In this article, an improved slime mould algorithm (SMA-CSA) is proposed for solving global optimization and the capacitated vehicle routing problem (CVRP). This improvement is based on the mixed-strategy optimization of Cauchy mutation and simulated annealing to alleviate the lack of global optimization capability of the SMA. By introducing the Cauchy mutation strategy, the optimal solution is perturbed to increase the probability of escaping from the local extreme value; in addition, the annealing strategy is introduced, and the Metropolis sampling criterion is used as the acceptance criterion to expand the global search space to enhance the exploration phase to achieve optimal solutions. The performance of the proposed SMA-CSA algorithm is evaluated using the CEC 2013 benchmark functions and the capacitated vehicle routing problem. In all experiments, SMA-CSA is compared with ten other state-of-the-art metaheuristics. The results are also analyzed by Friedman and the Wilcoxon rank-sum test. The experimental results and statistical tests demonstrate that the SMA-CSA algorithm is very competitive and often superior compared to the algorithms used in the experiments. The results of the proposed algorithm on the capacitated vehicle routing problem demonstrate its efficiency and discrete solving ability. Establishing a mathematical model to solve practical problems and realizing faster and better solutions to the model is one of the goals pursued by current academic research, and the way to achieve it depends on intelligent optimization algorithms with different strategies. The solution performance of intelligent optimization algorithms under different optimization strategies is different . The intThroughout the development of intelligent optimization algorithms, the shortfalls of classical optimization strategies have been the starting point for the creation of new algorithms, such as the time-out of Newton’s method in the face of complex mathematical processes, so people are paying attention to optimization algorithms inspired by nature. For examples, see the genetic algorithm (GA) , the difIt is precisely because the slime mold algorithm (SMA) has the advantages of a simple structure, high applicability, and strong optimization ability that the improvement of the slime mold algorithm and its application to the capacitated vehicle routing problems are the main research contents of this paper. The original SMA is a new algorithm proposed by simulating the foraging process of slime mold, the changes in the vein structure of slime mold, and the three forms formed by positive feedback and negative feedback generated by biological oscillators . But unfThe main contributions of this study are as follows:The global optimization accuracy of the slime mould algorithm is improved, the annealing link is introduced into the process of updating the position of the slime mould algorithm, and the Cauchy mutation strategy is used to perturb the optimal local solution to reduce the probability of falling into the optimal local solution, and then An improved slime mould algorithm (SMA-CSA) based on mixed strategy optimization of Cauchy mutation and simulated annealing is proposed.The paper employs the CEC2013 standard functions and the Wilcoxon rank-sum test to compare the development and exploration performance differences between SMA, SMA-CSA, and other comparative algorithms.The proponents of the slime mould algorithm and many improvers lack the solution verification of discrete problems such as the vehicle routing problem with capacity constraints. Therefore, this paper applies SMA and SMA-CSA to two CVRP standard example packages, respectively, and further analyzes the experimental results to obtain the performance difference under different optimization strategies and the supplementary research of the algorithm on such problems.The rest of the paper is organized as follows: Section II presents existing strategies for improving the slime mould algorithm and application areas. The third section introduces the mathematical description of the slime mould algorithm, as well as the improvement ideas for the slime mould algorithm, the description and expression of the mathematical formula, and the pseudo-code of the improved algorithm. In the fourth section, the CEC2013 and CVRP examples are simulated for SMA and SMA-CSA, and the differences between the calculation results and the comparison algorithms are tested. Finally, Section V introduces the main conclusions and limitations of this study.Previous studies have fully demonstrated the superiority of metaheuristic optimization algorithms in solving large-scale search and optimization problems . In the Like other metaheuristic algorithms, solving the balance between exploration and development in SMA can effectively improve the global search performance of the algorithm. Therefore, methods such as self-adaptive improvement of fixed parameters or the introduction of self-adaptive weight factors to balance the development and exploration performance of SMA have gradually become effective measures for many researchers. For example, ASMA  is propoSimilar to the adaptive improvement algorithm, many researchers also tend to use the chaotic map to optimize and improve the meta-heuristic optimization algorithm, and past research has confirmed that the use of the chaotic map can improve the solution performance of the optimization algorithm. The chaotic SMA (CSMA) proposed by reference  also conIn addition, borrowing the traditional algorithm position update strategy to optimize the original SMA algorithm and improve the solution performance of the original algorithm is also one of many research schemes. For example, borrowing the location update behavior of the Whale Optimization Algorithm (WOA) can enhance the global search behavior of the original slime mould algorithm , 33. SimBy reviewing the literature, it appears that the current slime mould algorithm is widely used. Researchers have applied the slime mould algorithm and its variants to engineering optimization problems and other research fields. For example, solving single- and du-al-objective economic and emission scheduling (EED) problems considering valve point effects ; determiReferring to the application scenarios of other optimization algorithms, the slime mold algorithm can also do a lot. For example, an improved whale optimization algorithm for COVID-19 medical feature selection ; a dynamIt can be seen from the literature results that the slime mould algorithm has applicability in solving optimization problems, and with the improvement of the original algorithm, the solution accuracy and convergence speed of the improved slime mould algorithm have been improved. Among the many problems solved, there is still a lack of verification solutions for vehicle routing problems such as CVRP, VRPTD, VRPTW, and GVRP, as well as discrete problems such as warehouse routing problems (LRP). Therefore, in the fourth section, this paper solves the CVRP problem discretely and uses two CVRP calculation examples to expand the application research of the slime mould algorithm and its variants.Because the original slime mould algorithm is easy to fall into the optimal local solution; therefore, in the algorithm design process, we need to introduce a new mechanism to improve the global optimization ability of the original slime mould algorithm and t represents the maximum iterations as shown in The slime mould spontaneously approaches the food according to the smell of the food, and the following mathematical expression can express its expansion pattern. S(i) represents the fitness of the mucilaginous individual, i ∈ ; DF represents the best fitness obtained by the slime mould individual in all iterations. The S(i) value in the first half of the optimal solution ordering, this condition serves to simulate the search pattern chosen by the mucor based on food concentration; the r is used to simulate the uncertainty in the form of mucor vein contraction, and the value is a random value in the interval ; the log contributes to reduce the rate of change of the numerical contraction. The bF value represents the optimal iteration value in the current iteration process; wF value is the worst value in the current iteration process; Smelllndex is the ranking of all iterations.The LB and UB represent the size of the upper and lower boundaries of the slime search process; rand denotes a random value in the interval , and how to determine the parameter z value need to be discussed according to specific experiments.The  according to the size of food concentration.The slime mold controls the thickness of their own venous network by their own oscillation fluctuations, the simulation process is shown in  oscillate randomly between the intervals  and , and eventually converge to zero. In addition, when the slime mold explores the food based on the food concentration, some of the slime will still be separated to explore other unknown areas. It is worth mentioning that the harsh environments encountered during exploration are informative for simulating real situations, such as strong sunlight and dryness.The values of In the original slime mould algorithm, the generation of the optimal position depends on the concentration of food odor when the slime mould searches the unknown area. When the population of individuals tends to aggregate due to the increasing number of iterations, the optimal individual will lack the ability to quickly jump out of the optimal local solution, which makes the algorithm prone to the premature phenomenon. Therefore, to strengthen the ability of SMA to jump out of the optimal local solution, this paper introduces the fusion Cauchy mutation strategy to perturb the current optimal solution to ensure that the algorithm has greater population diversity during local optimization.The Cauchy variation originates from the Cauchy distribution. According to the Cauchy distribution mechanism, the two ends of the Cauchy distribution function curve are longer, indicating that it can make it easier for individuals to escape from local extremes, and a smaller peak will guide individuals to spend less time searching for the optimal location. Therefore, the Cauchy mutation operator is introduced into the slime mould algorithm to fully use its strong perturbation ability to control the current optimal solution. The formula is as follows:Among them, rand1 is a random probability number that obeys the normal distribution. When rand1>0.5, the algorithm uses the Cauchy operator to mutate the optimal solution, and its powerful perturbation ability can greatly improve the diversity of the population around the optimal solution. When the optimal individual of the local extreme value is found, it can help it escape quickly to ensure the robust optimization of the algorithm; when rand1<0.5, the algorithm retains the current optimal solution.The SMA-CSA algorithm proposed in this section is derived from the original SMA, and In SMA-CSA, whether to accept the current solution is determined by Tc represents the current temperature, and the Metropolis sampling criterion PA(a) represents the possible probability that solution a is accepted. Each time a new solution is constructed, the current temperature is updated with ε is a parameter that controls the rate of decrease of the current temperature, and Tn represents the temperature of the next iteration. It should be noted that in order to prevent the temperature from converging too fast to affect the quality of the solution, we need to introduce Tp denotes the temperature at the last time when a feasible solution generated by SMA is accepted, where ω is a control parameter for the convergence rate, which is set to 0.998 in this paper.In The improved algorithm structure and steps are shown in In this section, SMA-CSA is tested and compared with other algorithms using 23 standard test functions : A distribution center O provides logistics services for N customers, where the number of logistics vehicles is M and the maximum load capacity of each vehicle is Q.The logistics vehicles must provide logistics services for customers from the distribution center and return to the center after completing their tasks.All logistics vehicles must serve customers at all nodes within their capacity Q limits, with no omissions.The final capacity of the vehicle is linked to the number of goods to be delivered at each node and the number of nodes (customers) to be served by the vehicle on the route.qi represents the quantity demanded by the customer, i ∈ V; (q0 represent the warehouse); cij represents the distance from customer i to customer j; cj0 indicates the distance from the warehouse to customer j; ci0 represents the distance from customer i to the warehouse; If vehicle k visits client i, let yik = 1, otherwise yik = 0; If vehicle k continues to visit customer j after visiting customer i, let xijk = 1, otherwise xijk = 0.Building the CVRP mathematical model:f1 is the desired objective function, that is, the shortest total distribution path length; f2 is the longest path for a single vehicle; f is the individual fitness; the constraint (4.4) indicates that there is one and only one vehicle from one node to another;  Initialization. First, the algorithm initialization parameters are defined, including population size, maximum iterations, and crossover (C-R), and then the algorithm randomly generates the initial population of slime mould.Xi) for each individual slime mould is based on the following steps:The formation of the optimal solution ((Step1). Create a path that uses the warehouse as the starting point (zero points);(Step2). select a customer from the customer list in a random non-replacement form;(Step3). Add the selected customer to the route;(Step4). Determine whether the total demand of all customers on the path is less than the vehicle capacity;(Step5). Repeat step2 and step3, otherwise add the warehouse to the route;(Step6). Add a route;(Step7). Repeat steps 1–6 until all customers have been traversed;Xi) has been calculated, sorting the solution Xi of all slime mould, and calculating the weight of the corresponding solution, finally updating the optimal solution.So far, each individual’s solution (2) Crossover. When using the SMA-CSA algorithm to solve CVRP, introduce crossover (C-R) in the process of position updating to improve the quality of the solution. In the crossover, an individual is selected first, and then new positions P1 and P2 are randomly generated between the solution set, and the positions of the newly generated solutions are positioned between P1 and P2.3) Local search. In order to expand the range of the solutions, three local search strategies are used, including point-swap, 2-opt, and 3-opt.(1) Point swap strategy. As shown in (2) 2-opt search. As shown in (3) 3-opt search. As shown in 4) Mutation. In order to ensure the global search ability of the algorithm, this paper uses three mutation operators with different selection probabilities to improve the diversity of the solutions. The first mutation randomly selects two customers in the CVRP solution with two paths and swaps the two customers in each of the two paths. The second mutation randomly selects two routes in the CVRP solution and swaps the customers within the two paths to form a new path. The third mutation is the 2-h-opt mutation and is one of the most effective mutations for complex problems [problems .First, the multi-vehicle path is converted into a single-vehicle path problem using the predefined probability M-R. Then, the 2-h-opt operator is used to find the twisted connections in the original path and reopen them to generate a new multi-vehicle problem.This section discusses the results of solving CVRP using SMA-CSA and analyzes its performance. Two standard benchmark datasets of CVRP are selected, and the results are compared with other algorithms to analyze the advantages and disadvantages of different algorithms for solving the problem. The algorithms used for comparison include SMA-CSA, ISOS, EACO , LNS-ACOThe test results of the selected cases are shown in Tables Secondly, the parameters related to SMA-CSA and the comparison algorithm are set, as shown in In It can be seen from In order to observe the results of SMA and SMA-CSA in multiple operations more intuitively, In order to verify the effect of the article search strategy, the article calculates the results when SMA-CSA does not apply a local search strategy or crossover mutation strategy. It can be seen from Metaheuristic algorithms show that they are able to arrive at optimal solution sets for global optimization and discrete problems in a reasonable amount of time. Some of the most representative metaheuristic algorithms include: Moth Search (MS) , EarthwoIt was the main inspiration of this study to propose an improved slime mold algorithm named SMA-CSA based on Cauchy mutation and simulated annealing hybrid strategy optimization and then recoded to solve two CVRP data sets. To address the SMA’s shortcomings, the SMA-CSA implemented the Cauchy mutation operator, random perturbation, and the Metropolis sampling criterion acceptance strategy.The proposed SMA-CSA algorithm is evaluated on global optimization problems using CEC 2013, and its performance is compared to that of SMA and other algorithms such as HHO, SMA, EO, TSA, GWO, ESMA, and L-SHADE, CMA-ES, and CSMA.Different mathematical and structural examples are considered for evaluating the performance of the new algorithm. The good results of SMA-CSA in benchmark functions (F1–F7) show the performance of the SMA-CSA algorithm in terms of exploitation and local optimum avoidance. Moreover, the algorithm is applied to the capacitated vehicle routing problem (CVRP) and compared to other algorithms such as ISOS, EACO , LNS-ACOAlthough the research results of the article confirm the feasibility of annealing and Cauchy mutation mixed strategy coordination optimization, there are still some limitations in the overall research. For example, although the convergence speed and global accuracy of the improved SMA are significantly improved, the calculation time is increased by 57% on average compared with the SMA due to the introduction of the annealing process, which requires longer computation time. Secondly, the improved algorithm does not further calculate the test results of different benchmark functions in more dimensions and does not verify the impact of dimensional changes on the algorithm simulation results. Thirdly, the amount of data analysis in the CVRP example used in this article is relatively small, and there is a lack of solution analysis for large-scale node data, so the conclusion about algorithm performance has limitations. Finally, the use of CVRP problems to test the discrete solution performance of the SMA-SA algorithm is still not convincing, and the ability of SMA-SA to solve discrete problems should be further tested in more practical optimization problems .In addition, future researchers can further optimize the slime mold algorithm from other perspectives, such as by introducing a reverse learning mechanism while adaptively controlling algorithm parameters, which may lead to better results. In addition, applying the SMA-SA algorithm to VRPTD, VRPTW, GVRP, and other similar vehicle routing problems and real-case applications to further verify the performance of the algorithm is an effective research idea.S1 Algorithm(TIF)Click here for additional data file.S2 Algorithm(TIF)Click here for additional data file.S1 Appendix(DOCX)Click here for additional data file.


The performance of deep neural networks and the low costs of computational hardware has made computer vision a popular choice in many robotic systems. An attractive feature of deep-learned methods is their ability to cope with appearance changes caused by day–night cycles and seasonal variations. However, deep learning of neural networks typically relies on large numbers of hand-annotated images, which requires significant effort for data collection and annotation. We present a method that allows autonomous, self-supervised training of a neural network in visual teach-and-repeat (VT&R) tasks, where a mobile robot has to traverse a previously taught path repeatedly. Our method is based on a fusion of two image registration schemes: one based on a Siamese neural network and another on point-feature matching. As the robot traverses the taught paths, it uses the results of feature-based matching to train the neural network, which, in turn, provides coarse registration estimates to the feature matcher. We show that as the neural network gets trained, the accuracy and robustness of the navigation increases, making the robot capable of dealing with significant changes in the environment. This method can significantly reduce the data annotation efforts when designing new robotic systems or introducing robots into new environments. Moreover, the method provides annotated datasets that can be deployed in other navigation systems. To promote the reproducibility of the research presented herein, we provide our datasets, codes and trained models online. Cameras are one of the most efficient and widely used sensors, especially in robotics. To mention some prominent advantages of cameras, they are affordable, small, and lightweight, without any interference with each other. Besides, they provide high-resolution real-time data that do not impose computational problems thanks to powerful computational hardware getting cheaper over time. Considering these advantages, onboard cameras are regularly used in mobile robots to gather information about the surrounding environment ,2, and aIn the context of mobile robot navigation, cameras are often used to segment out traversable areas, such as roads or pathways , or theyThe issue of long-term stability of vision-based maps for mobile robot navigation was also investigated in the context of visual teach-and-repeat (VTR), where the main task of the robot is to repeat a previously taught trajectory. Some of the efforts aimed at the use of multiple maps ,19 or imInspired by the fact that engineered features can achieve vision-based teach-and-repeat navigation in the short-term and deep-learned neural networks can do the same in the long-term, we propose a VTR pipeline that combines them in a fusion-learning scheme. The proposed pipeline, shown in In this paper, we contribute to state of the art by investigating the impact of the aforementioned self-supervised training in the context of visual teach-and-repeat navigation. We show that the robustness of VTLR gradually increases despite the seasonal changes, while the error of the classic VTR gradually increases. Moreover, we deploy the self-trained method in a different environment and show that it outperforms classic VTR as well. Finally, we compare the performance of the self-trained VTLR to VTLR, which uses ground truth data for training.The rest of the paper is organized as follows. In The use of computer vision has a long tradition in robotics, and robot vision methods are becoming sufficiently mature enough to be deployed in real-world systems. This applies especially to the field of visual SLAM, where a robot with a single camera can precisely estimate its position while creating a map of its operational environment ,8, and vThis challenge attracted researchers to propose solutions that would allow robots to operate over extended periods of time, where environment changes are inevitable. In , the wavTo boost the robots’ ability of long-term operation, several authors proposed various feature management schemes aimed at a gradual update of the maps to keep up with the environment changes. Some of the works aim to assess the temporal stability of individual features in sparse visual maps in order to update features that are going to be stable in the long-term while removing those that are no longer useful ,36,37,38Other approaches aimed to tackle the problem by using several maps gathered during multi-session mapping runs. In particular, Churchill and Newman  proposedAnother stream of research proposed not only to remember (and forget) the past experiences but to analyse them in order to forecast the future environment’s appearance. Neubert et al. proposed a method that can learn appearance changes based on a cross-seasonal dataset and use the learned model to predict the environment appearance ,43. LowrAlong with the aforementioned works, several teams contributed by collecting multi-session mapping datasets that captured the appearance and structural changes over long periods of time. Datasets like Nordland , KAIST dSome of these machine learning methods aimed to train classic feature descriptors in order to increase their robustness to seasonal changes. For example, the pixel brightness comparison sequence of the Binary Robust Independent Elementary Features (BRIEF)  was traiOverall, there was a significant work on long-term visual localisation and navigation in changing environments and it’s beyond the scope if this paper to systematise all the approaches. A number of survey papers provides a good insight into the problem. In particular, ref.  survey tSeveral of the aforementioned pipelines employ heavily engineered or hand-crafted features which gained huge popularity in robotic systems, due to their efficient memory usage and performance. The design of the image features aims at achieving invariance towards natural changes occurring in images such as illumination, occlusions, geometric transformations etc. and involves two stages, namely, detection and description ,13,15. DThe best known method for feature extraction is the Scale Invariant Feature Transform (SIFT)  which utAnother well known combination of detector and descriptor is the Speeded Up Robust Features (SURF) which uses a Hessian keypoint detector and an optimised description from SIFT . The SURA truly open-source combination is the Oriented FAST and Rotated BRIEF (ORB)  which usOur goal is to design a method that would allow visual teach-and-repeat navigation in changing environments over long periods of time. The navigation pipeline is based on a teach-and-repeat method that uses the visual data to correct the heading of a robot to keep it on the intended path ,63,64,65Our augmented feature detection and matching pipeline consist of two main parts, feature matcher (FM) and neural network (NN), see  network  first es network  along wid is the displacement of the images in pixels and Our pipeline is integrated the BearNav  visual tThe role of the neural network is to estimate the likelihood of horizontal displacements between two images—one from the map and one currently perceived by the robot. For that reason, the neural network is built so that it’s output is a histogram of likelihood values corresponding to possible displacements. The NN model used is a fully convolutional Siamese neural network with a backbone similar to AlexNet  inspiredw is the input image width. The final output of NN for each image pair therefore is a probability distribution over 63 possible pixel shifts between the two images. This is then used as a prior by our modified feature matching scheme.The input of the network are two images In a standard FM module, keypoints in images the FAST  detectorthe FAST  descriptthe FAST . In our the FAST  and SIFTthe FAST  featuresr is typically chosen around 0.8 as stated in the original paper [r coefficient set to 0.95.In a standard matching method, the extracted features form two sets al paper . In our d, the value However, in contrast to the standard feature matching, our module exploits the probabilistic distribution over possible displacements provided by the neural network. This is in the form of a probability mass function with values This filtering scheme has two effects: First, it prevents from matching features with positions that are inconsistent with the prior proposed by the neural network, reducing the number of false correspondences. Second, it improves the number of matches, because the ratio match is performed for lower number of features and thus, the chance of satisfying the ratio test in Equation  is highed of the set d is then considered as a horizontal displacement between d. The tuple d is passed to the robot steering controller.The image coordinates of the matches Once the robot completes the path, the training pair selector starts to process the information stored in the result accumulator The aforementioned filtering could be complemented by manual examination and rejection of incorrect training pairs. However as will be shown in The training scheme of the neural network is a bit different to the evaluation scheme already described in this section. Instead of taking whole images L is calculated as binary cross-entropy between the prediction and the target asnth element of the output of the NN bounded by a sigmoid to range of nth element of the target position displacement and N is the total number of all possible horizontal displacement between the image and the cutout.The target for the training pair is constructed to reflect the position of the cutout in the original image and the displacement To evaluate the proposed pipeline, we followed the methodology proposed in ,24,28 anTo simulate lifelong learning, the teaching was done in several batches on Nordland dataset . This daThe Nordland dataset includes the same track most of the time, and it captures heavy seasonal changes such as snow and fog and change in foliage as well as human-made changes such as newly constructed tunnels For evaluation, we decided to use the Stromovka dataset , which eThe ‘North Campus Long-Term Dataset’ Was collected on the ground of the Michigan university using a robot-mounted omnidirectional camera, planar and 3D lidars and GPS-RTK for truth . The whoThe first step of the evaluation methodology is aimed at emulating the teach-and-repeat scenario using the Nordland dataset. During the first iteration, a robot is guided by an operator to record a sequence of images. For this purpose, we used the first ‘spring’ sequence of the Nordland dataset, which we designate as sequence ribed in , and it In the second autonomous traversal, which is emulated by re-running the sequence k. For comparison, we also calculated the errors The subsequent runs are analogous. With each new sequence During navigation, the whole VTRL was able to run at 25 Hz on Intel NUC with i7 CPU and external GTX1050 GPU without heavy memory usage. This is sufficient for real-time control of most robotic platforms. The training was performed using an RTX3080 graphics card and AMD 3950X CPU, where each iteration of training took about 8 min for each training round, being about 35 ms per image pair at 28 HZ.For the training, not only computational power is required but storage of all the images as well. The whole dataset used on Nordland has 7 GB without any compression and consists of several hours of recorded rides. Considering the robot would have driven one path per day, the data consumption would be less than 1 TB per year. Such volumes are manageable with off-the-shelf SSD drives, which also offer fast access for training the networks.The results are visualised in the same way as in ,28,47. FThe left part of The comparison was conducted using a non-parametric Wilcoxon pair test, which does not pose any assumptions that might not be satisfied in our case. For two compared methods, the individual errors made by both methods were first paired over the locations where they appeared. The test was then conducted to reject the hypothesis that the methods performed equally well, which we did at a standard level of significance Although the results shown in Finally, we compare the performance of the VTRL scheme to the case where the network is trained using hand-annotated data rather than the output of the feature matcher. The results shown in We propose a novel method for obtaining accurate image registration of two images captured from the same location in a changing environment, aimed at application for visual teach-and-repeat navigation of autonomous mobile robots. This method incorporates online self-supervised learning techniques to improve vision-only navigation in changing environments, combining neural network and feature matching methods. We show that our new method can autonomously learn using data from different seasons and improve its performance with every passage through the environment. We also show that the network trained in one environment can improve the performance of the visual teach-and-repeat scheme in other environments as well. Additionally, automatic annotation and filtering of the training data that was implemented yields better results than training on all data using ground truth. Moreover, we will improve the proper selection of images for training and using additional information such as output histogram from the FM should be explored. In closing, (i) the proposed visual-based navigation method, which combines feature matching methods and neural network, (ii) does not require hand annotation and learns automatically, (iii) and outperforms the model trained on ground truth. (iv) furthermore, the proposed method yields generality by learning data from other datasets and seasons.


Bayesian techniques for engineering problems, which rely on Gaussian process (GP) regression, are known for their ability to quantify epistemic and aleatory uncertainties and for being data efficient. The mathematical elegance of applying these methods usually comes at a high computational cost when compared to deterministic and empirical Bayesian methods. Furthermore, using these methods becomes practically infeasible in scenarios characterized by a large number of inputs and thousands of training data. The focus of this work is on enhancing Gaussian process based metamodeling and model calibration tasks, when the size of the training datasets is significantly large. To achieve this goal, we employ a stochastic variational inference algorithm that enables rapid statistical learning of the calibration parameters and hyperparameter tuning, while retaining the rigor of Bayesian inference. The numerical performance of the algorithm is demonstrated on multiple metamodeling and model calibration problems with thousands of training data. Modern engineering tasks are often characterized by the need to perform large scale expensive laboratory experiments or amortize hours of computation, performing simulations that are based on sophisticated mathematical formulations. While these “high-fidelity” sources of information provide detailed insight into the complex physical process, one usually faces a heavy computational runtime or a massive financial investment. In addition to this, obtaining data by running experiments or simulations needs more advanced insight, that might not always be extricated from the data by applying state-of-the-art methods used to build data-driven metamodels . FinallySurrogate modeling methods that have shown promise in dealing with problems of the aforementioned kind, typically include Gaussian process (GP) regression ,4,5, proIn this work, our focus is on applying GP regression to problems that have thousands of data . SecondlMost of the above-mentioned works rely on computational power and heavy use of large-scale computing in order to overcome the challenges of training the models. Our main contribution in this work is to achieve computational efficiency by leveraging a variational formulation of Bayesian inference, commonly known as black-box variational inference (BBVI) , and by Variational methods ,36 to BaThe outline of the paper is as follows: We present the mathematical details of the autoregressive multifidelity calibration model in We consider the Kennedy and O’Hagan’s formulation , where ti, for the two kernels μyh.One common characteristic of the approaches mentioned above is that they all transform the problem of minimizing the KL divergence to an equivalent maximization problem by substituting  into 1111 to obtlogp(D)=Kq and the joint density can be expanded using Bayes’ rule to black-box variational inference [One of the most popular choices for optimizing  is to diimize is∇λF[q]=Eqnference .N times, that is, the number of Monte Carlo samples used to estimate To further scale the algorithm, we perform the log-joint function evaluations Equation , let DliEquation  is rewrice (SVI) .For the case where the approximating family of distributions gradient  as it isgradient .q that is defined asretraction mapping that approximates the exponential map of the manifold of symmetric positive semidefinite matrices [The natural gradient on Riemannian manifolds is defined asmatrices .vector transport that further projects the translated points back to the tangent space, as was first done in [Algorithm 1: Manifold gradient ascentIn our case, we use done in . For ourWe studied the performance of the proposed algorithm on three problems. One metamodeling problem and two multifidelity model calibration problems are used in the sections that follow.We first considered the following mathematical functionsN resulted in more robust convergence and attaining higher values closer to the true optimum that subsequently resulted in better posterior estimates. The decrease in mean predictive std indicated that the predictive accuracy was improved as well and the confidence increased.To test for the robustness of the approach, we first performed the ELBO optimization corresponding to training an autoregressive GP model on the available training data using a varying number of Monte Carlo samples used to evaluate the ELBO gradient estimate , namely Next, Query Analytics Workloads Dataset section, hosted by the University of California Irvine open-source machine learning data repository . This dataset was used in other recent works [https://data.cityofchicago.org/Public-Safety/Crimes-2001-to-Present/ijzp-q8t2 accessed on 31 May 2022). The quantity of interest being modeled was the number of crimes reported or simply the count of crimes in a particular region, in the city of Chicago [x and y coordinates of the center of the region and the radius of the region. Thus, the problem had three inputs and one output. The dataset had ten thousand pairs of inputs and outputs. We leveraged nine thousand points for training the fully Bayesian metamodel and left out one thousand points as test data in order to evaluate the predictive performance of the trained model and we ran In this section, we demonstrate the applicability of the proposed approach on a metamodeling task. The dataset used for this problem was one of the three datasets under the nt works ,61 in or Chicago . The varTwo clear observations from GPy package [In addition to these,  package  for the We considered the torsional vibration problem on the system depicted in The torsional stiffness values were given byKi=θ1πGidWe considered again an experimental scenario in the big data regime, where The posterior results for the calibrated parameters along with the runtime for each case are shown in untuned computer simulators, by enabling savings in computation. This speed-up is critical for engineering applications, especially in the industry, where repeated model calibration tasks are a common occurrence and can lead to accumulated savings using the proposed approach.We enhanced and extended the state-of-the-art stochastic variational Bayesian formulation for tasks that use GPs for multifidelity metamodeling and model calibration tasks, in order to treat problems with tens of thousands of training data and model calibration problems with more than ten inputs. The proposed mathematical formulation extended two classic approaches, the so-called black-box VI and stochastic VI, while utilizing a manifold gradient ascent scheme to accomplish the task of inferring the GP hyperparameters as well as the calibration parameters. The major impact of our work was being able to perform a fully Bayesian uncertainty quantification while training and calibrating models using multifidelity GPs, albeit with large datasets and a moderately large number of inputs. Numerical results on two challenging engineering problems visibly demonstrated a scale up of classical Bayesian GPs for multifidelity modeling to calibrate This work showed promise for accelerating the training procedure in Gaussian process based metamodels without relying on enormous computational power. The key characteristic in our approach was the batch-sampling step used in the stochastic variational inference framework, which allowed the fast computation of the likelihood term and accelerated the optimization task. One key challenge in our approach is that fine tuning of the optimization is required in order to ensure a sufficiently large updating step in the optimization scheme, while at the same time avoiding overshooting. Fine tuning the algorithm heavily depends on the size of the batch samples being used, which is also relative to the original data size that is available. Extremely small batch samples can result in very inaccurate likelihood evaluations and eventually miss the optimum. Another important aspect mentioned above is the number of Monte Carlo samples used for approximating the ELBO function. Very small number of samples can lead to inaccurate estimates with large variance that fail to converge, while on the other hand, a high number of samples makes the algorithm computationally expensive and fails to achieve the desired speed up. Typically, big data problems in Bayesian inference exhibit a well-defined posterior, therefore optimizing the ELBO should always be a feasible task given that some fine tuning has been performed. A limitation of the approach would the case where a big part of the data set is corrupted or contains high noise, in which case, the exploration of the posterior via VI might become challenging due to the complex nature of the true posterior. In such cases, more complex variational approximations need to be considered which could, however, make the algorithm less computationally efficient.Other general challenges, not associated specifically with our approach, are problems of extremely high input and output dimensions as well as highly nonsmooth response functions. In such cases, a further development of our framework might be necessary such that it aligns with similar approaches in the literature, for instance, enabling covariance matrix sparsity, employing nonsmooth correlation kernels and last, but not least, leveraging parallel computing.Directions for future work include scaling up the proposed approach to problems with higher input dimensionality, i.e., hundreds of inputs and with more than one sources of information with lower-fidelity and large training data. Additionally, the proposed approach needs more work in order to be applied to problems where the different sources do not share the same inputs.


Vitiligo is an acquired chronic pigmentation disorder of the skin. Even if the role of the immune system seems to be well established, new pathogenetic hypothesis are rising in these years. It has been recently suggested by the development of an animal model that a protein called Melanoma Inhibitory Activity (MIA) is involved in the pathogenesis of vitiligo. This protein interacts with the adhesion molecules expressed on the melanocytes causing its detachment from extracellular matrix proteins and creating the depigmented macules. A topical preparation based on oligopeptides able to inhibit the actions of the MIA protein has been introduced to the market, claiming activity on vitiligo.A patient affected by non-segmental vitiligo for 10 years, recalcitrant to any treatment  came to our observation.We used this topical preparation containing the MIA inhibitors peptides in selected areas (face and sides of the trunk) leaving untreated other areas as control (legs and arms). The patient was required to be sun exposed or to have some UVA sessions during the treatment to stimulate the melanocytes replications.After 9 months of treatments, he recovered from 50% to 80% of repigmentation only in the treated areas, without any side effects locally or systemically.Even if other studies are required to better determine the efficacy of this approach, this first observation about the use of the MIA-inhibitors peptides for the treatment of non-segmental vitiligo indicates that this topical preparation containing the MIA inhibitors peptides could be a very promising option for the cure of this disease. The exact pathogenesis of the dermatosis is still to be fully clarified.Vitiligo is an acquired chronic pigmentation disorder of the skin that affects 0.5–2% of the population worldwide. MIA is a small protein firstly described as secreted from malignant melanoma cells, which is able to interact with a particular group of adhesion molecules called alpha5beta1 integrins (a5b1ints). This protein has been found present also in skin of vitiligo-affected patients, interacting with the same adhesion molecules. The binding of MIA to these proteins at the cell surface is responsible for the detachment of melanocytes from extracellular matrix proteins, creating the depigmented macules through melanocytorrhagy, as recently demonstrate also in an animal model .Considering all these evidences, the MIA protein could surely be a very interesting target for treating patients affected by vitiligo, since the inhibition of this molecule would leave the melanocytes unperturbed and able to replicate more easily to recover the skin color. Thus, the inhibition strategy of the MIA protein consists in using a particular sequence of 12 amino acids able to bind the protein in its dimerization site avoiding the creation of the active forms , kellin, UVB-NB and UVA exposure, without any benefit and with progressive enlargement of the white spots.The spots were localized mainly in the face .After full explanation, taking a personal consent of the patient and agreement on regular follow up, we decided to use the cosmetic topical treatment based on the MIA-inhibitors technology . The other parts affected by vitiligo were left untreated because of the well-known difficulty to achieve any result (hands and feet) or as control to evaluate the role of UV exposure (legs and arms). The patient was asked to be sun-exposed daily or to have some session of UVA lamps  in order to have melanocytes stimulation. The patient was forbidden to perform UVB-NB in order to avoid possible bias in interpreting the results of the treatment and asked to continue the antioxidants assumption.During the months, the repigmentation started to be restored only in the application sites (face and sides of the trunk) after 3 months of treatment and after 9 months of observation it reached from the 50% to 80% of the basal situation  was available for the topical treatment of white macules.Melanocytorrhagy induced by the MIA protein is a new and very interesting pathogenetic hypothesis for vitiligo,The technology of the inhibitory peptides is a very interesting tool for the treatment of skin condition because, through the proper vehiculation, these peptides could be very targeted and effective with poor whereas completely absent side effects. This kind of approach is surely very complicated to develop due to the fact that it is required to find a specific aminoacidic sequence interacting with a specific part of the protein to be inhibited. Once the right sequence is found, anyway, the benefits are very important because the peptide interacts with its target or otherwise it is simply degraded into basic amino acid giving a very elevated safety profile of the treatment, like reported in previous studies.Regarding the peptides able to block the MIA protein, they are a series of different chains of amino acids with the property to interact with the protein itself. Among these, one particular sequence of 12 amino acids  is able to bind the MIA protein at its dimerization site, avoiding in this manner the formation of the dimeric or tetrameric active form.We use this new treatment in case of recalcitrant and very diffuse non segmental vitiligo, in combination with sun or UVA exposure and oral antioxidants with very interesting results. The treatment was able to restore up to 80% of the pigmentation of the white patches, without any side effects locally or systemically. We use the treatment in combination with sun or UVA exposure because of the necessity of stimulate the replication and activity of the melanocytes once the activity of the MIA protein was blocked by the peptides present in the topical treatment. Antioxidants, moreover, were used to reduce the possible side effects of the UV exposure on the skin.The role of the MIA-inhibitors seems to be very decisive for achieving the clinical improvement in this patient. In fact, the patient was already subjected in the past to UV or sun exposure without any results and at the same way he was using antioxidants in the last 12 months, without any sign of improvement. Moreover, the part not treated with the MIA-inhibitors cream but anyway benefited by UV or sun exposure and the action of antioxidants did not show any sign of repigmentation.From a safety point of view, very interestingly the treatment did not show any side effects, both topically and systemically. The use of the MIA-inhibitors in this patient involved very diffused spots for a prolonged amount of time, without the appearance of any undesired effects. This observation is very promising for the use of this kind of approach in the vitiligo affected patients as it is well known that this kind of patients required a long period of treatment in often very wide patches diffused in all the body. To be still determined anyway is the theoretical risk of sensitization and if the same safety profile  is maintained also for more thin part of the skin such as eyelids.In conclusion, this case report is the first observation of a successful treatment of non-segmental vitiligo using the MIA-inhibitors technology. Based on the very interesting results reported, this treatment could be considered a possible therapeutic option of non-segmental vitiligo. Other studies are mandatory to establish the real efficacy of this treatment with or without UV exposure and to determine the exact safety profile of this approach (which seems to be very elevated) together with the efficacy in other and more resistant areas such as hands and feet.The authors thank Dr A.P. De Cata, Mr. A.E.D. Bordignon and Mr J. M. Martinez Ribes for supporting their work.Conceptualization: Jordi Segura Tejedor, Matteo Bordignon, Sergi Hernandez Navarro.Data curation: Annalisa Angelini, Chiara Castellani, Jordi Segura Tejedor, Matteo Bordignon, Marny Fedrigo, Marta Bajona Roig, Roberto Luisetto, Sergi Hernandez Navarro.Formal analysis: Matteo Bordignon.Investigation: Matteo Bordignon.Supervision: Mauro Alaibac, Matteo Bordignon.Validation: Mauro Alaibac, Matteo Bordignon.Writing – original draft: Jordi Segura Tejedor, Marta Bajona Roig, Matteo Bordignon, Sergi Hernandez Navarro.Writing – review & editing: Annalisa Angelini, Chiara Castellani, Jordi Segura Tejedor, Marta Bajona Roig, Matteo Bordignon, Mauro Alaibac, Roberto Luisetto, Sergi Hernandez Navarro.


Methane and volatile fatty acids are important products of rumen fermentation in dairy cows. Quantitative research on them is of great significance for environmental protection and animal production. The aim of this study was to develop a prediction model using the stacking ensemble learning method and predict the production of rumen fermentation products based on the nutrient level of the diet. The results show that the stacking model has good performance in terms of prediction accuracy. The model proposed in this study can be used as a guideline to optimize diet compositions and improve feeding efficiency.Volatile fatty acids (VFAs) and methane are the main products of rumen fermentation. Quantitative studies of rumen fermentation parameters can be performed using in vitro techniques and machine learning methods. The currently proposed models suffer from poor generalization ability due to the small number of samples. In this study, a prediction model for rumen fermentation parameters , and propionic acid (PA)) of dairy cows is established using the stacking ensemble learning method and in vitro techniques. Four factors related to the nutrient level of total mixed rations (TMRs) are selected as inputs to the model: neutral detergent fiber (NDF), acid detergent fiber (ADF), crude protein (CP), and dry matter (DM). The comparison of the prediction results of the stacking model and base learners shows that the stacking ensemble learning method has better prediction results for rumen methane (coefficient of determination ( Methane is a greenhouse gas with a long half-life. Methane emissions from ruminants are an important source of anthropogenic greenhouse gases. Volatile fatty acids (VFAs) affect the health of dairy cows. The production of VFAs in the rumen can cause changes in milk production and composition . ExcessiMethane and VFAs can be measured directly by an in vivo technique, but the measurements are time-consuming, laborious, expensive, and unsuitable for large-scale feed evaluation . The in Many scholars have discussed the correlation between diet composition and rumen fermentation ,14,15. BTo accurately predict the rumen fermentation parameters of dairy cows, this study obtained the sample data required for the prediction model through actual feeding and digestion experiments. Different TMR  were collected for the in vitro fermentation experiment. Multi-point collection was carried out after feeding by the feeding truck, and (500 ± 50 g) TMR samples were obtained by the quadrat method. The TMR were dried at 65 °C for 48 h, ground into 40 meshes, weighed 0.2 g, and loaded into a fiber bag as a fermentation substrate. The nutrient levels  of TMR were measured according to the literature . Rumen fThe experiment was completed at the A-cheng Experimental Base  of Northeast Agricultural University in 2018. A total of 120 groups of data were obtained, and the nutrient levels are shown in 1 (C:F ratio of 40:60) and T2 (C:F ratio of 60:40). Both T1 and T2 met the animals’ requirements for nutrition based on the CPM-Dairy model  [To prove the robustness and strong generalization ability of the prediction model proposed in this paper, an independent validation experiment was conducted in Changchun, China (2021). Different diet compositions and rumen fluid were used in this experiment. Rumen fluid was collected from three dairy cows weighing (500 ± 50 kg) before the morning feeding. The in vitro incubation procedure was the same as the previous study. The methane production was determined by a real-time in vitro fermentation system  . Nitroge3.08.01) . The ingEnsemble learning is a popular machine learning strategy. There are three core ideas in ensemble learning: bagging, boosting, and stacking. Ensemble learning combines multiple models, and the error of a single base learner is likely to be compensated by other base learners. Therefore, the overall prediction performance will be better than that of a single base learner . StackinGBRT is one of the boosting-based ensemble learning methods proposed by Friedman . GBRT maThe generic GBRT method is: first input training set samples Initialize weak learners:For Using For each sample in each leaf node, the output value Update the strong learner:This leads to the final strong learner expression:GPR is a machine learning regression method developed in recent years with a rigorous statistical theoretical foundation that is well adapted to handle complex problems with high dimensionality, small samples, and nonlinearity and has a high generalization capability. Compared with other machine learning techniques, the advantages of GPR are its seamless integration of various tasks, including parameter estimation, model training, and uncertainty estimation . The metA GP is defined by its mean and covariance function (kernel function). In GPR, the data can be divided into training data The form of the mean function and covariance kernel function in the GP prior is chosen and adjusted during the model selection process. The mean function is typically constant, either zero or the mean of the training dataset. There are many options for the covariance kernel function: it can have many forms as long as it follows the properties of a kernel . In this study, a combination of a constant kernel and a radial basis function (RBF) kernel is used as the kernel function.This kernel has two hyperparameters: signal variance Bagging  is a welBagging is composed of two parts: bootstrapping and aggregation. Bootstrapping is a sampling method in which a sample is chosen from a set using the replacement method. The learning algorithm is then run on the selected samples. The bootstrapping technique uses sampling with replacements to make the selection procedure completely random. When a sample is selected without replacement, the subsequent selections of variables are always dependent on the previous selections, making the criteria non-random. Model predictions undergo aggregation to combine them for the final prediction, which considers all the possible outcomes. The aggregation can be done based on the total number of outcomes or the probability of predictions derived from the bootstrapping of every model in the procedure.The bagging algorithm uses the model averaging strategy. The reason why model averaging works is that different models usually do not produce the same error on the test set. Model averaging is a powerful and reliable method for reducing generalization error.The random sample consensus (RANSAC) algorithm takes the linear regression algorithm to the next level by excluding the outliers in the training dataset. RANSAC regression is a non-deterministic algorithm that tries to separate the training data into inliers and outliers. Outliers can come from extreme values of the noise, erroneous measurements, or incorrect hypotheses about the interpretation of data. Outliers have no value for the estimation of the model, and the final result of the RANSAC algorithm is obtained based on the set of inliers determined by the algorithm.RANSAC regression is a robustness regression. One of the advantages of RANSAC is its ability to provide robust estimates of the model parameters, i.e., it can estimate the parameters with a high degree of accuracy even when a significant number of outliers are present in the data set. The RANSAC algorithm was first proposed by Fischler and Bolles .The stacking ensemble learning framework of our study is illustrated in The model evaluation method uses the mean absolute error (MAE), mean absolute percent error (MAPE), root mean square error (RMSE), and coefficient of determination  were used to make predictions on the same test set. Four predictor error metrics  to verify the feasibility and generalization ability of the rumen fermentation prediction model. The observed values and the comparison of simulated values by different models are shown in The purpose of this study was to predict the production of rumen fermentation products using the stacking ensemble learning method. By comparing each base learner, it is concluded that the stacking model can be used to predict the rumen fermentation parameters. In this experiment, the stacking model had better predictive performance than the base learners; it had a larger When performing regression prediction on the rumen fermentation parameters of dairy cows, previous studies compared multiple machine learning models and selected models through evaluating metrics, while each model has its own characteristics, strengths, and weaknesses. The stacking ensemble learning method solves the model selection problem by combining each model rather than choosing between them, while also achieving better generalization performance. In this study, GPR had a smaller d Lennox  use the In this study, the levels of methane, AA, and PA produced during rumen fermentation were predicted for different diets. Dietary changes induce rumen microbial community adaptations that alter fermentation patterns and contribute to changes in VFAs . And chaBroadly speaking, rumen metabolism can be divided into three layers . In the As shown in 2 was greater than that of T1, which can provide more rumen fermentation substrates and produce more PA. Therefore, the diet composition of T2 is more reasonable [The C:F ratio of the diet has a significant effect on the VFA production in the rumen and determines the type of rumen fermentation . Increasasonable . Our mod2-sim value is lower than the T1-sim value, which is consistent with the conclusions of previous studies. It is worth noting that the methane predictions of all models are slightly underestimated, and one possible reason for this analysis is that methane generation in the rumen of ruminants mainly comes from rumen microorganisms. In vitro experiments control the consistency of rumen microflora and reduce the factors affecting the model results. Another reason may be related to the different collection methods for methane. In the validation experiment, methane production was measured by the real-time in vitro fermentation system, whereas the data used in the previous modeling was collected manually and may be incomplete.Studies have shown that rumen methane production can be influenced by changing the C:F ratio of the diet . ThroughIn this study, we propose a technique for predicting methane, AA, and PA content in the rumen of dairy cows using a stacking ensemble learning algorithm combined with in vitro fermentation technology. The prediction accuracy of the stacking model is significantly higher than that of the separate machine learning methods in all evaluation metrics, especially for small samples. The generalization ability of the model has also been proven by validation experiments. Our proposed research method provides an idea that can solve the problem of simulating rumen fermentation, which can assist the in vitro method for quantitative study of rumen fermentation products and provide guidance for optimizing diet compositions and improving feeding efficiency.


Small proteins, encoded by small open reading frames, are only beginning to emerge with the current advancement of omics technology and bioinformatics. There is increasing evidence that small proteins play roles in diverse critical biological functions, such as adjusting cellular metabolism, regulating other protein activities, controlling cell cycles, and affecting disease physiology. In prokaryotes such as bacteria, the small proteins are largely unexplored for their sequence space and functional groups. For most bacterial species from a natural community, the sample cannot be easily isolated or cultured, and the bacterial peptides must be better characterized in a metagenomic manner. The bacterial peptides identified from metagenomic samples can not only enrich the pool of small proteins but can also reveal the community-specific microbe ecology information from a small protein perspective. In this study, metaBP  has been developed as a comprehensive toolkit to explore the small protein universe from metagenomic samples. It takes raw sequencing reads as input, performs protein-level meta-assembly, and computes bacterial peptide homolog groups with sample-specific mutations. The metaBP also integrates general protein annotation tools as well as our small protein-specific machine learning module metaBP-ML to construct a full landscape for bacterial peptides. The metaBP-ML shows advantages for discovering functions of bacterial peptides in a microbial community and increases the yields of annotations by up to five folds. The metaBP toolkit demonstrates its novelty in adopting the protein-level assembly to discover small proteins, integrating protein-clustering tool in a new and flexible environment of RBiotools, and presenting the first-time small protein landscape by metaBP-ML. Taken together, metaBP (and metaBP-ML) can profile functional bacterial peptides from metagenomic samples with potential diverse mutations, in order to depict a unique landscape of small proteins from a microbial community. Small proteins or peptides, translated from short open reading frames, largely exist in biological systems in both eukaryotes  and prokBacterial peptides are much harder to decompose and they annotate in a natural community. While detecting and testing a small gene can be difficult in a single organism, microbiome at community level brings additional challenges in the data complexity and sparsity for small protein detection, classification, and function annotation. Metagenomics from short gun sequencing provides information from the community-specific population to gene functions, but there haven’t been many previous efforts specifically focusing on the role of bacterial peptides from a natural community. The lack of detection power and poor analytical resolution indicate the limitation from both the computation and experiment. First, the peptides detection from mass spectrometry needs abundant input materials and suffers from large search spaces in an unbiased and untargeted scenario. It usually requires a confident database from reference genomes or from metagenomes. Poor annotation of small genes in reference genomes is also an obstacle of the direct detection from mass spectrometry. Even by combining multiple types of omics data, the false positives can still be high in small bacterial peptides detection . Second,In order to address the limitations from the nucleotide-level metagenomic assembly and the current shortages of small protein annotation from microbe communities, metaBP  has been developed as a comprehensive and user-friendly toolkit to explore the small protein universe in a more thorough and detailed way. The metaBP applies protein-level assembly from the metagenomic sequencing data to maximize the protein recovery and search from the open reading frames . The metThe metaBP is an integrated and automated toolkit for identifying and annotating small proteins from the metagenomic sequencing data. MetaBP’s implementation consists of three major modules , and five main procedures : proteinThe input data for metaBP is the raw sequencing reads (paired-end short gun sequencing) in a FASTQ format. The output data consists of mainly three parts of the information, protein clusters with mutations, small protein annotations, and a protein copy number table from annotations, which will be demonstrated in this study. For the purpose of this study, only the small protein analysis is mentioned and emphasized. In fact, the metaBP toolkit can also identify the entire proteome wide space of open reading frames, other than just small proteins.The raw FASTQ files used in this study are downloaded from NCBI SRA by the sra-toolkit. The sample IDs and general sequencing information are summarized in the supplementary table , with diRaw sequencing reads in FASTQ files are pre-processed by BBTools . The preThe assembled protein sequences are used in the clustering process. Linclust is one of the most recent protein clustering techniques that can approach both the good accuracy and linear time complexity . The metThe protein clustering by Linclust has two purposes: one is to remove the redundancy from proteins and protein fragments, and the other is to group protein families by homology for mutations. The protein sequences generated from the PLASS example dataset are duplicated to test the effects of truncated sequences. Each protein is truncated up to 50% of the total length from either beginning or end of the sequence, mixed with their intact versions, and then they are clustered by Linclust at different settings. When the default parameter for Linclust is applied, the sequences truncated to 90% of the original length can still be clustered with its full-length version, but sequences truncated to 80% of the length cannot be clustered well. When using the customized setting in Linclust and setting the coverage rate to 50%, most of the truncated protein can still be clustered with the original full-length protein . For smaThe strategy to isolate small proteins from metagenomics data is as follows. First, sequences with longer than 100 amino acids are separated. Second, short sequences clustered with long sequences are removed so that the protein fragments can be minimized in the final output. Third, in this study, only protein clusters with four or more protein members are considered as confident protein families. This means that the same small protein should occur at least four times in a single sample. In addition, only protein clusters with a large size can display a meaningful sequence diversity. On average, after these criteria are applied to the datasets, less than 5% from the metagenomics data are small bacteria peptides, which is consistent with the study from MAGs (metagenome-assembled genomes) or contigs .The database for small protein sequences (not more than 100 amino acids) is constructed from the sequence files in the FASTA format downloaded from the Uniprot  . In totaAs a transformer-based machine learning model inspired from natural language processing, ESM  is used After the database is constructed with vectorized small protein sequences, small proteins from metagenomic samples must be processed in the same ESM model . Each ofThe final protein annotation strategy based on the ten nearest neighbors is heuristic. First, rule of thumb is used if there is a most frequent annotation in the neighborhood. Second, if there is no difference between annotation frequencies, the top annotation is always picked. Third, if useful annotation cannot be extracted from the top ten neighbors, the protein will be left as unannotated.6 to represent the copy numbers per million proteins.In this study, the enzyme commission (EC) number and the taxonomy information will be provided in the small protein annotation. For simplicity of this research, protein copy numbers are used to quantify the abundance of every annotation so that different samples are compared. The protein copy numbers are added together from different clusters with the same annotation. The protein copy numbers can be normalized by the total number of small protein copies in the data set. The normalized protein copy number  for a certain annotation A is calculated with the following formula, where The metaBP is applied on various metagenomic data sets, including sixteen mice gut samples , one hump-value correction, none of the EC numbers are significant in the high-fat diet mice anymore. So, the EC numbers displayed in the heatmap are simply ranked by its original p-value (less than 5%). It is noticeable that the quantification pattern of these EC numbers from the human gut sample is more like the mice gut samples compared with the other samples. Human saliva samples do not have good yield of small proteins compared to the other samples.The analysis from mice samples shows interesting enzyme activities. In order to compare EC numbers across samples, only those ECs existing in all the samples are used in this analysis. First, the normalized counts of every EC number from mice samples are tested by ANOVA and the top ten important EC functions enriched in the high-fat diet of 12-week-old mice are presented in the heatmap . The comIn this study, 29 of the known short proteins derived from bacteria are searched from the metaBP output and only four of those are discovered in our samples . The UniBesides the search for the known 29 small genes, sixteen mice gut samples are used to systematically compare the annotation outcomes from eggNOG and metaBP-ML for small protein families. As known that not many small proteins have clear enzyme activities, EC number annotation overall has lower yields compared with the taxonomy (organism group) annotation, no matter by eggNOG or metaBP-ML.For the EC number annotation, metaBP-ML can annotate almost five times more proteins than eggNOG . Both meFor taxonomy annotation, metaBP-ML can annotate almost twice of the proteins than eggNOG . In ordeAs mentioned above, the entire small protein database composed of 3 million of short sequences are transformed into a 1,280-dimension vector space. In order to visualize the landscape within two dimensions, principal components analysis is performed, and the first two principal dimensions are shown in a dot plot . The colTo explore several interesting clusters identified in the mice gut samples, we pull out the protein cluster sequences from metaBP results and conduct further analyses. The clusters shown in this section are from the 12-week-old mice with a high-fat diet. One of the known small genes, senS, is widely discovered in the mice gut samples, and its sequence diversity is shown after the sequence alignment . The senAnother interesting cluster is from catalase EC1.11.1.6. The alignment of the sequences shows very few possible mutations are detected in the high-fat diet mice . The strThe metaBP adopts protein level assembly by PLASS, and therefore it is not constraint by the requirement of long contigs or high-quality MAGs from the nucleotide level assembly. As we know, low-abundant rare species may overall constitute a large amount of the sequencing reads in the complex metagenomic samples but may not yield long contigs. When the sequencing depth is low, more than half of the data could be wasted as unassembled sequencing reads. But for small proteins this fragmented sequencing data should already provide sufficient information for both the sequence and function. The metaBP together with metaBP-ML provide users with a complete toolkit to explore small proteins in natural metagenomic samples. For potential extension, the metaBP-ML does allow users to build their application specific models for protein annotation. In addition to metaBP-ML, we still provide eggNOG in the package to annotate proteins alternatively. In terms of the running time, eggNOG is more efficient with their pre-built reference database. The metaBP-ML is relatively taking more time when annotating proteins through vectorization and nearest neighbors. But due to our constructed small protein database, metaBP-ML can be very specific to identify and annotate small proteins. With the integration of both the tools, the metaBP can be used in various kinds of metagenomic data and annotate arbitrary protein classes.However, there are still concerns and limitations from the current version of metaBP. Clusters with singletons at this moment are not used for the downstream analysis in the current metaBP. We assume that only re-occurred sequences within the same cluster can indicate the reliability of small proteins and their mutations. Generally, high quality metagenomic data should be sufficient in the sequence depth. However, in many unexpected cases, metagenomic dataset can be sparse, and the clusters with lower number of protein members can also be informative for small proteins. Computationally, there has not been a perfect strategy to balance the false positives and false negatives without knowing the ground truth in the real data sets. But with the metaBP, we can at least provide a short list for the experimental detection through mass spectrometry and biochemical analysis.The metaBP quantify the annotated features using the normalized protein copy numbers. Due to the protein level assembly, the protein copy numbers are the most straightforward quantification obtained from the data set. Although metaBP can recover more annotations than eggNOG, the quantification may not be sufficient to statistically recover significant features when comparing the samples. One future direction is to improve the resolution of the quantification using the original sequencing reads. The metaBP also displays the protein diversity by homologous protein clustering, but the current metaBP cannot quantify the confidence level of each amino acid mutation. So, the current metaBP is only for the discovery of the potential sequence diversity in a protein family, not for the strict quantification of mutation occurrence.This study proposes a new and comprehensive toolkit, metaBP (and metaBP-ML), to discover and annotate the community specific bacterial (microbe derived) peptides from the metagenomic samples. It is built upon a new idea of direct protein level assembly and one of the current protein clustering tools, as well as machine learning based approaches. The exploration of the small protein landscape and the analyses of peptides annotation demonstrate the efficacy of this work and the value of machine learning.


Medical image segmentation is a technique for detecting boundaries in a 2D or 3D image automatically or semiautomatically. The enormous range of the medical image is a considerable challenge for image segmentation. Magnetic resonance imaging (MRI) scans to aid in the detection and existence of brain tumors. This approach, however, requires exact delineation of the tumor location inside the brain scan. To solve this, an optimization algorithm will be one of the most successful techniques for distinguishing pixels of interest from the background, but its performance is reliant on the starting values of the centroids. The primary goal of this work is to segment tumor areas within brain MRI images. After converting the gray MRI image to a color image, a multiobjective modified ABC algorithm is utilized to separate the tumor from the brain. The intensity determines the RGB color generated in the image. The simulation results are assessed in terms of performance metrics such as accuracy, precision, specificity, recall, F-measure, and the time in seconds required by the system to segment the tumor from the brain. The performance of the proposed algorithm is computed with other algorithms like the single-objective ABC algorithm and multiobjective ABC algorithm. The results prove that the proposed multiobjective modified ABC algorithm is efficient in analyzing and segmenting the tumor from brain images. Image segmentation is a branch of digital image processing that focuses on segmenting images based on their features and qualities. Its fundamental purpose is to simplify the image so that it can be analyzed more easily. Medical image segmentation is a technique for automatically or semiautomatically detecting boundaries in a 2D or 3D image. The enormous range of medical images  is a subIn this study, to detect the tumor of the brain, image segmentation is accomplished using a multiobjective optimization approach. For this, multiobjective-based modified ABC algorithms are utilized. Multiobjective optimization is a subset of multiple-criteria decision-making that is concerned with problems related to mathematical optimization that involves the simultaneous optimization of numerous objective functions. Multiobjective programming, vector optimization, multicriteria optimization, multiattribute optimization, and Pareto optimization are other names for it. Many fields of study, including engineering, have employed multiobjective optimization to achieve optimal decisions when faced with trade-offs between two or more competing objectives. In many real-world engineering applications, designers must choose between competing goals. The image segmentation problem necessitates dividing a single image into segments, or portions, that contain comparable pixels. Segments are areas of an image that depict the same thing. It is generally termed as an exhaustive partitioning of the image given as input into regions, each of which is homogeneous concerning some image quality of interest.In this paper, a multiobjective method is developed to improve intercluster distance and hence reduce misclassification. To segregate the tumor from the brain, the modified ABC algorithm-based multiobjective K-means approach is used for the MRI image. The effectiveness algorithm suggested will be determined by measures of  confusioTo detect the brain tumor by image segmentation using a modified multiobjective Artificial Bee Colony AlgorithmTo analyze the proposed ABC algorithm with other existing algorithms like single-objective ABC and single-objective modified ABCThe main contributions of the research are as follows:Furthermore, the article is structured such that This section covers the related work of several researchers on MRI segmentation approaches.The adaptive k-means clustering segmentation method divides the MRI image into segments from which a meaningful extract of the brain tumor may be extracted. Finally, the segmented image is classified using a Support Vector Machine classifier. This classifier determines the kind of tumor. When the linear kernel function of three SVM classifier kernel functions is compared, it yields a more accurate result . In 2021Authors have proposed an ABC-based method for tackling limited optimization problems that use Deb's principles as a selection mechanism . Their sThe Artificial Bee Colony (ABC) and Fuzzy-C Means (FCM) algorithms are used by Neeraja Menon and Rohit Ramakrishnan  to prese3D Magnetic Resonance Imaging (3D-MRI) segmentation of brain tumors is an essential tool for gathering information needed for diagnosis and disease treatment planning. One of the key obstacles in tumor segmentation is variation in tumor size, structure, and shape, and picking the starting contour plays a vital role in lowering segmentation error and the number of iterations in the level set technique. To solve this problem, Khalil et al.  propose Brain cancer must be discovered sooner so that the treatment procedure may be carried out more accurately and patients' lives can be extended. Machine learning algorithms may be used to aid brain cancer prediction based on the kind of tumor using microarray data. A multiclass classification issue may be used to describe this situation. . As a feAside from numerical function optimization, there are several research investigations on ABC applications in domains including data clustering , 17 and A modified multiobjective ABC algorithm optimization strategy is proposed after evaluating the data and using the suggested algorithms to segment the images to find the centroid of each cluster, and the model is compared to other optimization strategies to show its efficacy.The suggested algorithm's process is as follows.The BTS (Brain Tumor Segmentation) data set, which is made up of images from magnetic resonance imaging (MRI) scans, was used in the research. A total of 50 DICOM files comprising brain images were extracted from the data set and statistically analyzed. For tumor segmentation, a single image is used from the data. With each of the three methods, the same image is utilized for analysis.The initial step in doing analysis is to load the data and prepare it so that it can be analyzed properly. The uploaded image was determined to be in monochrome format; however, grayscale photographs are difficult to detect to identify cancers; thus, we converted the image to color. The application of color labeling allowed for more precise tumor site designation. The loaded image is subjected to image enhancement and image contrast techniques. The goal of image enhancement is to improve the image either subjectively or objectively. Intensity adjustment is an image-enhancing technique that remaps an image's intensity values to a new range. The difference between the image's peak and lowest intensity values is calculated using image contrast.Preprocessing MRI images with a color band to increase their quality and make the tumor zone segmentation process easier.This research employs three segmentation techniques. They include single-objective K-means based on ABC, single-objective K-means based on modified ABC algorithms, and multiobjective K-means based on modified ABC algorithms. A grayscale image is difficult to analyze, as stated above in the preparation section; thus, the image is transformed into a color image for easier analysis. The image is then segmented using the above-stated methods, and a comparative study is carried out to validate their strengths in tumor segmentation.Before pattern identification, feature extraction, and image reduction, segmentation is often employed as a preprocessing step. There are various methods available; however, the K-Means clustering technique is one of the most often utilized. The K-Means clustering methodology is an unsupervised method for distinguishing the region of interest, which is a tumor, from the surrounding area. It divides the input three-dimensional MRI image into two clusters or sections based on the two centroids. The goal is to detect and group the background pixels and tumor pixels.K-means organizes three-dimensional data vectors into predetermined number clusters . The centroid vector of each cluster is started with an arbitrary vector . The mea(i)Initiate the cluster means of the background and tumor pixels at random(ii)(1)Using Euclidean distance, assign each pixel in the MRI image(2)Determine the means of each cluster usingmi = total pixels from cluster i and Ci = C represents the pixel subset that constitutes cluster i up to the point at which a halting requirement is met.where RepeatAs a result, the K-means clustering algorithm may be described astmax) as the stopping condition. This provides for a fair comparison of the performance of the two methods. If there are no significant changes in the mean vectors, the clustering process may be terminated, which is an alternative technique [In this study, K-means and modified ABC algorithms are evaluated using a fixed number of iterations  suggests compact and well-separated clusters.In the case of a single objective-based algorithm, the first half of equation (2) is only used for segmentation; however, it has a propensity to misclassify. This may be avoided by incorporating the second portion, which encourages the increase of intercluster distance, or the distance between centroids, and therefore reduces the number of misclassifications. According to the fitness function's derivation, a small value w1 and w2. The flow chart of the modified ABC algorithm-based image clustering algorithm is depicted in As a consequence, the fitness function is a problem with several objectives. The majority of multiobjective problem-solving approaches have been created for evolutionary algorithms. Lately, multiobjective optimization approaches based on the genetic algorithm have been created. A simple method is used to handle various aims as our purpose is to illustrate the application and usability of an algorithm for image clustering. The subobjectives are given different priorities by suitably initializing the values of i = 1,…, SN and j = 1,…, D. D is the number of optimization parameters or D is the dimension. The parameter bounds are xmin and xmax.Among the most current swarm-based algorithms is the Artificial Bee Colony (ABC) algorithm. ABC replicates a honeybee swarm's clever foraging activity. The honey bee colony model in the ABC algorithm has three types of bees: worker, spectator, and scout . ABC staVi in the vicinity of its present location by the following equation:Each engaged bee creates a new potential solution i is computed by the following equation:Onlooker bees begin to work once employed bees have finished their assignments. An observer bee selects a food source based on its nectar value, which is calculated using the following equation:i is the solution's nectar (fitness) value. It's worth noting that onlooker bees employ , the food source is deemed abandoned. In such a scenario, a scout bee is sent to search for a new food source for replacing the one that has been abandoned. This new location was created with the help of .The proposed algorithm in this paper is modified ABC which was taken from the . The modMATLAB 2020a was used to implement this model. For analysis, a sample of four MRI scan test images was selected, as indicated in Tables 1TP= true positive, TN= true negative, FP= false positive, and FN= false negative.To assess the effectiveness of the algorithms, performance parameters , namely,Initially, a data set of ten samples was used for the experiment, and the performance parameters were examined. The parameters and time required by the system to segment the image have been analyzed. Sensitivity refers to the recall levels of the findings utilized for segmentation. The specificity values of the three techniques are shown in This implementation was carried out using MATLAB 2020a. The BTS (Brain Tumor Segmentation) data set was employed in the study, which comprises scans from magnetic resonance imaging (MRI) scans. The data set had 50 DICOM files with brain scans that were statistically evaluated. A random sample of four images is chosen from the data set and evaluated using the suggested technique. K-means is based on multiobjective modified ABC algorithm and comparison with single-objective modified ABC algorithm and single-objective ABC algorithm. A grayscale image is selected from the data set and converted to a color image. Image enhancement and image contrast methods are used to improve the image and determine the highest and lowest intensity values. Color labeling is applied to the image to distinguish the tumor from the native brain, and the image is then segmented to emphasize the tumor pixels. The suggested method's performance is assessed using performance parameters and the time required by the specific algorithm to segment the tumor from the brain. According to the above tables and graphs, it is depicted that the performance parameters of the proposed model and the existing algorithms are evaluated. The precision, sensitivity, F-measure, accuracy, specificity, and time in sec are evaluated. 10 sample images are chosen for the analysis, and the proposed model is implemented along with the existing algorithms . The hig