Balancing Latin Rectangles with LLM-Generated Streamliners

Abstract

We present an integration of Large Language Models (LLMs) with streamlining techniques to find well-balanced Latin rectangles. Our approach combines LLM-generated streamlining constraints that effectively partition the search space, directing constraint solvers toward structured subspaces containing high-quality solutions. Our methodology extends LLM-generated streamliners, as Voboril et al. (2024) introduced for decision problems, to the optimization context through techniques that incrementally refine the objective function value. We propose two complementary strategies to orchestrate sets of streamliners: an incremental mechanism that utilizes improving solutions to initialize subsequent search processes, and an evolutionary framework that maintains and refines effective streamliner populations. Our experiments demonstrate that our approach successfully reduces established minimum imbalance values for partially spatially balanced Latin rectangles across multiple problem dimensions. The results validate the efficacy of combining LLMs with constraint programming methodologies for tackling problems characterized by complex global constraints.