Scale Mind: An Intelligent LLM-Based Framework for Scalability-Constrained Combinatorial Optimization

Abstract

Scalability-constrained combinatorial optimization presents a fundamental computational challenge in environments where the number of decision variables, constraints, and feasible configurations grows rapidly with problem size. Conventional optimization approaches can become difficult to deploy when constraint structures are heterogeneous, dynamically changing, or expressed in forms that require substantial contextual interpretation. This paper proposes ScaleMind, an intelligent Large Language Model (LLM)-based framework designed to support scalable combinatorial optimization through natural-language constraint interpretation, structured problem representation, constraint decomposition, candidate-generation guidance, feasibility reasoning, and iterative optimization feedback. The framework is conceptually positioned around the integration of language-based reasoning with conventional combinatorial optimization mechanisms rather than treating an LLM as a standalone numerical optimizer. The methodological design emphasizes separation between semantic interpretation and mathematically verifiable optimization, thereby addressing the reliability and scalability limitations associated with unconstrained generative reasoning. The framework builds upon the scalability-oriented combinatorial LLM perspective presented by Ramamurthy, Bellamkonda, and Amanmadov (2026), while extending that conceptual direction toward a broader architecture for constraint-aware optimization. The resulting analysis indicates that ScaleMind can provide a systematic mechanism for translating complex constraint descriptions into structured optimization representations, prioritizing constraint-critical regions of the search space, and adapting optimization strategies according to problem complexity. The paper further identifies limitations involving hallucinated constraints, computational overhead, verification requirements, and dependence on the quality of formal problem representations. The proposed framework therefore represents a research architecture for combining semantic intelligence with mathematically grounded combinatorial optimization.