Adversarial examples for heuristics in combinatorial optimization: An LLM based approach

ICLR 2026 Conference Submission18710 Authors

Keywords: combinatorial optimization, FunSearch, LLMs, analysis of algorithms

TL;DR: We explore the potential of FunSearch to generate adversarial examples for heuristics in combinatorial optimization.

Abstract:

This work employs LLMs to generate adversarial examples for heuristics in combinatorial optimization.
The problem, given a heuristic for an optimization problem, is to generate a problem instance where the heuristic performs poorly. We find improved adversarial constructions for well-known heuristics for k-median clustering, bin packing, the knapsack problem, and a generalization of Lov\'asz's gasoline problem. Specifically, we adapt the FunSearch framework [Romera-Paredes et al., Nature 2023] to obtain adversarial constructions for these problems. We note that using FunSearch is crucial to our improved constructions --- local search does not give comparable results.
The advantage of FunSearch is that it produces structured instances that yield theoretical insights which are post-processed and generalized by a human researcher while other metaheuristics usually produce only unstructured instances that are harder to generalize.

Primary Area: other topics in machine learning (i.e., none of the above)

Submission Number: 18710