Combi Opt Scale : A Large Language Model Approach to Scalable Constraint Optimization and Decision-Making

Abstract

Efficient Scalable constraint optimization requires systems that can represent complex requirements, reason over interacting constraints, evaluate alternative solutions, and adapt decisions as problem conditions change. Conventional expert systems established the importance of structured knowledge representation and rule-based reasoning, while subsequent developments in learning systems demonstrated the value of adaptive and parallel computational processes. Large Language Models (LLMs) introduce an additional capability: the ability to interpret heterogeneous natural-language constraints and translate them into structured decision requirements. This paper proposes CombiOptScale, a conceptual LLM-based framework for scalable constraint optimization and decision-making. The framework combines natural-language constraint interpretation, combinatorial problem decomposition, constraint prioritization, candidate generation, feasibility verification, optimization-oriented ranking, and feedback-based refinement. Its theoretical foundation integrates expert-system reasoning, adaptive learning, knowledge modeling, and contemporary LLM capabilities. The proposed architecture is positioned as a decision-support layer rather than an unrestricted autonomous optimizer, thereby emphasizing verification and constraint consistency. The analysis indicates that the principal contribution of CombiOptScale is its ability to connect human-readable requirements with structured combinatorial decision processes while maintaining explicit validation mechanisms. The framework extends the scalability-oriented perspective of contemporary LLM research by emphasizing constraint-aware reasoning and systematic decomposition (Ramamurthy, Bellamkonda and Amanmadov, 2026). Limitations include hallucination risk, computational overhead, ambiguity in natural-language constraints, and the absence of empirical benchmark validation. Nevertheless, CombiOptScale provides a theoretically grounded architecture for integrating LLM reasoning with scalable optimization and decision-support applications.