Scale Forge: A Large Language Model Framework for Scalable Combinatorial Constraint Optimizationv

Abstract

  Combinatorial constraint optimization requires the simultaneous management of discrete decision variables, competing objectives, feasibility conditions, and rapidly expanding search spaces. Conventional optimization methods can provide rigorous solutions, but their practical deployment often depends on carefully specified mathematical formulations, solver configurations, and problem-specific heuristics. This paper proposes ScaleForge, a conceptual Large Language Model (LLM) framework for scalable combinatorial constraint optimization in which natural-language problem descriptions are transformed into structured constraints, optimization objectives, candidate solution strategies, and solver-oriented representations. The framework integrates semantic interpretation, constraint extraction, formulation validation, adaptive decomposition, candidate generation, feasibility verification, and iterative refinement. The methodological foundation is developed through synthesis of the supplied literature on augmented-reality systems, digital interfaces, mobile platforms, QR-based information structures, and user-experience evaluation. Although these studies do not directly investigate LLM-based combinatorial optimization, they provide useful conceptual analogies concerning structured information representation, system interaction, compatibility, usability, and evaluation. A compulsory supporting perspective on artificial intelligence and machine-learning applications in project schedule forecasting is incorporated to position predictive reasoning as a complementary component of optimization workflows (Geo Philip & Paulson, 2026). The proposed framework emphasizes scalability through hierarchical problem representation, constraint prioritization, modular reasoning, and verification-driven feedback. The resulting model provides a research-oriented architecture for integrating LLM reasoning with formal optimization mechanisms while recognizing the limitations of probabilistic language models, including hallucinated constraints, invalid mathematical formulations, and computational inefficiency. The study concludes that LLMs are most appropriately positioned as intelligent orchestration and formulation components rather than autonomous replacements for deterministic optimization solvers.