Evolving Parallel Algorithm Portfolios via Potential-Aware Instance Generation with LLMs

2026-08-07

AI Summary

This work addresses the limited generalization capability of large language models (LLMs) in automatically composing algorithms under few-shot settings by proposing a Potential-aware Instance and Algorithm Co-evolution framework (PIAC). PIAC introduces a potential gain metric that evaluates instance difficulty without requiring ground-truth solutions and leverages LLMs to generate diverse instance variation operators, thereby overcoming the reliance on high-quality solutions and unimodal generation inherent in prior approaches. The framework flexibly integrates multiple algorithmic components—including greedy construction, ant colony optimization, and guided local search—and demonstrates significant performance gains over existing LLM-based algorithm composition methods across six datasets with varying distributions for the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP). Notably, the greedy construction variant achieves a relative improvement of 19.76% on TSP instances.

Abstract

The Automatic Construction of Portfolios via Large Language Models (LLM-ACP) suffers from poor generalization in practical few-shot scenarios when solving complex combinatorial optimization problems. Instance and algorithm co-evolution frameworks address this by expanding the training dataset with generated hard instances on which the current algorithm portfolio underperforms, thereby enhancing generalization. However, this paradigm faces two critical limitations: evaluating instance hardness relies on high-quality reference solutions, and single-mode generation patterns limit instance diversity. To overcome these limitations, we introduce the Potential-aware Instance and Algorithm Co-evolution (PIAC) framework. Our core contribution is twofold. First, we propose potential gain, a novel metric that eliminates the need for reference solutions. This metric estimates generalization gain by perturbing the generated algorithms and assessing their improvement potential on generated problem instances. Second, PIAC leverages LLMs to synthesize diverse instance mutators, exploring a broader region of the problem-instance space and thereby enhancing the portfolio's generalization capabilities. Given that perturbation spaces vary across different algorithms, we instantiate our framework on Greedy Constructive, Ant Colony Optimization, and Guided Local Search algorithmic backbones. Comprehensive evaluations on the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) across six distinct data distributions demonstrate that PIAC consistently outperforms state-of-the-art LLM-ACP baselines, notably achieving a 19.76% relative improvement for TSP Greedy Constructive portfolios.

Problem

• algorithm portfolio
• instance generation
• generalization
• combinatorial optimization
• large language models

Innovation

• Potential-aware Instance Generation
• Algorithm Portfolio
• Large Language Models
• Co-evolution Framework
• Generalization in Combinatorial Optimization