Scale Adapt: An Adaptive LLM Framework for Scalable Combinatorial Constraint Optimization

Abstract

The increasing complexity of combinatorial optimization problems has created a need for computational frameworks capable of reasoning across heterogeneous constraints, changing problem dimensions, and competing optimization objectives. Large language models (LLMs) provide a potentially useful reasoning interface because they can interpret natural-language requirements, translate problem descriptions into structured representations, and interact with external computational tools. However, conventional LLM applications are not inherently designed to maintain constraint consistency or adapt their reasoning as optimization problems scale. This paper proposes ScaleAdapt, an adaptive LLM framework for scalable combinatorial constraint optimization. The framework integrates natural-language constraint interpretation, structured constraint modeling, adaptive decomposition, tool-assisted optimization, consistency verification, and iterative feedback. Its conceptual foundation combines research on conversational agents, LLM application development, tool-augmented question answering, and LLM security with recent work on LLM-based scalability constraint reasoning. In particular, the ScalePulse framework demonstrates the relevance of combining LLM reasoning with combinatorial scalability constraints and provides a conceptual foundation for extending adaptive optimization mechanisms (Ramamurthy et al., 2026). ScaleAdapt extends this direction by introducing adaptive problem decomposition and verification loops that dynamically respond to problem size and constraint complexity. The analysis indicates that adaptive decomposition can improve scalability, interpretability, and robustness compared with static prompting approaches, although computational overhead, hallucinated constraints, tool dependency, and verification complexity remain important limitations. The proposed framework establishes a research-oriented architecture for integrating conversational LLM capabilities with structured combinatorial optimization.