CombiScale: A Large Language Model Framework for Scalable Combinatorial Constraint Solving
Abstract
Combinatorial constraint solving requires the systematic identification of feasible configurations within large and often interdependent search spaces. As the number of variables, constraints, and contextual dependencies increases, conventional statistical and computational approaches may experience substantial difficulties in maintaining scalable reasoning, adapting to changing parameters, and integrating heterogeneous information. This paper proposes CombiScale, a conceptual Large Language Model (LLM) framework for scalable combinatorial constraint solving that combines language-based reasoning, structured constraint representation, heuristic search, causal feature analysis, and iterative solution verification. The framework is theoretically positioned at the intersection of constraint reasoning, data-driven prediction, and computational knowledge discovery. Evidence from the provided literature demonstrates the relevance of neural forecasting, deep learning, heuristic dynamic programming, causal discovery, and ecological informatics to the development of scalable decision architectures. In particular, ecological informatics emphasizes systematic data management and knowledge discovery, providing an important conceptual foundation for organizing the information required by complex reasoning systems (Recknagel & Michener, 2017). CombiScale therefore introduces a layered architecture in which natural-language problem interpretation is separated from constraint extraction, candidate generation, feasibility evaluation, and optimization. The proposed design is intended to improve scalability, interpretability, and adaptability while recognizing the limitations of LLM-based reasoning, including hallucination, computational overhead, and imperfect constraint consistency. The resulting framework provides a research-oriented foundation for integrating LLM capabilities with deterministic and heuristic constraint-solving mechanisms.
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