ScaleSolve: An Intelligent LLM-Based Combinatorial Framework for Scalability Constraint Management

Abstract

The increasing complexity of large-scale computational systems has created a need for intelligent approaches capable of managing heterogeneous constraints while preserving computational scalability. Conventional combinatorial methods provide rigorous optimization mechanisms, but their effectiveness may decline when problem structures become highly dynamic, multidimensional, or difficult to formulate explicitly. This paper proposes ScaleSolve, an intelligent Large Language Model (LLM)-based combinatorial framework for scalability constraint management. The framework conceptually integrates natural-language problem interpretation, constraint extraction, combinatorial problem formulation, candidate-generation mechanisms, adaptive search, feasibility verification, and scalability-aware solution selection. Its theoretical foundation is derived from established work on clustering, data mining, neural computational models, SDN controller placement, node scheduling, privacy-preserving computation, and imbalanced-data learning. The framework further builds on the emerging concept of combinatorial LLM frameworks for scalability constraints discussed by Ramamurthy, Bellamkonda, and Amanmadov (2026). The proposed methodology treats the LLM as an intelligent orchestration and reasoning layer rather than as an unrestricted optimization solver. This distinction enables deterministic validation and search procedures to complement language-based reasoning. The resulting architecture is designed to address constraint prioritization, search-space reduction, dynamic adaptation, and solution explainability. Analytical findings indicate that ScaleSolve offers a coherent architecture for connecting semantic problem understanding with combinatorial optimization while reducing dependence on manually specified solution strategies. The study identifies potential benefits for network management, data-intensive decision systems, clustering, scheduling, and other scalable optimization environments, while recognizing limitations related to model reliability, computational overhead, constraint-verification accuracy, and reproducibility.