Mixed-Integer Linear Programs (MIPs) are powerful and flexible tools for modeling a wide range of real-world combinatorial optimization problems. Predict-and-Search methods operate by using a predictive model to estimate promising variable assignments and then guiding a search procedure toward high-quality solutions. Recent research has demonstrated that incorporating machine learning (ML) into the Predict-and-Search framework significantly enhances its performance. Still, it is restricted to binary-only problems and overlooks the presence of fixed variables structure that commonly arise in real-world settings. This work extends the current Predict-and-Search (PaS) framework to parametric general MIPs and introduces ID-PaS+, an identity-aware learning framework that enables the ML model to handle heterogeneous variables more effectively. Experiments on several real-world large-scale problems demonstrate that ID-PaS+ consistently achieves superior performance compared to the state-of-the-art solver Gurobi and PaS.
Junyang Cai, El Mehdi Er Raqabi, Pascal Van Hentenryck et al.· Proceedings of the Internati...· 0 citations
Learning-to-optimize (L2O) methods accelerate repeated optimization by training models to predict solutions, warm starts, branching decisions, or other forms of solver guidance. A critical yet largely overlooked component of these pipelines is the feature function that maps problem instances to inputs for machine learning models. Existing L2O methods typically rely on hand-crafted features, making representation design manual and largely fixed across domains. We introduce FunL2O, the first unified framework for automating feature design through LLM-driven program evolution for L2O. In a FunSearch-style loop, an LLM proposes executable feature functions, while a fixed evaluation process retrains the original L2O model and measures downstream optimization performance. We evaluate FunL2O on linear and quadratic programming tasks involving solution prediction and warm-starting, as well as on mixed-integer optimization tasks using GNN-guided backdoor branching and Predict-and-Search. Across continuous and discrete optimization tasks and four LLMs, the evolved features consistently outperform hand-crafted representations. These results establish LLM-driven feature evolution as a general and effective approach to automating representation design in L2O.
Bingheng Li, Junyang Cai, Yupeng Zhang et al.· 0 citations