RoME: Domain-Robust Mixture-of-Experts for MILP Solution Prediction across Domains
Tianle Pu, Zijie Geng, Haoyang Liu, Shixuan Liu, Jie Wang, Li Zeng, Chao Chen, Changjun Fan
Mixed-Integer Linear Programming (MILP) is a fundamental and powerful framework for modeling complex optimization problems across diverse domains.Recently, learning-based methods have shown great promise in accelerating MILP solvers by predicting high-quality solutions.However, most existing approaches are developed and evaluated in single-domain settings, limiting their ability to generalize to unseen problem distributions.This limitation poses a major obstacle to building scalable and general-purpose learning-augmented solvers.To address this challenge, we introduce RoME, a domain-Robust Mixture-of-Experts (MoE) framework for predicting MILP solutions across domains.RoME dynamically routes problem instances to specialized experts based on learned task embeddings.The model is trained using a two-level distributionally robust optimization strategy: inter-domain to mitigate global shifts across domains, and intra-domain to enhance local robustness by introducing perturbations on task embeddings.We reveal that cross-domain training not only enhances the model's generalization capability to unseen domains but also improves performancewithin each individual domain by encouraging the model to capture more general intrinsic combinatorial patterns.Specifically, a single RoME model trained on three domains achieves an average improvement of $67.7\%$ then evaluated on five diverse domains.We further test the pretrained model on MIPLIB in a zero-shot setting, demonstrating its ability to deliver measurable performance gains on challenging real-world instances where existing learning-based approaches often struggle to generalize.