Gaussian Algorithm Research Articles

Quantification of Native Lignin Structural Features with Gel-Phase 2D-HSQC0 Reveals Lignin Structural Changes During Extraction.

Our ability to study and valorize the lignin fraction of biomass is hampered by the fundamental and still unmet challenge of precisely quantifying native lignin's structural features. Here, we developed a rapid elevated-temperature 1H-13C Heteronuclear Single-Quantum Coherence Zero (HSQC0) NMR method that enables this precise quantification of native lignin structural characteristics even with whole plant cell wall (WPCW) NMR spectroscopy, overcoming fast spin relaxation in the gel phase. We also formulated a Gaussian fitting algorithm to perform automatic and reliable spectral integration. By combining HSQC0 measurements with yield measurements following depolymerisation, we can confirm the combinatorial nature of radical coupling reactions during biosynthesis leading to a random sequential organization of linkages within a largely linear lignin chain. Such analyses illustrate how this analytical method can greatly facilitate the study of native lignin structure, which can then be used for fundamental studies or to understand lignin depolymerization methods like reductive catalytic fractionation or aldehyde-assisted fractionation.

A machine learning model to predict spontaneous vaginal delivery failure for term nulliparous women: An observational study.

This study aims to construct and evaluate a model to predict spontaneous vaginal delivery (SVD) failure in term nulliparous women based on machine learning algorithms. In this retrospective observational study, data on nulliparous women without contraindications for vaginal delivery with a singleton pregnancy ≥37 weeks and before the onset of labor from September 2020 to September 2021 were divided into a training set and a temporal validation set. Transperineal ultrasound was performed to collect angle of progression, head-perineum distance, subpubic arch angle, and their levator hiatal dimensions. The cervical length was measured via transvaginal ultrasound. The delivery methods were later recorded. Through LASSO regression analysis, indicators that can affect SVD failure were selected. Seven common machine learning algorithms were selected for model training, and the optimal algorithm was selected based on the area under the curve (AUC) to evaluate the effectiveness of the validation model. Four indicators related to SVD failure were identified through LASSO regression screening: angle of progression, cervical length, subpubic arch angle, and estimated fetal weight. The Gaussian NB algorithm was found to yield the highest AUC (0.82, 95% confidence interval [CI] 0.65-0.98) during model training, and hence it was chosen for verification with the temporal validation set, in which an AUC of 0.79 (95% CI 0.64-0.95) was obtained with accuracy, sensitivity, and specificity rates of 80.9%, 72.7%, and 75.0%, respectively. The Gaussian NB model showed good predictive effect, proving its potential as a clinical reference for predicting SVD failure of term nulliparous women before actual delivery.

Bayes_Opt-SWMM: A Gaussian process-based Bayesian optimization tool for real-time flood modeling with SWMM

Real-time flood model plays a pivotal role in averting urban flood damage, particularly when there is minimal lead time for preparatory measures. However, urban flood modeling in real-time often contends with inherent uncertainties arising from input data uncertainty and parameter ambiguities. This study introduces a real-time calibration (RTC) tool called Bayes_Opt-SWMM , specifically tailored for real-time urban flood modeling and uncertainty optimization. This tool leverages the Gaussian process-based Bayesian optimization algorithm and interfaces seamlessly with the Stormwater Management Model (SWMM). It integrates real-time model forcing data and flood monitoring collected through sensors and gauges which are strategically placed within critical locations of urban drainage systems. Our approach hinges on the Surrogate Model based Uncertainty Optimization (SMUO) concept, providing an avenue for enhancing real-time flood modeling. Bayes_Opt-SWMM runs the optimization process using a surrogate model called Gaussian Process emulator with two inference methods: (1) the Gaussian Process (GP) model and (2) Markov Chain Monte Carlo (MCMC) algorithm in GP model (GP_MCMC). Furthermore, three acquisition functions, namely Expected Improvement (EI), Maximum Probability of Improvement (MPI), and Lower Confidence Bound (LCB), facilitate optimal parameter fitting within the surrogate models. The efficiency of GP-based surrogate models in learning SWMM model parameters, leads to an improved uncertainty quantification and accelerated real-time flood modeling in urban areas. Overall, Bayes_Opt-SWMM emerges as a cost-effective and valuable tool for real-time flood modeling and monitoring, with significant potential for managing intelligent storm water systems in urban environments.

FFT-Based Probability Density Imaging of Euler Solutions.

When using traditional Euler deconvolution optimization strategies, it is difficult to distinguish between anomalies and their corresponding Euler tails (those solutions are often distributed outside the anomaly source, forming "tail"-shaped spurious solutions, i.e., misplaced Euler solutions, which must be removed or marked) with only the structural index. The nonparametric estimation method based on the normalized B-spline probability density (BSS) is used to separate the Euler solution clusters and mark different anomaly sources according to the similarity and density characteristics of the Euler solutions. For display purposes, the BSS needs to map the samples onto the estimation grid at the points where density will be estimated in order to obtain the probability density distribution. However, if the size of the samples or the estimation grid is too large, this process can lead to high levels of memory consumption and excessive computation times. To address this issue, a fast linear binning approximation algorithm is introduced in the BSS to speed up the computation process and save time. Subsequently, the sample data are quickly projected onto the estimation grid to facilitate the discrete convolution between the grid and the density function using a fast Fourier transform. A method involving multivariate B-spline probability density estimation based on the FFT (BSSFFT), in conjunction with fast linear binning appropriation, is proposed in this paper. The results of two random normal distributions show the correctness of the BSS and BSSFFT algorithms, which is verified via a comparison with the true probability density function (pdf) and Gaussian kernel smoothing estimation algorithms. Then, the Euler solutions of the two synthetic models are analyzed using the BSS and BSSFFT algorithms. The results are consistent with their theoretical values, which verify their correctness regarding Euler solutions. Finally, the BSSFFT is applied to Bishop 5X data, and the numerical results show that the comprehensive analysis of the 3D probability density distributions using the BSSFFT algorithm, derived from the Euler solution subset of x0,y0,z0, can effectively separate and locate adjacent anomaly sources, demonstrating strong adaptability.

Multi-sensor multi-target tracking with generalized labeled multi-Bernoulli filter based on track-before-detect observation model using Gaussian belief propagation

Tracking an unknown number of low-observable targets is notoriously challenging problem. This paper extends the multi-sensor multi-target tracking with generalized labeled multi-Bernoulli (GLMB) filter into the track-before-detect (TBD) observation model and presents its efficient implementation. The Gaussian belief propagation (BP) is applied into multi-sensor GLMB-TBD filter to address the computational bottleneck of computing GLMB filtering density for tracking multiple targets in challenging scenario. The Gaussian BP algorithm is used to directly compute marginal densities from the joint posterior density through the BP belief update wherein the GLMB filtering density at given time serves as prior information for next recursion. Compared to the Gibbs sampling-version implementation, the Gaussian BP-version implementation avoids the pruning of GLMB components without association information loss and the relevant association is preserved for BP belief update. Hence, the proposed Gaussian BP-version implementation can improve the tracking accuracy. Moreover, the computational complexity of our proposed Gaussian BP-version implementation scales linear complexity in the total number of measurements from all sensors. More importantly, the linear scaling in number of Bernoulli components for our proposed Gaussian BP-version implementation improves on the quadratic complexity exhibited by the Gibbs-version one. The experiment results show that the computational cost of the Gaussian BP-version implementation is significantly less than that of the Gibbs sampling-version implementation for the multi-sensor GLMB-TBD filter.

Robust distance measurement using illumination map estimation and MAHNet in underground coal mines

An effective binocular stereo distance measurement method is proposed to address challenges posed by low brightness and weak texture of images captured in underground coal mines for the machine vision method. This approach is based on illumination map estimation and the MobileNetV3 attention hourglass stereo matching network (MAHNet) model. First, a binocular stereo vision system is established in which infrared LEDs are uniformly distributed on both sides of the belt conveyor bracket as visual feature points. Second, images are preprocessed using illumination map estimation, and the optimization of inhomogeneous brightness image enhancement is achieved by adopting adaptive Gamma correction. Third, the YOLOv5 target detection network and Gaussian fitting fusion algorithm are utilized to detect infrared LED feature points. Fourth, the MAHNet model is employed to generate the cost volume and perform disparity regression, resulting in the acquisition of accurate disparity images. Finally, triangulation is applied to determine the depth of feature points. The experimental results of distance measurement demonstrate that an average relative ranging accuracy of 1.52% within the range of 50.0 cm to 250.0 cm can be achieved by the optimized method, thereby validating the effectiveness of this binocular distance measurement method in underground coal mines.

Enhanced Gaussian Bare-Bone Imperialist Competition Algorithm Based on Doubling Sampling and Quasi-oppositional Learning for Global Optimization

Gaussian bare-bone imperialist competitive algorithm (GBB-ICA) is an effective variant of imperialist competitive algorithm (ICA), which updates the position of colonies by sampling a Gaussian distribution. However, the mean and standard deviation adopted by GBB-ICA is calculated only using the positions of imperialist and the colony itself, making the searching tends to trap into local optimum. To overcome this drawback, a new double Gaussian sampling strategy is proposed in this paper. An extra Gaussian sampling point, whose mean and standard is calculated using the positions of the second best colony and the current colony itself, is introduced into GBB-ICA. To further speed up the convergence and explore informative region, the quasi-oppositional learning technique is incorporated into GBB-ICA to produce more potential candidates in the assimilation step as well as generating a higher quality initial population. The proposed algorithm is called quasi-oppositional learning-based double Gaussian sampling bare-bone imperialist competitive algorithm (QOLBDGSBB-ICA) and is tested on 20 benchmark functions and four engineering design problems. Experimental results show that the proposed algorithm outperforms over other referenced ICA variants on 19 benchmark functions, which well validates the effectiveness of the proposed algorithm.

An improved hidden Markov model with magnetic Barkhausen noise and optimized Gaussian mixture feature for fatigue prediction

Evaluating fatigue states of metallic materials is essential for predicting their failures and ensuring structural safety. Magnetic Barkhausen noise (MBN) analysis, a non-destructive testing method, provides efficient and reliable methods for identifying and categorising material parameters such as hardness and residual stresses. To establish a quantitative relationship between MBN signals and fatigue states, an improved hidden Markov model (HMM) is proposed based on optimised Gaussian mixture features (GMFs) and the Kullback–Leibler (KL) divergence measure for fatigue prediction. The MBN-GMFs replicate the probability characteristics of MBN signals and track the fatigue degradation trend throughout the fatigue life; thus, they are superior to some widely used statistical features. A Gaussian component optimisation algorithm is proposed to automatically adjust the appropriate number of components in the Gaussian mixture model and enhance the representation of MBN-GMFs. Then, the KL divergence is introduced to quantify the similarity and accurately classify the degree of MBN-GMF migration. The HMM is constructed to obtain the probability transfer relationship between the observations and states and obtain accurate fatigue predictions. Experiments on two 20R metallic materials at three excitation frequencies are conducted to collect the MBN signals. The experimental results and comparisons indicate that the proposed HMM can accurately predict fatigue states and provide a practical and robust analysis tool for MBN-based fatigue predictions.

Projected Gaussian Markov Improvement Algorithm for High-Dimensional Discrete Optimization via Simulation

This article considers a discrete optimization via simulation (DOvS) problem defined on a graph embedded in the high-dimensional integer grid. Several DOvS algorithms that model the responses at the solutions as a realization of a Gaussian Markov random field (GMRF) have been proposed exploiting its inferential power and computational benefits. However, the computational cost of inference increases exponentially in dimension. We propose the projected Gaussian Markov improvement algorithm (pGMIA), which projects the solution space onto a lower-dimensional space creating the region-layer graph to reduce the cost of inference. Each node on the region-layer graph can be mapped to a set of solutions projected to the node; these solutions form a lower-dimensional solution-layer graph. We define the response at each region-layer node to be the average of the responses within the corresponding solution-layer graph. From this relation, we derive the region-layer GMRF to model the region-layer responses. The pGMIA alternates between the two layers to make a sampling decision at each iteration. It first selects a region-layer node based on the lower-resolution inference provided by the region-layer GMRF, then makes a sampling decision among the solutions within the solution-layer graph of the node based on the higher-resolution inference from the solution-layer GMRF. To solve even higher-dimensional problems (e.g., 100 dimensions), we also propose the pGMIA+: a multi-layer extension of the pGMIA. We show that both pGMIA and pGMIA+ converge to the optimum almost surely asymptotically and empirically demonstrate their competitiveness against state-of-the-art high-dimensional Bayesian optimization algorithms.

FocusDet: an efficient object detector for small object

The object scale of a small object scene changes greatly, and the object is easily disturbed by a complex background. Generic object detectors do not perform well on small object detection tasks. In this paper, we focus on small object detection based on FocusDet. FocusDet refers to the small object detector proposed in this paper. It consists of three parts: backbone, feature fusion structure, and detection head. STCF-EANet was used as the backbone for feature extraction, the Bottom Focus-PAN for feature fusion, and the detection head for object localization and recognition.To maintain sufficient global context information and extract multi-scale features, the STCF-EANet network backbone is used as the feature extraction network.PAN is a feature fusion module used in general object detectors. It is used to perform feature fusion on the extracted feature maps to supplement feature information.In the feature fusion network, FocusDet uses Bottom Focus-PAN to capture a wider range of locations and lower-level feature information of small objects.SIOU-SoftNMS is the proposed algorithm for removing redundant prediction boxes in the post-processing stage. SIOU multi-dimension accurately locates the prediction box, and SoftNMS uses the Gaussian algorithm to remove redundant prediction boxes. FocusDet uses SIOU-SoftNMS to address the missed detection problem common in dense tiny objects.The VisDrone2021-DET and CCTSDB2021 object detection datasets are used as benchmarks, and tests are carried out on VisDrone2021-det-test-dev and CCTSDB-val datasets. Experimental results show that FocusDet improves mAP@.5% from 33.6% to 46.7% on the VisDrone dataset. mAP@.5% on the CCTSDB2021 dataset is improved from 81.6% to 87.8%. It is shown that the model has good performance for small object detection, and the research is innovative.

SYSTEM DESIGN FOR CALCUALTING THE NUMBER AND DENSITY OF MOTORCYCLES IN PARKING AREA BASED ON BACKGROUND SUBTRACTION METHOD

There are still issues with a number of students parking their vehicles improperly in the parking spaces provided. This causes suboptimal parking capacity due to a lack of information about parking capacity. In recent years, at a certain library, vehicle detection has been implemented using a Gaussian mixture model algorithm using a Raspberry Pi. However, this library does not provide information about the density status of the parking area. Therefore, an information system was created to determine the level of density of the parking area based on the ratio of vehicles entering and exiting compared to the maximum capacity of the parking area. The system uses the Gaussian mixture model algorithm with the machine learning method of background subtraction MOG2, which can calculate the number of vehicles based on the difference between objects and the background of objects, using test data in the form of videos recorded using a camera positioned horizontally to the entrance and exit lanes of the parking area. This research resulted in an accuracy of 89.7% for Video1TA, precision of 93.2%, a crowded parking area density level, and a value of 129.12. Video2TA had a value of 101.08, precision of 100%, and accuracy of 90%, while Video3TA had an accuracy of 35%, precision of 56.7%, and a value of 49.48. The density levels of videos 2 and 3 are the same, indicating that the parking area is still empty. The test results show that the value can affect the system in detecting an object.

Lateral Heat Distribution Characteristics of CLP S275 Using Gaussian FFT Algorithm in Optical Thermographic Testing

In general, when using infrared thermography (IRT) techniques to excite a heat source on the surface of an inspection object, the heat source is focused on the center of the image of the infrared (IR) camera. If the object to be inspected is small, uniform excitation of the heat source is possible, but if the area is large, the heat source is concentrated locally, resulting in uneven heat distribution. Therefore, in this study, heat distribution was analyzed after inducing a non-uniform heat source by exciting the heat source at different locations. Additionally, the fast Fourier transform (FFT) algorithm with Gaussian filtering was applied to resolve the non-uniform distribution of the heat sources. Excellent results were obtained from the amplitude image, and the effectiveness of the FFT algorithm was verified using the Otsu algorithm. Finally, the signal-to-noise ratio (SNR) was calculated, and the detection ability according to each thinning rate was analyzed.

Gesture Scoring Based on Gaussian Distance-Improved DTW

The power industry has been dedicated to applying virtual reality (VR) technology to build training systems in virtual environments, enabling personnel to complete skill training in real simulated environments while ensuring their safety. Conventional action scoring systems struggle to provide accurate scores for fine movements. Accurate scoring of fine movements can help workers identify their shortcomings during power operations, thus improving learning efficiency. This is of great significance for training on virtual environment-based power operation. This paper proposes a power operation-orientated VR action evaluation method based on the Gaussian distance-improved dynamic time warping (DTW) algorithm and the temporal convolutional network (TCN) model. First, the adaptive adapter is used to extract one-dimensional features from the three-dimensional data of the data gloves. Then, based on the TCN model, action data with significant discrepancies are filtered out. Finally, the obtained data are input into the Gaussian distance-improved DTW algorithm, where the path size is calculated. Corresponding scoring criteria are established on the basis of the path size to evaluate the actions. The results demonstrate that the VR action evaluation method based on the Gaussian distance-improved DTW algorithm and the TCN model significantly improves the accuracy of evaluating fine movements compared to traditional evaluation algorithms.

Does the Too-Big-To-Fail status affect depositor’s discipline: a Gaussian mixture model algorithm approach

PurposeThis study empirically demonstrates a contradiction between pillar 3 of Basel norms III and the designation of Systemically Important Banks (SIBs), also known as Too Big to Fail (TBTF). The objective of this study is threefold, which has been approached in a phased manner. The first is to determine the systemic importance of the banks under study; second, to examine if market discipline exists at different levels of systemic importance of banks and lastly, to examine if the strength of market discipline varies at different levels of systemic importance.Design/methodology/approachThis study is based on all the public and private sector banks operating in the Indian banking sector. The Gaussian Mixture Model algorithm has been utilized to classify banks into distinct levels of systemic importance. Thereafter, market discipline has been observed by analyzing depositors' sentiments toward banks' risk (CAMEL indicators). The analysis has been performed by employing the system Generalized Method of Moments (GMM) to estimate models with different dependent variables.FindingsThe findings affirm the existence of market discipline across all levels of systemic importance. However, the strength of market discipline varies with the systemic importance of the banks, with weak market discipline being a negative externality of the SIBs designation.Originality/valueBy employing the Gaussian Mixture Model algorithm to develop a framework for categorizing banks on the basis of their systemic importance, this study is the first to go beyond the conventional method as outlined by the Reserve Bank of India (RBI).

Assessment of food safety risk using machine learning-assisted hyperspectral imaging: Classification of fungal contamination levels in rice grain

A rapid and nondestructive assessment of food safety risk using machine learning-assisted hyperspectral imaging was developed for classification of fungal contamination in brown rice grain. Brown rice was inoculated with Penicillium. The fungal infected rice was then mixed with healthy rice to obtain 0 %, 5 %, 25 %, 50 % and 100 % (w/w) contamination of infected rice. Volatile compounds including pentamethyl-heptane, decane, dodecane, 3-octanone, and 1-octen-3-ol were found in fungal infected rice, as analyzed using gas chromatography-mass spectrometry. The HSI system was used to collect spectral reflectance and spatial data of the samples covering the wavelength range of 400–1000 nm. The hypercubed data were analyzed using machine learning algorithms, including principal component analysis (PCA), discriminant factor analysis (DFA) and support vector machine (SVM). Using PCA for data reduction, 3 principal components were extracted with a cumulative variance of 90.53 %. DFA (linear and quadratic algorithms) and SVM (linear, quadratic, cubic, and Gaussian algorithms) were then used to classify the samples. HSI integrated with Gaussian SVM gave 93.4% accuracy which was best for classifying rice with different percentages of contamination. The image analysis gave a pseudo-color distribution map which facilitated the visualization of the contaminated rice by presenting data in an uncomplicated image. The machine learning-assisted HSI can be used as a rapid, nondestructive and chemical-free tool for an assessment of food safety risk for rice grain.

Grading the Dominant Pathological Indices in Liver Diseases from Pathological Images Using Radiomics Methods

Purpose: This study aims to diagnose the severity of important pathological indices, i.e., fibrosis, steatosis, lobular inflammation, and ballooning from the pathological images of the liver tissue based on extracted features by radiomics methods.
 Materials and Methods: This research uses the pathological images obtained from liver tissue samples for 258 laboratory mice. After preprocessing the images and data augmentation, a collection of texture feature sets extracted by gray-level-based algorithms, including Global, Gray-level Co-Occurrence Matrix (GLCM), Gray-level Run length Matrix (GLRLM), Gray-level Size Zone Matrix (GLSZM), and Neighboring Gray Tone Difference Matrix (NGTDM) algorithms. Then, advanced methods of classification, namely Support Vector Machine (SVM), Random Forest (RF), Quadratic Discriminant Analysis (QDA), K-Nearest Neighbors (KNN), Logistic Regression (LR), Naïve Bayes (NB), and Multi-layer Perceptrons (MLP) are employed. This procedure is provided separately for each of the four indices of fibrosis level in 6 grading classes, steatosis in 5 grading classes, inflammation in 4 grading classes, and ballooning in 3 grading classes. For a comparison of the output of these algorithms, the accuracy value obtained from the evaluation data is presented for the performance of different methods.
 Results: The results showed that, compared to other methods, the Gaussian SVM algorithm provides a better response to the classification of the grading of liver disease among all the indices from the pathological images due to its structural features. This value of accuracy was calculated at 84.30% for fibrosis, 90.55% for steatosis, 81.11% for inflammation, and 95.98% for ballooning.
 Conclusion: This fully automatic framework based on advanced radiomics algorithms and machine learning from pathological images can be very useful in clinical procedures and be considered as an assistant or a substitute for pathologists’ diagnoses.

Delayed non‐fragile robust control of civil structure considering structural uncertainties, actuator faults, and control force time delays

Active control is an effective strategy for suppressing unwanted structural vibrations. The uncertainties in computational models, actuator faults, and time delays in control forces are the potential threats for control performance improvements. These factors are interconnected and may lead to control system instability and poor control effectiveness. The paper presents a delayed non-fragile robust control (DNR) algorithm for uncertain systems with consideration of actuator faults and time delays. To this end, the existence conditions for the DNR multi-objective controller are derived by utilizing the Lyapunov stability proof and introducing a pole constraint inequality. Then, a dynamic output feedback DNR algorithm is further developed. Finally, two numerical simulation examples are discussed for several ground motions. The results show that the control system based on the proposed algorithm exhibits better stability, robustness, and fault tolerance than the linear quadratic Gaussian (LQG) algorithm. Furthermore, there is no need for additional control energy. Significantly, the control performance of the proposed algorithm can be further enhanced with the decentralized control strategy.

Histological interpretation of spitzoid tumours: an extensive machine learning-based concordance analysis for improving decision making.

The histopathological classification of melanocytic tumours with spitzoid features remains a challenging task. We confront the complexities involved in the histological classification of these tumours by proposing machine learning (ML) algorithms that objectively categorise the most relevant features in order of importance. The data set comprises 122 tumours (39 benign, 44 atypical and 39 malignant) from four different countries. BRAF and NRAS mutation status was evaluated in 51. Analysis of variance score was performed to rank 22 clinicopathological variables. The Gaussian naive Bayes algorithm achieved in distinguishing Spitz naevus from malignant spitzoid tumours with an accuracy of 0.95 and kappa score of 0.87, utilising the 12 most important variables. For benign versus non-benign Spitz tumours, the test reached a kappa score of 0.88 using the 13 highest-scored features. Furthermore, for the atypical Spitz tumours (AST) versus Spitz melanoma comparison, the logistic regression algorithm achieved a kappa value of 0.66 and an accuracy rate of 0.85. When the three categories were compared most AST were classified as melanoma, because of the similarities on histological features between the two groups. Our results show promise in supporting the histological classification of these tumours in clinical practice, and provide valuable insight into the use of ML to improve the accuracy and objectivity of this process while minimising interobserver variability. These proposed algorithms represent a potential solution to the lack of a clear threshold for the Spitz/spitzoid tumour classification, and its high accuracy supports its usefulness as a helpful tool to improve diagnostic decision-making.

Design of fruit fly optimization algorithm based on Gaussian distribution and its application to image processing

The Fruit Fly Optimization Algorithm (FOA) has strong applicability, which can be optimized directly after the objective is determined not by building a complex model. Due to the problems of the algorithm such as easy prematureness, low solution accuracy, and easy to fall into local optimality. Therefore, the Gaussian Distribution Fruit Fly Optimization Algorithm (GaussFOA) based on Gaussian distribution was first proposed to solve the shortcomings of FOA. Then GaussFOA was applied to image segmentation processing. Finally, the experimental results were compared with FOA, the improved Fruit Fly Optimization Algorithm with Changing Step and Strategy (CSSFOA), and the Linear Generation Mechanism of Candidate Solution of Fruit Fly Optimization Algorithm (LGMSFOA). The results showed that GaussFOA had 100 % success rate compared with FOA, CSSFOA, and LGMSFOA under the same function. This algorithm also had the best finding mean and standard deviation. The low and high threshold division was compared in terms of the number of segmentation thresholds. The GaussFOA had the best value of both the average and the standard deviation of the search for merit. The segmentation results under high threshold were more obvious when compared with the segmentation results of low threshold GaussFOA. The image immunity of GaussFOA was 8.57 %, 10 %, and 29.97 % higher than that of FOA, Particle Swarm Optimization (PSO), and Genetic Algorithm (GA). This indicated that the model constructed based on GaussFOA had improved the image segmentation effect and stability compared with other algorithms. The findings of the research can offer a new path for the processing techniques of images.

A self-adaptive Gaussian mutation-based arithmetic optimiser algorithm for integrated production scheduling and vehicle routing problem in the distributed manufacturing environment

ABSTRACT In response to the challenges posed by economic globalisation and increasing customer demands, enterprises are compelled to adapt and refine their production models and operational objectives, which motivates this paper to address the integrated production scheduling and vehicle routing problem in the distributed manufacturing environment (IPSVRP-DME). The objective is to simultaneously minimise both total energy consumption and total earliness/tardiness. Initially, a mixed integer programming model is proposed to address small-scale problems using Gurobi. Considering the NP-hardness of the problem, a novel Self-adapted Gaussian Mutation-based Arithmetic Optimiser Algorithm (SGMAOA) is developed to handle medium-scale and large-scale instances. To address the complexity of decision-making, an innovative two-level encoding method that encompasses four decision dimensions is introduced. Additionally, an incremental repair strategy is devised to rectify infeasible solutions caused by unreasonable delivery batching, while a time relaxation strategy is proposed to further enhance service levels without compromising energy consumption. Comparative experiments are conducted to demonstrate the effectiveness of SGMAOA, which is benchmarked against five prominent metaheuristics. In addition, a specific example is applied for the discussion of managerial applications and to illustrate the practicality of the proposed model and solution method.