descriptions, generate problem-specific data structures, and assemble algorithms through monolithic, reduction-based, or component-based approaches, with a focus on robustness through validation and error correction. Across four benchmark problems, the study finds that component-based FAOGs with offline training (CMCS) provide the most consistent performance, while MIP-based reductions excel for polynomial problems like AP but are unreliable for NP-hard cases. The work demonstrates the feasibility of automated OS generation and argues for offline training and modular prompting as key drivers of practical performance, highlighting a path toward broader accessibility of decision-support tools in SMEs.

Abstract

Over the last few decades, researchers have made considerable efforts to make decision support more accessible for small and medium enterprises by reducing the cost of designing, developing and maintaining automated decision support systems. However, due to the diversity of the underlying combinatorial optimisation problems, reusability of such systems has been limited; in most cases, expensive expertise has been required to implement bespoke software components. We explore the feasibility of fully automated generation of combinatorial optimisation systems using large language models (LLMs). An LLM will be responsible for interpreting the user-provided problem description in natural language and designing and implementing problem-specific software components. We discuss the principles of fully automated LLM-based optimisation system generation, and evaluate several proof-of-concept generators, comparing their performance on four optimisation problems.

Fully Automated Generation of Combinatorial Optimisation Systems Using Large Language Models

TL;DR

The paper investigates fully automated generation of combinatorial optimisation systems (OSs) using large language models (LLMs) to eliminate the need for human expert software development. It proposes FAOGs that interpret natural-language problem descriptions, generate problem-specific data structures, and assemble algorithms through monolithic, reduction-based, or component-based approaches, with a focus on robustness through validation and error correction. Across four benchmark problems, the study finds that component-based FAOGs with offline training (CMCS) provide the most consistent performance, while MIP-based reductions excel for polynomial problems like AP but are unreliable for NP-hard cases. The work demonstrates the feasibility of automated OS generation and argues for offline training and modular prompting as key drivers of practical performance, highlighting a path toward broader accessibility of decision-support tools in SMEs.

Abstract

Over the last few decades, researchers have made considerable efforts to make decision support more accessible for small and medium enterprises by reducing the cost of designing, developing and maintaining automated decision support systems. However, due to the diversity of the underlying combinatorial optimisation problems, reusability of such systems has been limited; in most cases, expensive expertise has been required to implement bespoke software components. We explore the feasibility of fully automated generation of combinatorial optimisation systems using large language models (LLMs). An LLM will be responsible for interpreting the user-provided problem description in natural language and designing and implementing problem-specific software components. We discuss the principles of fully automated LLM-based optimisation system generation, and evaluate several proof-of-concept generators, comparing their performance on four optimisation problems.

Paper Structure

This paper contains 20 sections, 1 equation, 9 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Principles of fully automated OS generation
  3. FAOG design objectives
  4. FAOG architecture
  5. Data structures and input/output routines generation
  6. Optimisation algorithm generation
  7. FAOG design
  8. Problem description
  9. OS design
  10. General principles of LLM prompt engineering
  11. Instance and solution class generation
  12. Algorithm generation
  13. Monolithic algorithm generator.
  14. Reduction-based algorithm generator.
  15. Component-based algorithm generator.
  16. ...and 5 more sections

Figures (9)

  • Figure 1: The architectures of a FAOG and the generated OS.
  • Figure 2: UML diagram of the auto-generated OS.
  • Figure 3: Instance class prompt.
  • Figure 4: Solution class prompt.
  • Figure 5: Monolithic algorithm class prompt. The value of 'approach' defines the type of the algorithm that the LLM is expected to generate.
  • ...and 4 more figures