arXiv subjects

Mengjie Zhang

Publications and source records attributed to Mengjie Zhang.

At least 73 records · Page 4Linked to original sources

arXiv2025

Meta-heuristic Hypergraph-Assisted Robustness Optimization for Higher-order Complex Systems

In complex systems (e.g., communication, transportation, and biological networks), high robustness ensures sustained functionality and stability even when resisting attacks. However, the inherent structure complexity and the unpredictability of attacks make robustness optimization challenging. Hypergraphs provide a framework for modeling complicated higher-order interactions in complex systems naturally, but their potential has not been systematically investigated. Therefore, we propose an effective method based on genetic algorithms from Artificial Intelligence to optimize the robustness of complex systems modeled by hypergraphs. By integrating percolation-based metrics with adaptive computational techniques, our method achieves improved accuracy and efficiency. Experiments on both synthetic and real-world hypergraphs demonstrate the effectiveness of the proposed method in mitigating malicious attacks, with robustness improvements ranging from 16.6% to 205.2%. Further in-depth analysis reveals that optimized hypergraph-based systems exhibit a preferential connection mechanism in which high-hyperdegree nodes preferentially connect to lower-cardinality hyperedges, forming a distinctive Lotus topology that significantly improves robustness. Based on this finding, we propose a robust hypergraph generation method that allows robustness to be controlled via a single parameter rb. Notably, for rb<-1, a distinct Cactus topology emerges as an alternative to the Lotus topology observed for rb>1. The discovery of the Lotus and Cactus topologies offers valuable insights for designing robust higher-order networks while providing a useful foundation for investigating cascading failure dynamics in complex systems.

physics.soc-ph↗

arXiv2025

Fractional Laplace operator and related Schrödinger equations on locally finite graphs

In this paper, we first define a discrete version of the fractional Laplace operator $(-Δ)^{s}$ through the heat semigroup on a stochastically complete, connected, locally finite graph $G = (V, E, μ, w)$. Secondly, we define the fractional divergence and give another form of $(-Δ)^s$. The third point, and the foremost, is the introduction of the fractional Sobolev space $W^{s,2}(V)$, which is necessary when we study problems involving $(-Δ)^{s}$. Finally, using the mountain-pass theorem and the Nehari manifold, we obtain multiplicity solutions to a discrete fractional Schrödinger equation on $G$. We caution the readers that though these existence results are well known in the continuous case, the discrete case is quite different.

math.AP↗

arXiv2025

Fractional Sobolev spaces and fractional $p$-Laplace equations on locally finite graphs

Graph-based analysis holds both theoretical and applied significance, attracting considerable attention from researchers and yielding abundant results in recent years. However, research on fractional problems remains limited, with most of established results restricted to lattice graphs. In this paper, fractional Sobolev spaces are constructed on general graphs that are connected, locally finite and stochastically complete. Under certain assumptions, these spaces exhibit completeness, reflexivity, and other properties. Moreover, we propose a fractional $p$-Laplace operator, and study the existence of solutions to some nonlinear Schrödinger type equations involving this nonlocal operator. The main contribution of this paper is to establish a relatively comprehensive set of analytical tools for studying fractional problems on graphs.

math.AP↗

arXiv2025

Symbolically Regressing Fish Biomass Spectral Data: A Linear Genetic Programming Method with Tunable Primitives

Machine learning techniques play an important role in analyzing spectral data. The spectral data of fish biomass is useful in fish production, as it carries many important chemistry properties of fish meat. However, it is challenging for existing machine learning techniques to comprehensively discover hidden patterns from fish biomass spectral data since the spectral data often have a lot of noises while the training data are quite limited. To better analyze fish biomass spectral data, this paper models it as a symbolic regression problem and solves it by a linear genetic programming method with newly proposed tunable primitives. In the symbolic regression problem, linear genetic programming automatically synthesizes regression models based on the given primitives and training data. The tunable primitives further improve the approximation ability of the regression models by tuning their inherent coefficients. Our empirical results over ten fish biomass targets show that the proposed method improves the overall performance of fish biomass composition prediction. The synthesized regression models are compact and have good interpretability, which allow us to highlight useful features over the spectrum. Our further investigation also verifies the good generality of the proposed method across various spectral data treatments and other symbolic regression problems.

cs.NE↗

arXiv2025

Bridging Fitness With Search Spaces By Fitness Supremums: A Theoretical Study on LGP

Genetic programming has undergone rapid development in recent years. However, theoretical studies of genetic programming are far behind. One of the major obstacles to theoretical studies is the challenge of developing a model to describe the relationship between fitness values and program genotypes. In this paper, we take linear genetic programming (LGP) as an example to study the fitness-to-genotype relationship. We find that the fitness expectation increases with fitness supremum over instruction editing distance, considering 1) the fitness supremum linearly increases with the instruction editing distance in LGP, 2) the fitness infimum is fixed, and 3) the fitness probabilities over different instruction editing distances are similar. We then extend these findings to explain the bloat effect and the minimum hitting time of LGP based on instruction editing distance. The bloat effect happens because it is more likely to produce better offspring by adding instructions than by removing them, given an instruction editing distance from the optimal program. The analysis of the minimum hitting time suggests that for a basic LGP genetic operator (i.e., freemut), maintaining a necessarily small program size and mutating multiple instructions each time can improve LGP performance. The reported empirical results verify our hypothesis.

cs.NE↗

arXiv2025

LiBOG: Lifelong Learning for Black-Box Optimizer Generation

Meta-Black-Box Optimization (MetaBBO) garners attention due to its success in automating the configuration and generation of black-box optimizers, significantly reducing the human effort required for optimizer design and discovering optimizers with higher performance than classic human-designed optimizers. However, existing MetaBBO methods conduct one-off training under the assumption that a stationary problem distribution with extensive and representative training problem samples is pre-available. This assumption is often impractical in real-world scenarios, where diverse problems following shifting distribution continually arise. Consequently, there is a pressing need for methods that can continuously learn from new problems encountered on-the-fly and progressively enhance their capabilities. In this work, we explore a novel paradigm of lifelong learning in MetaBBO and introduce LiBOG, a novel approach designed to learn from sequentially encountered problems and generate high-performance optimizers for Black-Box Optimization (BBO). LiBOG consolidates knowledge both across tasks and within tasks to mitigate catastrophic forgetting. Extensive experiments demonstrate LiBOG's effectiveness in learning to generate high-performance optimizers in a lifelong learning manner, addressing catastrophic forgetting while maintaining plasticity to learn new tasks.

cs.LG↗

arXiv2025

Curriculum Learning in Genetic Programming Guided Local Search for Large-scale Vehicle Routing Problems

Manually designing (meta-)heuristics for the Vehicle Routing Problem (VRP) is a challenging task that requires significant domain expertise. Recently, data-driven approaches have emerged as a promising solution, automatically learning heuristics that perform well on training instances and generalize to unseen test cases. Such an approach learns (meta-)heuristics that can perform well on the training instances, expecting it to generalize well on the unseen test instances. A recent method, named GPGLS, uses Genetic Programming (GP) to learn the utility function in Guided Local Search (GLS) and solved large scale VRP effectively. However, the selection of appropriate training instances during the learning process remains an open question, with most existing studies including GPGLS relying on random instance selection. To address this, we propose a novel method, CL-GPGLS, which integrates Curriculum Learning (CL) into GPGLS. Our approach leverages a predefined curriculum to introduce training instances progressively, starting with simpler tasks and gradually increasing complexity, enabling the model to better adapt and optimize for large-scale VRP (LSVRP). Extensive experiments verify the effectiveness of CL-GPGLS, demonstrating significant performance improvements over three baseline methods.

cs.NE↗

arXiv2025

Automated Detection of Salvin's Albatrosses: Improving Deep Learning Tools for Aerial Wildlife Surveys

Recent advancements in deep learning and aerial imaging have transformed wildlife monitoring, enabling researchers to survey wildlife populations at unprecedented scales. Unmanned Aerial Vehicles (UAVs) provide a cost-effective means of capturing high-resolution imagery, particularly for monitoring densely populated seabird colonies. In this study, we assess the performance of a general-purpose avian detection model, BirdDetector, in estimating the breeding population of Salvin's albatross (Thalassarche salvini) on the Bounty Islands, New Zealand. Using drone-derived imagery, we evaluate the model's effectiveness in both zero-shot and fine-tuned settings, incorporating enhanced inference techniques and stronger augmentation methods. Our findings indicate that while applying the model in a zero-shot setting offers a strong baseline, fine-tuning with annotations from the target domain and stronger image augmentation leads to marked improvements in detection accuracy. These results highlight the potential of leveraging pre-trained deep-learning models for species-specific monitoring in remote and challenging environments.

cs.CV↗

arXiv2025

Explaining Deep Convolutional Neural Networks for Image Classification by Evolving Local Interpretable Model-agnostic Explanations

Deep convolutional neural networks have proven their effectiveness, and have been acknowledged as the most dominant method for image classification. However, a severe drawback of deep convolutional neural networks is poor explainability. Unfortunately, in many real-world applications, users need to understand the rationale behind the predictions of deep convolutional neural networks when determining whether they should trust the predictions or not. To resolve this issue, a novel genetic algorithm-based method is proposed for the first time to automatically evolve local explanations that can assist users to assess the rationality of the predictions. Furthermore, the proposed method is model-agnostic, i.e., it can be utilised to explain any deep convolutional neural network models. In the experiments, ResNet is used as an example model to be explained, and the ImageNet dataset is selected as the benchmark dataset. DenseNet and MobileNet are further explained to demonstrate the model-agnostic characteristic of the proposed method. The evolved local explanations on four images, randomly selected from ImageNet, are presented, which show that the evolved local explanations are straightforward to be recognised by humans. Moreover, the evolved explanations can explain the predictions of deep convolutional neural networks on all four images very well by successfully capturing meaningful interpretable features of the sample images. Further analysis based on the 30 runs of the experiments exhibits that the evolved local explanations can also improve the probabilities/confidences of the deep convolutional neural network models in making the predictions. The proposed method can obtain local explanations within one minute, which is more than ten times faster than LIME (the state-of-the-art method).

cs.CV↗

arXiv2025

Generalized Phase Pressure Control Enhanced Reinforcement Learning for Traffic Signal Control

Appropriate traffic state representation is crucial for learning traffic signal control policies. However, most of the current traffic state representations are heuristically designed, with insufficient theoretical support. In this paper, we (1) develop a flexible, efficient, and theoretically grounded method, namely generalized phase pressure (G2P) control, which takes only simple lane features into consideration to decide which phase to be actuated; 2) extend the pressure control theory to a general form for multi-homogeneous-lane road networks based on queueing theory; (3) design a new traffic state representation based on the generalized phase state features from G2P control; and 4) develop a reinforcement learning (RL)-based algorithm template named G2P-XLight, and two RL algorithms, G2P-MPLight and G2P-CoLight, by combining the generalized phase state representation with MPLight and CoLight, two well-performed RL methods for learning traffic signal control policies. Extensive experiments conducted on multiple real-world datasets demonstrate that G2P control outperforms the state-of-the-art (SOTA) heuristic method in the transportation field and other recent human-designed heuristic methods; and that the newly proposed G2P-XLight significantly outperforms SOTA learning-based approaches. Our code is available online.

cs.LG↗

arXiv2025

Fractional Laplace operator on finite graphs

Nowadays a great attention has been focused on the discrete fractional Laplace operator as the natural counterpart of the continuous one. In this paper, we discretize the fractional Laplace operator $(-Δ)^{s}$ for an arbitrary finite graph and any positive real number $s$. It is shown that $(-Δ)^{s}$ can be explicitly represented by eigenvalues and eigenfunctions of the Laplace operator $-Δ$. Moreover, we study its important properties, such as $(-Δ)^{s}$ converges to $-Δ$ as $s$ tends to $1$; while $(-Δ)^{s}$ converges to the identity map as $s$ tends to $0$ on a specific function space. For related problems involving the fractional Laplace operator, we consider the fractional Kazdan-Warner equation and obtain several existence results via variational principles and the method of upper and lower solutions.

math.AP↗

arXiv2025

A Genetic Algorithm-Based Approach for Automated Optimization of Kolmogorov-Arnold Networks in Classification Tasks

To address the issue of interpretability in multilayer perceptrons (MLPs), Kolmogorov-Arnold Networks (KANs) are introduced in 2024. However, optimizing KAN structures is labor-intensive, typically requiring manual intervention and parameter tuning. This paper proposes GA-KAN, a genetic algorithm-based approach that automates the optimization of KANs, requiring no human intervention in the design process. To the best of our knowledge, this is the first time that evolutionary computation is explored to optimize KANs automatically. Furthermore, inspired by the use of sparse connectivity in MLPs in effectively reducing the number of parameters, GA-KAN further explores sparse connectivity to tackle the challenge of extensive parameter spaces in KANs. GA-KAN is validated on two toy datasets, achieving optimal results without the manual tuning required by the original KAN. Additionally, GA-KAN demonstrates superior performance across five classification datasets, outperforming traditional methods on all datasets and providing interpretable symbolic formulae for the Wine and Iris datasets, thereby enhancing model transparency. Furthermore, GA-KAN significantly reduces the number of parameters over the standard KAN across all the five datasets. The core contributions of GA-KAN include automated optimization, a new encoding strategy, and a new decoding process, which together improve the accuracy and interpretability, and reduce the number of parameters.

cs.NE↗

arXiv2025

Multifractal analysis of the convergence exponents for the digits in $d$-decaying Gauss like dynamical systems

Let $\{a_n(x)\}_{n\geq1}$ be the sequence of digits of $x\in(0,1)$ in infinite iterated function systems with polynomial decay of the derivative. We first study the multifractal spectrum of the convergence exponent defined by the sequence of the digits $\{a_n(x)\}_{n\geq1}$ and the weighted products of distinct digits with finite numbers respectively, and then calculate the Hausdorff dimensions of the intersection of sets defined by the convergence exponent of the weighted product of distinct digits with finite numbers and sets of points whose digits are non-decreasing in such iterated function systems.

math.DS↗

arXiv2024

Cost-Aware Dynamic Cloud Workflow Scheduling using Self-Attention and Evolutionary Reinforcement Learning

The Cost-aware Dynamic Multi-Workflow Scheduling (CDMWS) in the cloud is a kind of cloud workflow management problem, which aims to assign virtual machine (VM) instances to execute tasks in workflows so as to minimize the total costs, including both the penalties for violating Service Level Agreement (SLA) and the VM rental fees. Powered by deep neural networks, Reinforcement Learning (RL) methods can construct effective scheduling policies for solving CDMWS problems. Traditional policy networks in RL often use basic feedforward architectures to separately determine the suitability of assigning any VM instances, without considering all VMs simultaneously to learn their global information. This paper proposes a novel self-attention policy network for cloud workflow scheduling (SPN-CWS) that captures global information from all VMs. We also develop an Evolution Strategy-based RL (ERL) system to train SPN-CWS reliably and effectively. The trained SPN-CWS can effectively process all candidate VM instances simultaneously to identify the most suitable VM instance to execute every workflow task. Comprehensive experiments show that our method can noticeably outperform several state-of-the-art algorithms on multiple benchmark CDMWS problems.

cs.AI↗

arXiv2024

EvoSampling: A Granular Ball-based Evolutionary Hybrid Sampling with Knowledge Transfer for Imbalanced Learning

Class imbalance would lead to biased classifiers that favor the majority class and disadvantage the minority class. Unfortunately, from a practical perspective, the minority class is of importance in many real-life applications. Hybrid sampling methods address this by oversampling the minority class to increase the number of its instances, followed by undersampling to remove low-quality instances. However, most existing sampling methods face difficulties in generating diverse high-quality instances and often fail to remove noise or low-quality instances on a larger scale effectively. This paper therefore proposes an evolutionary multi-granularity hybrid sampling method, called EvoSampling. During the oversampling process, genetic programming (GP) is used with multi-task learning to effectively and efficiently generate diverse high-quality instances. During the undersampling process, we develop a granular ball-based undersampling method that removes noise in a multi-granular fashion, thereby enhancing data quality. Experiments on 20 imbalanced datasets demonstrate that EvoSampling effectively enhances the performance of various classification algorithms by providing better datasets than existing sampling methods. Besides, ablation studies further indicate that allowing knowledge transfer accelerates the GP's evolutionary learning process.

cs.LG↗

arXiv2024

Drone Stereo Vision for Radiata Pine Branch Detection and Distance Measurement: Utilizing Deep Learning and YOLO Integration

This research focuses on the development of a drone equipped with pruning tools and a stereo vision camera to accurately detect and measure the spatial positions of tree branches. YOLO is employed for branch segmentation, while two depth estimation approaches, monocular and stereo, are investigated. In comparison to SGBM, deep learning techniques produce more refined and accurate depth maps. In the absence of ground-truth data, a fine-tuning process using deep neural networks is applied to approximate optimal depth values. This methodology facilitates precise branch detection and distance measurement, addressing critical challenges in the automation of pruning operations. The results demonstrate notable advancements in both accuracy and efficiency, underscoring the potential of deep learning to drive innovation and enhance automation in the agricultural sector.

cs.CV↗

arXiv2024

Machine Learning for Raman Spectroscopy-based Cyber-Marine Fish Biochemical Composition Analysis

The rapid and accurate detection of biochemical compositions in fish is a crucial real-world task that facilitates optimal utilization and extraction of high-value products in the seafood industry. Raman spectroscopy provides a promising solution for quickly and non-destructively analyzing the biochemical composition of fish by associating Raman spectra with biochemical reference data using machine learning regression models. This paper investigates different regression models to address this task and proposes a new design of Convolutional Neural Networks (CNNs) for jointly predicting water, protein, and lipids yield. To the best of our knowledge, we are the first to conduct a successful study employing CNNs to analyze the biochemical composition of fish based on a very small Raman spectroscopic dataset. Our approach combines a tailored CNN architecture with the comprehensive data preparation procedure, effectively mitigating the challenges posed by extreme data scarcity. The results demonstrate that our CNN can significantly outperform two state-of-the-art CNN models and multiple traditional machine learning models, paving the way for accurate and automated analysis of fish biochemical composition.

cs.LG↗

arXiv2024

Drone Stereo Vision for Radiata Pine Branch Detection and Distance Measurement: Integrating SGBM and Segmentation Models

Manual pruning of radiata pine trees presents significant safety risks due to their substantial height and the challenging terrains in which they thrive. To address these risks, this research proposes the development of a drone-based pruning system equipped with specialized pruning tools and a stereo vision camera, enabling precise detection and trimming of branches. Deep learning algorithms, including YOLO and Mask R-CNN, are employed to ensure accurate branch detection, while the Semi-Global Matching algorithm is integrated to provide reliable distance estimation. The synergy between these techniques facilitates the precise identification of branch locations and enables efficient, targeted pruning. Experimental results demonstrate that the combined implementation of YOLO and SGBM enables the drone to accurately detect branches and measure their distances from the drone. This research not only improves the safety and efficiency of pruning operations but also makes a significant contribution to the advancement of drone technology in the automation of agricultural and forestry practices, laying a foundational framework for further innovations in environmental management.

cs.CV↗