LLMs Enhance Algorithm Portfolios with Potential-Aware Instance Generation

Current methods for automatically constructing algorithm portfolios using Large Language Models (LLMs) often struggle with generalization, especially in real-world scenarios involving complex combinatorial optimization problems. These methods typically rely on expanding training data by generating difficult problem instances where existing algorithms perform poorly. However, this approach faces challenges: evaluating instance hardness usually requires high-quality reference solutions, and the instance generation process often lacks diversity. To address these limitations, researchers have developed the Potential-aware Instance and Algorithm Co-evolution (PIAC) framework. A key innovation is the "potential gain" metric, which estimates how much an algorithm's performance could improve on a generated instance, eliminating the need for pre-computed reference solutions. Additionally, PIAC utilizes LLMs to create a wider variety of instance mutators, allowing for a more thorough exploration of the problem space and significantly boosting the portfolio's ability to generalize. Evaluations on classic problems like the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP) show that PIAC consistently outperforms existing LLM-based baselines. For instance, it achieved a nearly 20% relative improvement for TSP Greedy Constructive portfolios, demonstrating its effectiveness in enhancing the robustness and adaptability of AI-driven optimization solutions.