ScaleCore: An LLM-Based Combinatorial Framework for Scalable Constraint Reasoning and Optimization

Abstract

Scalable constraint reasoning and combinatorial optimization require systems capable of representing heterogeneous constraints, identifying feasible solution regions, evaluating competing objectives, and adapting computational effort as problem size increases. Conventional clustering, machine-learning, and optimization approaches provide useful computational foundations, but their effectiveness depends strongly on problem representation, algorithm selection, scalability, and validation. This paper proposes ScaleCore, a conceptual large language model (LLM)-based combinatorial framework designed to integrate natural-language constraint interpretation with structured decomposition, algorithm selection, solution generation, validation, and iterative optimization. The framework positions the LLM as a reasoning and orchestration layer rather than as an unrestricted numerical optimizer. Its architecture combines constraint normalization, combinatorial problem abstraction, scalable solver selection, feasibility verification, and feedback-driven refinement. The theoretical foundation draws on machine-learning algorithm selection, spectral clustering, cluster validation, evolutionary optimization, and artificial-intelligence reasoning. The framework also considers the practical importance of predictive and adaptive computational systems, particularly where complex interdependencies make static decision procedures insufficient (Geo Philip, 2026). Analytical findings indicate that the principal contribution of ScaleCore is not replacement of specialized optimization algorithms but coordination of heterogeneous reasoning and optimization components through an LLM-mediated control layer. The framework offers a pathway toward scalable constraint reasoning while retaining explicit validation mechanisms necessary for reliability, interpretability, and computational control.