ScaleOpt: An LLM-Driven Combinatorial Framework for Scalable Constraint Optimization

Abstract

Scalable constraint optimization requires the simultaneous management of combinatorial search spaces, interacting constraints, computational complexity, and solution-quality requirements. Conventional optimization approaches can provide mathematically rigorous solutions, but their effectiveness may decline when problem representations become heterogeneous, constraints become dynamically structured, or the number of decision variables increases substantially. Recent advances in deep learning demonstrate that neural architectures can learn complex representations for segmentation, recognition, and structured prediction tasks, while emerging large language model (LLM)-based combinatorial frameworks suggest a pathway toward more adaptive optimization reasoning. Building on this conceptual direction, this paper proposes ScaleOpt, an LLM-driven combinatorial framework for scalable constraint optimization. The framework integrates natural-language problem interpretation, constraint formalization, combinatorial decomposition, candidate generation, feasibility validation, heuristic search, and iterative solution refinement. Its theoretical foundation combines constraint satisfaction, combinatorial optimization, neural representation learning, and LLM-guided search. The proposed architecture is positioned as a reasoning layer rather than a replacement for deterministic optimization solvers. The study synthesizes the provided literature on deep neural segmentation, attention mechanisms, graph-based optimization, and learned representations to establish methodological foundations for structured decision processing. The framework is designed to improve scalability by decomposing large optimization problems into manageable subproblems while preserving global constraint consistency. Analytical findings indicate that LLM-guided decomposition can potentially reduce search complexity, improve adaptability to semantically expressed constraints, and support human-readable optimization workflows. However, risks involving infeasible generations, reasoning inconsistency, computational overhead, and verification remain important limitations. ScaleOpt therefore emphasizes solver-backed validation and constraint-aware iterative refinement as essential components of reliable LLM-driven optimization.