arXiv subjects

Junyang Cai

Publications and source records attributed to Junyang Cai.

10 recordsLinked to original sources

arXiv2026

FunL2O: LLM-Guided Feature Function Design for Learning to Optimize

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.

cs.LG↗

arXiv2025

ID-PaS+ : Identity-Aware Predict-and-Search for General Mixed-Integer Linear Programs

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 variable structures that commonly arise in real-world settings. This work extends the current Predict-and-Search (PAS) framework to parametric general parametric MIPs and introduces ID-PAS+, an identity-aware learning framework that enables the ML model to handle heterogeneous variable types 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.

cs.AI↗

arXiv2025

Gala: Global LLM Agents for Text-to-Model Translation

Natural language descriptions of optimization or satisfaction problems are challenging to translate into correct MiniZinc models, as this process demands both logical reasoning and constraint programming expertise. We introduce Gala, a framework that addresses this challenge with a global agentic approach: multiple specialized large language model (LLM) agents decompose the modeling task by global constraint type. Each agent is dedicated to detecting and generating code for a specific class of global constraint, while a final assembler agent integrates these constraint snippets into a complete MiniZinc model. By dividing the problem into smaller, well-defined sub-tasks, each LLM handles a simpler reasoning challenge, potentially reducing overall complexity. We conduct initial experiments with several LLMs and show better performance against baselines such as one-shot prompting and chain-of-thought prompting. Finally, we outline a comprehensive roadmap for future work, highlighting potential enhancements and directions for improvement.

cs.AI↗

arXiv2025

Domain-Aware Machine Learning for Accelerating MILP-Based Motion Planning with Temporal Logic and Chance Constraints

Motion-planning problems with temporal-logic or chance constraints are often encoded as mixed-integer linear programs (MILPs). Although these encodings provide rigorous specifications, their combinatorial structure can make planning prohibitively slow. Machine learning for combinatorial optimization (ML4CO) has accelerated general-purpose MILP solving, but its standard graph representations discard semantic information available in control problems, such as variable roles, time indices, sample identities, and formula structure. We introduce a domain-aware ML4CO framework for MILP-based motion planning with temporal logic and chance constraints. The framework augments a conventional variable--constraint bipartite graph with features derived from the planning formulation and uses the resulting representation for two solver-guidance tasks: selecting branching backdoors and configuring solver parameters. We study three domains---Signal Temporal Logic (STL) planning, chance-constrained planning through Conformal Predictive Programming (CPP), and multi-agent Capability Temporal Logic (CaTL) planning---and compare against solver defaults, domain-agnostic learned methods, non-learned branching rules, MCTS transfer, and SMAC3 transfer. Across the tested distributions, domain-aware backdoor selection has the lowest reported mean solve time in all three domains, improving on default Gurobi by 14.4--20.4%. Domain-aware configuration also has the lowest mean primal gap and primal integral in all three domains under a fixed SCIP time limit. These results show that exposing control-specific structure can improve learned MILP guidance beyond generic optimization features.

eess.SY↗

arXiv2025

ParBalans: Parallel Multi-Armed Bandits-based Adaptive Large Neighborhood Search

Solving Mixed-Integer Programming (MIP) problems often requires substantial computational resources due to their combinatorial nature. Parallelization has emerged as a critical strategy to accelerate solution times and enhance scalability to tackle large, complex instances. This paper investigates the parallelization capabilities of Balans, a recently proposed multi-armed bandits-based adaptive large neighborhood search for MIPs. While Balans's modular architecture inherently supports parallel exploration of diverse parameter configurations, this potential has not been thoroughly examined. To address this gap, we introduce ParBalans, an extension that leverages both solver-level and algorithmic-level parallelism to improve performance on challenging MIP instances. Our experimental results demonstrate that ParBalans exhibits competitive performance compared to the state-of-the-art commercial solver Gurobi, particularly on hard optimization benchmarks.

cs.AI↗

arXiv2024

Balans: Multi-Armed Bandits-based Adaptive Large Neighborhood Search for Mixed-Integer Programming Problem

Mixed-integer programming (MIP) is a powerful paradigm for modeling and solving various important combinatorial optimization problems. Recently, learning-based approaches have shown a potential to speed up MIP solving via offline training that then guides important design decisions during the search. However, a significant drawback of these methods is their heavy reliance on offline training, which requires collecting training datasets and computationally costly training epochs yet offering only limited generalization to unseen (larger) instances. In this paper, we propose Balans, an adaptive meta-solver for MIPs with online learning capability that does not require any supervision or apriori training. At its core, Balans is based on adaptive large-neighborhood search, operating on top of an MIP solver by successive applications of destroy and repair neighborhood operators. During the search, the selection among different neighborhood definitions is guided on the fly for the instance at hand via multi-armed bandit algorithms. Our extensive experiments on hard optimization instances show that Balans offers significant performance gains over the default MIP solver, is better than committing to any single best neighborhood, and improves over the state-of-the-art large-neighborhood search for MIPs. Finally, we release Balans as a highly configurable, MIP solver agnostic, open-source software.

cs.AI↗

arXiv2024

Multi-task Representation Learning for Mixed Integer Linear Programming

Mixed Integer Linear Programs (MILPs) are highly flexible and powerful tools for modeling and solving complex real-world combinatorial optimization problems. Recently, machine learning (ML)-guided approaches have demonstrated significant potential in improving MILP-solving efficiency. However, these methods typically rely on separate offline data collection and training processes, which limits their scalability and adaptability. This paper introduces the first multi-task learning framework for ML-guided MILP solving. The proposed framework provides MILP embeddings helpful in guiding MILP solving across solvers (e.g., Gurobi and SCIP) and across tasks (e.g., Branching and Solver configuration). Through extensive experiments on three widely used MILP benchmarks, we demonstrate that our multi-task learning model performs similarly to specialized models within the same distribution. Moreover, it significantly outperforms them in generalization across problem sizes and tasks.

cs.AI↗

arXiv2024

Learning Backdoors for Mixed Integer Linear Programs with Contrastive Learning

Many real-world problems can be efficiently modeled as Mixed Integer Linear Programs (MILPs) and solved with the Branch-and-Bound method. Prior work has shown the existence of MILP backdoors, small sets of variables such that prioritizing branching on them when possible leads to faster running times. However, finding high-quality backdoors that improve running times remains an open question. Previous work learns to estimate the relative solver speed of randomly sampled backdoors through ranking and then decide whether to use the highest-ranked backdoor candidate. In this paper, we utilize the Monte-Carlo tree search method to collect backdoors for training, rather than relying on random sampling, and adapt a contrastive learning framework to train a Graph Attention Network model to predict backdoors. Our method, evaluated on several common MILP problem domains, demonstrates performance improvements over both Gurobi and previous models.

cs.AI↗

arXiv2024

Optimization Over Trained Neural Networks: Taking a Relaxing Walk

Besides training, mathematical optimization is also used in deep learning to model and solve formulations over trained neural networks for purposes such as verification, compression, and optimization with learned constraints. However, solving these formulations soon becomes difficult as the network size grows due to the weak linear relaxation and dense constraint matrix. We have seen improvements in recent years with cutting plane algorithms, reformulations, and an heuristic based on Mixed-Integer Linear Programming (MILP). In this work, we propose a more scalable heuristic based on exploring global and local linear relaxations of the neural network model. Our heuristic is competitive with a state-of-the-art MILP solver and the prior heuristic while producing better solutions with increases in input, depth, and number of neurons.

math.OC↗

arXiv2023

Getting Away with More Network Pruning: From Sparsity to Geometry and Linear Regions

One surprising trait of neural networks is the extent to which their connections can be pruned with little to no effect on accuracy. But when we cross a critical level of parameter sparsity, pruning any further leads to a sudden drop in accuracy. This drop plausibly reflects a loss in model complexity, which we aim to avoid. In this work, we explore how sparsity also affects the geometry of the linear regions defined by a neural network, and consequently reduces the expected maximum number of linear regions based on the architecture. We observe that pruning affects accuracy similarly to how sparsity affects the number of linear regions and our proposed bound for the maximum number. Conversely, we find out that selecting the sparsity across layers to maximize our bound very often improves accuracy in comparison to pruning as much with the same sparsity in all layers, thereby providing us guidance on where to prune.

cs.LG↗