arXiv subjects

Fangzhou Zhu

Publications and source records attributed to Fangzhou Zhu.

At least 19 recordsLinked to original sources

arXiv2026

Collab-Solver: Collaborative Solving Policy Learning for Mixed-Integer Linear Programming

Mixed-integer linear programming (MILP) has been a fundamental problem in combinatorial optimization. Conventional MILP solving mainly relies on carefully designed heuristics embedded in the branch-and-bound framework. Driven by the strong capabilities of neural networks, recent research is exploring the value of machine learning alongside conventional MILP solving. Although learning-based MILP methods have shown great promise, existing works typically learn policies for individual modules in MILP solvers in isolation, without considering their interdependence, which limits both solving efficiency and solution quality. To address this limitation, we propose Collab-Solver, a novel multi-agent-based policy learning framework for MILP that enables collaborative policy optimization for multiple modules. Specifically, we formulate the collaboration between cut selection and branching in MILP solving as a Stackelberg game. Under this formulation, we develop a two-phase learning paradigm to stabilize collaborative policy learning: the first phase performs data-communicated policy pretraining, and the second phase further orchestrates the policy learning for various modules. Extensive experiments on both synthetic and large-scale real-world MILP datasets demonstrate that the jointly learned policies significantly improve solving performance. Moreover, the policies learned by Collab-Solver have also demonstrated excellent generalization abilities across different instance sets.

cs.AI↗

arXiv2026

GRIMIP: A General Framework for Instance-Specific Configuration of MIP Solvers Using LLMs

Configuring the hyperparameters of Mixed-integer programming (MIP) solvers is a high-dimensional, instance-dependent optimization problem where suboptimal settings can degrade solving time by orders of magnitude. Default configurations are often suboptimal, while traditional tuning methods either suffer from the ``cold-start'' problem and inefficient search or heavily rely on expert experience. This paper introduces \textbf{GRIMIP} (\textbf{\underline{G}}eneral \textbf{\underline{R}}easoning for \textbf{\underline{I}}nstance-specific \textbf{\underline{MIP}} configuration), a novel hybrid intelligence framework that synergistically integrates the semantic reasoning capabilities of Large Language Models (LLMs) with the sample-efficient search of Bayesian Optimization (BO). GRIMIP enables the LLM to function as a complete probabilistic surrogate within the BO loop, significantly improving performance and reducing sampling and evaluation costs. On seven benchmarks including MIPLIB, GRIMIP achieves over 40\% reduction in Primal-Dual Integral on hard instances, outperforming SMAC and other LLM-assisted BO methods. By granting LLMs sufficient autonomy, GRIMIP combines the expert-level reasoning of LLMs with the efficient search of BO, achieving state-of-the-art performance.

cs.LG↗

arXiv2026

Opt-Verifier: Unleashing the Power of LLMs for Optimization Modeling via Dual-Side Verification

Building mathematical optimization models is critical in operations research (OR), while it requires substantial human expertise. Recent advancements have utilized large language models (LLMs) to automate this modeling process. However, existing works often struggle to verify the correctness of the generated optimization models, without checking the rationality of the constraints and variables or the validity of solutions to the generated models. This hampers the subsequent verification and correction steps, and thus it severely hurts the modeling accuracy. To address this challenge, we propose a novel LLM-based framework with Dual-side Verification (Opt-Verifier) from both structure and solution perspectives, thereby improving the modeling accuracy. The structure-side verification ensures that the modeling structure of the generated optimization models aligns with the original problem description, accurately capturing the problem's constraints and requirements. Meanwhile, the solution-side verification interprets and evaluates the solutions' validity, confirming that the optimization models are logically and mathematically sound. Experiments on popular benchmarks demonstrate that our approach achieves over 20\% improvement in accuracy.

cs.AI↗

arXiv2025

BPP-Search: Enhancing Tree of Thought Reasoning for Mathematical Modeling Problem Solving

LLMs exhibit advanced reasoning capabilities, offering the potential to transform natural language questions into mathematical models. However, existing open-source datasets in operations research domain lack detailed annotations of the modeling process, such as variable definitions, focusing solely on objective values, which hinders reinforcement learning applications. To address this, we release the StructuredOR dataset, annotated with comprehensive labels that capture the complete mathematical modeling process. We further propose BPP-Search, an algorithm that integrates reinforcement learning into a tree-of-thought structure using Beam search, a Process reward model, and a pairwise Preference algorithm. This approach enables efficient exploration of tree structures, avoiding exhaustive search while improving accuracy. Extensive experiments on StructuredOR, NL4OPT, and MAMO-ComplexLP datasets show that BPP-Search significantly outperforms state-of-the-art methods. In tree-based reasoning, BPP-Search excels in accuracy and efficiency, enabling faster retrieval of correct solutions. The StructuredOR dataset is available on Huggingface https://huggingface.co/datasets/LLM4OR/StructuredOR and GitHub https://github.com/LLM4OR/StructuredOR.

cs.AI↗

arXiv2025

Efficient Gaussian Process Classification-based Physical-Layer Authentication with Configurable Fingerprints for 6G-Enabled IoT

The future 6G-enabled IoT will facilitate seamless global connectivity among ubiquitous wireless devices, but this advancement also introduces heightened security risks such as spoofing attacks. Physical-Layer Authentication (PLA) has emerged as a promising, inherently secure, and energy-efficient technique for authenticating IoT terminals. Nonetheless, the direct application of state-of-the-art PLA schemes to 6G-enabled IoT encounters two major hurdles: inaccurate channel fingerprints and the inefficient utilization of prior fingerprint information. To tackle these challenges, we leverage Reconfigurable Intelligent Surfaces (RISs) to enhance fingerprint accuracy. Additionally, we integrate active learning and Gaussian Processes (GPs) to propose an Efficient Gaussian Process Classification (EGPC)-based PLA scheme, aiming for reliable and lightweight authentication. Following Bayes' theorem, we model configurable fingerprints using GPs and employ the expectation propagation method to identify unknown fingerprints. Given the difficulty of obtaining sufficient labeled fingerprint samples to train PLA models, we propose three fingerprint selection algorithms. These algorithms select unlabeled fingerprints and query their identities using upper-layer authentication mechanisms. Among these methods, the optimal algorithm reduces the number of training fingerprints needed through importance sampling and eliminates the requirement for PLA model retraining through joint distribution calculation. Simulations results reveal that, in comparison with non-RIS-based approaches, the RIS-aided PLA framework decreases the authentication error rate by 98.69%. In addition, our designed fingerprint selection algorithms achieve a reduction in the authentication error rate of up to 86.93% compared to baseline active learning schemes.

eess.SP↗

arXiv2025

Apollo-MILP: An Alternating Prediction-Correction Neural Solving Framework for Mixed-Integer Linear Programming

Leveraging machine learning (ML) to predict an initial solution for mixed-integer linear programming (MILP) has gained considerable popularity in recent years. These methods predict a solution and fix a subset of variables to reduce the problem dimension. Then, they solve the reduced problem to obtain the final solutions. However, directly fixing variable values can lead to low-quality solutions or even infeasible reduced problems if the predicted solution is not accurate enough. To address this challenge, we propose an Alternating prediction-correction neural solving framework (Apollo-MILP) that can identify and select accurate and reliable predicted values to fix. In each iteration, Apollo-MILP conducts a prediction step for the unfixed variables, followed by a correction step to obtain an improved solution (called reference solution) through a trust-region search. By incorporating the predicted and reference solutions, we introduce a novel Uncertainty-based Error upper BOund (UEBO) to evaluate the uncertainty of the predicted values and fix those with high confidence. A notable feature of Apollo-MILP is the superior ability for problem reduction while preserving optimality, leading to high-quality final solutions. Experiments on commonly used benchmarks demonstrate that our proposed Apollo-MILP significantly outperforms other ML-based approaches in terms of solution quality, achieving over a 50% reduction in the solution gap.

cs.LG↗

arXiv2024

Learning to Cut via Hierarchical Sequence/Set Model for Efficient Mixed-Integer Programming

Cutting planes (cuts) play an important role in solving mixed-integer linear programs (MILPs), which formulate many important real-world applications. Cut selection heavily depends on (P1) which cuts to prefer and (P2) how many cuts to select. Although modern MILP solvers tackle (P1)-(P2) by human-designed heuristics, machine learning carries the potential to learn more effective heuristics. However, many existing learning-based methods learn which cuts to prefer, neglecting the importance of learning how many cuts to select. Moreover, we observe that (P3) what order of selected cuts to prefer significantly impacts the efficiency of MILP solvers as well. To address these challenges, we propose a novel hierarchical sequence/set model (HEM) to learn cut selection policies. Specifically, HEM is a bi-level model: (1) a higher-level module that learns how many cuts to select, (2) and a lower-level module -- that formulates the cut selection as a sequence/set to sequence learning problem -- to learn policies selecting an ordered subset with the cardinality determined by the higher-level module. To the best of our knowledge, HEM is the first data-driven methodology that well tackles (P1)-(P3) simultaneously. Experiments demonstrate that HEM significantly improves the efficiency of solving MILPs on eleven challenging MILP benchmarks, including two Huawei's real problems.

cs.AI↗

arXiv2024

Machine Learning Insides OptVerse AI Solver: Design Principles and Applications

In an era of digital ubiquity, efficient resource management and decision-making are paramount across numerous industries. To this end, we present a comprehensive study on the integration of machine learning (ML) techniques into Huawei Cloud's OptVerse AI Solver, which aims to mitigate the scarcity of real-world mathematical programming instances, and to surpass the capabilities of traditional optimization techniques. We showcase our methods for generating complex SAT and MILP instances utilizing generative models that mirror multifaceted structures of real-world problem. Furthermore, we introduce a training framework leveraging augmentation policies to maintain solvers' utility in dynamic environments. Besides the data generation and augmentation, our proposed approaches also include novel ML-driven policies for personalized solver strategies, with an emphasis on applications like graph convolutional networks for initial basis selection and reinforcement learning for advanced presolving and cut selection. Additionally, we detail the incorporation of state-of-the-art parameter tuning algorithms which markedly elevate solver performance. Compared with traditional solvers such as Cplex and SCIP, our ML-augmented OptVerse AI Solver demonstrates superior speed and precision across both established benchmarks and real-world scenarios, reinforcing the practical imperative and effectiveness of machine learning techniques in mathematical programming solvers.

cs.AI↗

arXiv2023

Accelerate Presolve in Large-Scale Linear Programming via Reinforcement Learning

Large-scale LP problems from industry usually contain much redundancy that severely hurts the efficiency and reliability of solving LPs, making presolve (i.e., the problem simplification module) one of the most critical components in modern LP solvers. However, how to design high-quality presolve routines -- that is, the program determining (P1) which presolvers to select, (P2) in what order to execute, and (P3) when to stop -- remains a highly challenging task due to the extensive requirements on expert knowledge and the large search space. Due to the sequential decision property of the task and the lack of expert demonstrations, we propose a simple and efficient reinforcement learning (RL) framework -- namely, reinforcement learning for presolve (RL4Presolve) -- to tackle (P1)-(P3) simultaneously. Specifically, we formulate the routine design task as a Markov decision process and propose an RL framework with adaptive action sequences to generate high-quality presolve routines efficiently. Note that adaptive action sequences help learn complex behaviors efficiently and adapt to various benchmarks. Experiments on two solvers (open-source and commercial) and eight benchmarks (real-world and synthetic) demonstrate that RL4Presolve significantly and consistently improves the efficiency of solving large-scale LPs, especially on benchmarks from industry. Furthermore, we optimize the hard-coded presolve routines in LP solvers by extracting rules from learned policies for simple and efficient deployment to Huawei's supply chain. The results show encouraging economic and academic potential for incorporating machine learning to modern solvers.

cs.LG↗

arXiv2023

Effective cosmic density field reconstruction with convolutional neural network

We present a cosmic density field reconstruction method that augments the traditional reconstruction algorithms with a convolutional neural network (CNN). Following Shallue $\&$ Eisenstein (2022), the key component of our method is to use the $\textit{reconstructed}$ density field as the input to the neural network. We extend this previous work by exploring how the performance of these reconstruction ideas depends on the input reconstruction algorithm, the reconstruction parameters, and the shot noise of the density field, as well as the robustness of the method. We build an eight-layer CNN and train the network with reconstructed density fields computed from the Quijote suite of simulations. The reconstructed density fields are generated by both the standard algorithm and a new iterative algorithm. In real space at $z=0$, we find that the reconstructed field is $90\%$ correlated with the true initial density out to $k\sim 0.5 h{\rm Mpc}^{-1}$, a significant improvement over $k\sim 0.2 h{\rm Mpc}^{-1}$ achieved by the input reconstruction algorithms. We find similar improvements in redshift space, including an improved removal of redshift space distortions at small scales. We also find that the method is robust across changes in cosmology. Additionally, the CNN removes much of the variance from the choice of different reconstruction algorithms and reconstruction parameters. However, the effectiveness decreases with increasing shot noise, suggesting that such an approach is best suited to high density samples. This work highlights the additional information in the density field beyond linear scales as well as the power of complementing traditional analysis approaches with machine learning techniques.

astro-ph.CO↗

arXiv2022

Learning to Reformulate for Linear Programming

It has been verified that the linear programming (LP) is able to formulate many real-life optimization problems, which can obtain the optimum by resorting to corresponding solvers such as OptVerse, Gurobi and CPLEX. In the past decades, a serial of traditional operation research algorithms have been proposed to obtain the optimum of a given LP in a fewer solving time. Recently, there is a trend of using machine learning (ML) techniques to improve the performance of above solvers. However, almost no previous work takes advantage of ML techniques to improve the performance of solver from the front end, i.e., the modeling (or formulation). In this paper, we are the first to propose a reinforcement learning-based reformulation method for LP to improve the performance of solving process. Using an open-source solver COIN-OR LP (CLP) as an environment, we implement the proposed method over two public research LP datasets and one large-scale LP dataset collected from practical production planning scenario. The evaluation results suggest that the proposed method can effectively reduce both the solving iteration number ($25\%\downarrow$) and the solving time ($15\%\downarrow$) over above datasets in average, compared to directly solving the original LP instances.

math.OC↗

arXiv2020

Electrostatically tunable axisymmetric vibrations of soft electro-active tubes

Due to their unique electromechanical coupling properties, soft electro-active (SEA) resonators are actively tunable, extremely suitable, and practically important for designing the next-generation acoustic and vibration treatment devices. In this paper, we investigate the electrostatically tunable axisymmetric vibrations of SEA tubes with different geometric sizes. We consider both axisymmetric torsional and longitudinal vibrations for an incompressible SEA cylindrical tube under inhomogeneous biasing fields induced by radial electric voltage and axial pre-stretch. We then employ the state-space method, which combines the state-space formalism in cylindrical coordinates with the approximate laminate technique, to derive the frequency equations for two separate classes of axisymmetric vibration of the tube subjected to appropriate boundary conditions. We perform numerical calculations to validate the convergence and accuracy of the state-space method and to illuminate that the axisymmetric vibration characteristics of SEA tubes may be tuned significantly by adjusting the electromechanical biasing fields as well as altering the tube geometry. The reported results provide a solid guidance for the proper design of tunable resonant devices composed of SEA tubes

cond-mat.soft↗

arXiv2018

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: a tomographic measurement of cosmic structure growth and expansion rate based on optimal redshift weights

We develop a new method, which is based on the optimal redshift weighting scheme, to extract the maximal tomographic information of baryonic acoustic oscillations (BAO) and redshift space distortions (RSD) from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 14 quasar (DR14Q) survey. We validate our method using the EZ mocks, and apply our pipeline to the eBOSS DR14Q sample in the redshift range of $0.8<z<2.2$. We report a joint measurement of $fσ_8$ and two-dimensional BAO parameters $D_{\rm A}$ and $H$ at four effective redshifts of $z_{\rm eff}=0.98, 1.23, 1.52$ and $1.94$, and provide the full data covariance matrix. Using our measurement combined with BOSS DR12, MGS and 6dFGS BAO measurements, we find that the existence of dark energy is supported by observations at a $7.4σ$ significance level. Combining our measurement with BOSS DR12 and Planck observations, we constrain the gravitational growth index to be $γ=0.580\pm0.082$, which is fully consistent with the prediction of general relativity. This paper is part of a set that analyses the eBOSS DR14 quasar sample.

astro-ph.CO↗

arXiv2018

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: Anisotropic Baryon Acoustic Oscillations measurements in Fourier-space with optimal redshift weights

We present a measurement of the anisotropic and isotropic Baryon Acoustic Oscillations (BAO) from the extended Baryon Oscillation Spectroscopic Survey Data Release 14 quasar sample with optimal redshift weights. Applying the redshift weights improves the constraint on the BAO dilation parameter $α(z_{\rm eff})$ by 17\%. We reconstruct the evolution history of the BAO distance indicators in the redshift range of $0.8<z<2.2$. This paper is part of a set that analyses the eBOSS DR14 quasar sample.

astro-ph.CO↗

arXiv2018

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: measuring the evolution of the growth rate using redshift space distortions between redshift 0.8 and 2.2

We measure the growth rate and its evolution using the anisotropic clustering of the extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 14 (DR14) quasar sample, which includes $148\,659$ quasars covering the wide redshift range of $0.8 < z < 2.2$ and a sky area of $2112.90$ $\rm deg^2$. To optimise measurements we deploy a redshift-dependent weighting scheme, which allows us to avoid binning, and perform the data analysis consistently including the redshift evolution across the sample. We perform the analysis in Fourier space, and use the redshift evolving power spectrum multipoles to measure the redshift space distortion parameter $fσ_8$ and parameters controlling the anisotropic projection of the cosmological perturbations. We measure $f σ_8(z=1.52)=0.43 \pm 0.05 $ and $dfσ_8/dz (z=1.52)= - 0.16 \pm 0.08$, consistent with the expectation for a $Λ$CDM cosmology as constrained by the Planck experiment.

astro-ph.CO↗

arXiv2018

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: Measuring the anisotropic Baryon Acoustic Oscillations with redshift weights

We present an anisotropic analysis of Baryon Acoustic Oscillation (BAO) signal from the SDSS-IV extended Baryon Oscillation Spectroscopic Survey (eBOSS) Data Release 14 (DR14) quasar sample. The sample consists of 147,000 quasars distributed over a redshift range of $0.8 < z < 2.2$. We apply the redshift weights technique to the clustering of quasars in this sample and achieve a 4.6 per cent measurement of the angular distance measurement $D_M$ at $z = 2.2$ and Hubble parameter $H$ at $z=0.8$. We parameterize the distance-redshift relation, relative to a fiducial model, as a quadratic expansion. The coefficients of this expansion are used to reconstruct the distance-redshift relation and obtain distance and Hubble parameter measurements at all redshifts within the redshift range of the sample. Reporting the result at two characteristic redshifts, we determine $D_M(z=1) = 3405\pm305 \ (r_{\rm d} / r_{\rm d, fid}) \ {\rm Mpc}$, $H(z=1) = 120.7\pm 7.3 \ (r_{\rm d,fid} / r_{\rm d}) \ {\rm km} \ {\rm s}^{-1}{\rm Mpc}^{-1}$ and $D_M(z=2) = 5325\pm249 \ (r_{\rm d} / r_{\rm d, fid}) \ {\rm Mpc}$, $H(z=2) = 189.9\pm 32.9 \ (r_{\rm d,fid} / r_{\rm d}) \ {\rm km} \ {\rm s}^{-1}{\rm Mpc}^{-1}$. These measurements are highly correlated. We assess the outlook of BAO analysis from the final quasar sample by testing the method on a set of mocks that mimic the noise level in the final sample. We demonstrate on these mocks that redshift weighting shrinks the measurement error by over 25 per cent on average. We conclude redshift weighting can bring us closer to the cosmological goal of the final quasar sample.

astro-ph.CO↗

arXiv2017

The extended Baryon Oscillation Spectroscopic Survey (eBOSS): testing a new approach to measure the evolution of the structure growth

The extended Baryon Oscillation Spectroscopic Survey (eBOSS) is one of the first of a new generation of galaxy redshift surveys that will cover a large range in redshift with sufficient resolution to measure the baryon acoustic oscillations (BAO) signal. For surveys covering a large redshift range we can no longer ignore cosmological evolution, meaning that either the redshift shells analysed have to be significantly narrower than the survey, or we have to allow for the averaging over evolving quantities. Both of these have the potential to remove signal: analysing small volumes increases the size of the Fourier window function, reducing the large-scale information, while averaging over evolving quantities can, if not performed carefully, remove differential information. It will be important to measure cosmological evolution from these surveys to explore and discriminate between models. We apply a method to optimally extract this differential information to mock catalogues designed to mimic the eBOSS quasar sample. By applying a set of weights to extract redshift space distortion measurements as a function of redshift, we demonstrate an analysis that does not invoke the problems discussed above. We show that our estimator gives unbiased constraints.

astro-ph.CO↗

arXiv2017

The clustering of the SDSS-IV extended Baryon Oscillation Spectroscopic Survey DR14 quasar sample: First measurement of Baryon Acoustic Oscillations between redshift 0.8 and 2.2

We present measurements of the Baryon Acoustic Oscillation (BAO) scale in redshift-space using the clustering of quasars. We consider a sample of 147,000 quasars from the extended Baryon Oscillation Spectroscopic Survey (eBOSS) distributed over 2044 square degrees with redshifts $0.8 < z < 2.2$ and measure their spherically-averaged clustering in both configuration and Fourier space. Our observational dataset and the 1400 simulated realizations of the dataset allow us to detect a preference for BAO that is greater than 2.8$σ$. We determine the spherically averaged BAO distance to $z = 1.52$ to 3.8 per cent precision: $D_V(z=1.52)=3843\pm147 \left(r_{\rm d}/r_{\rm d, fid}\right)\ $Mpc. This is the first time the location of the BAO feature has been measured between redshifts 1 and 2. Our result is fully consistent with the prediction obtained by extrapolating the Planck flat $Λ$CDM best-fit cosmology. All of our results are consistent with basic large-scale structure (LSS) theory, confirming quasars to be a reliable tracer of LSS, and provide a starting point for numerous cosmological tests to be performed with eBOSS quasar samples. We combine our result with previous, independent, BAO distance measurements to construct an updated BAO distance-ladder. Using these BAO data alone and marginalizing over the length of the standard ruler, we find $Ω_Λ > 0$ at 6.6$σ$ significance when testing a $Λ$CDM model with free curvature.

astro-ph.CO↗