OptiDSL Framework Boosts Optimization Modeling Accuracy and Speed

Solving combinatorial optimization problems (COPs) requires not only efficient algorithms but also carefully constructed mathematical formulations. While large language models (LLMs) have been leveraged to automate optimization modeling, existing frameworks predominantly rely on the rigid mixed-integer linear programming (MILP) paradigm. This paper argues that forcing complex problem domains into linear constraints can lead to prohibitive modeling complexity and restrict solver flexibility.To address this, the researchers propose OptiDSL, a framework that reorients the focus from strict MILP formulations to domain-specific language (DSL) representations. OptiDSL uses LLMs to translate natural language problem descriptions into standardized, domain-accepted DSL structures. This decoupling of problem formulation from execution allows for seamless integration with a broad library of specialized solvers, encompassing traditional heuristics and modern learning-based methods.Experimental results across 44 types of COPs demonstrate that OptiDSL significantly outperforms MILP-based pipelines. It achieves a 51.66% gain in formulation accuracy and a remarkable 91.71% decrease in modeling time. Even when compared to existing MILP benchmarks, OptiDSL shows a 23.09% higher formulation accuracy. The code for OptiDSL has been made available.