Not All Problems Are Best Modeled as MILP: A DSL-Centric Framework for Flexible and Accurate Optimization Modeling

2026-08-07

AI Summary

Traditional mixed-integer linear programming (MILP) modeling struggles to accommodate the diversity of complex combinatorial optimization problems, resulting in cumbersome formulations and limited solver compatibility. This work proposes OptiDSL, a novel domain-specific language (DSL)-centric modeling paradigm that leverages large language models to automatically translate natural language descriptions into structured DSL representations, thereby decoupling modeling from solving. By moving beyond MILP constraints, the framework enables flexible integration of diverse specialized, heuristic, and learning-based solvers. Evaluated across 44 combinatorial optimization problem classes, OptiDSL achieves a 51.66% improvement in modeling accuracy and reduces modeling time by 91.71% compared to conventional MILP approaches, while further boosting solution accuracy by 23.09% over existing benchmarks.

Abstract

Solving combinatorial optimization problems (COPs) requires not only efficient algorithms but also carefully crafted formulations. While recent works have leveraged LLMs to automate optimization modeling, current frameworks predominantly rely on a rigid mixed-integer linear programming (MILP) paradigm. In this paper, we argue that not all problems are best modeled as MILP, as forcing complex domains into linear constraints can induce prohibitive modeling complexity and severely restrict solver flexibility. To address this, we propose OptiDSL, a framework that shifts the focus from rigid MILP formulations to domain-specific language (DSL) representations. By utilizing LLMs to map natural language onto standardized, domain-accepted structures, OptiDSL decouples problem formulation from execution. This paradigm enables seamless integration with a diverse library of specialized solvers, ranging from traditional heuristics to modern learning-based methods. Experimental results on the comprehensive benchmark of 44 COP types show that OptiDSL significantly surpasses MILP-based pipelines, yielding a 51.66% gain in formulation accuracy and a 91.71% decrease in modeling time. Notably, it also outperforms MILP-based pipelines on the existing benchmark, achieving a 23.09% higher formulation accuracy. Our code is available at https://anonymous.4open.science/r/OptiDSL.

Problem

• combinatorial optimization
• MILP
• modeling flexibility
• domain-specific language
• optimization formulation

Innovation

• domain-specific language
• combinatorial optimization
• LLM-based modeling
• solver flexibility
• optimization formulation