Number Of Variables Research Articles

Machine Learning System Aware Optimization

ABSTRACT New computer systems have emerged in response to the increasing size and complexity of modern data sets. In order to ensure optimum performance, software approaches have to be closely matched with the basic features of systems. This research demonstrates the impact of system-sensitive machine learning using an optimizer lens, a crucial design and solution factor in the majority of machine learning problems. The exactness and convergence rates are traditionally measured for the optimization method. In contrast, a number of system-related variables are crucial to modern computing systems' overall efficiency. Specifications such as data or parameters for the device and higher-level meanings, such as communication and computer interconnections may be included. We propose CoCoA, an overall learning method that closely reviews and incorporates device parameters into the process and theory. We have shown the impact of CoCoA on two conventional distributed systems, that being the traditional cluster environment and the increasingly (founded) machine learning environment. Our results show that we get orders of magnitude quick, by combining system parameters and optimization techniques, to solve current machine learning difficulties. These empirical findings support the assumption that device parameters give more knowledge about the scientific performance.

A two-layer planning method for location and capacity determination of public electric vehicle charging stations

The planning of public charging stations is crucial for the growth of electric vehicles (EVs). To improve the accuracy of predicting EV charging demand in urban areas, we propose a charging decision-making model based on fuzzy logic. Meanwhile, the influence of private charging piles is considered to further enhance the accuracy of predicting public charging demand. To address the issue of optimization algorithms easily getting stuck in local optima due to the vast quantity of variables involved in the location and capacity planning process, this paper introduces a two-layer planning method. In specific, the upper-level location model optimizes the locations of charging stations, while the lower-layer capacity model determines the number of charging piles within each station, leading to a reduction in the number of variables for each layer. Moreover, through iterative exchange results between the upper-layer location model and lower-layer capacity model, the optimal solution can be attained. The simulation results demonstrate that the proposed method can simultaneously consider the perspectives of both EV drivers and charging station investors, while also enhancing the utilization rates of public charging piles.

Identification of maize seed vigor based on hyperspectral imaging and deep learning

BackgroundSeed vigor identification is critical to guaranteeing the quality and yield of maize. Although seeds with impaired vigor may germinate under normal conditions, planting under unfavorable conditions makes it difficult to produce healthy plants. Therefore, non-destructive and rapid detection of seed vigor using hyperspectral imaging (HSI) technology is crucial for improving crop production efficiency.MethodsHyperspectral images of maize seeds were acquired employing the HSI system, the original spectra were preprocessed using Savitzky–Golay smoothing and multiplicative scatter correction, and the feature wavelengths were extracted using the successive projections algorithm (SPA). Discriminant models were constructed based on support vector machine (SVM), random forest, artificial neural network (ANN), and convolutional neural network (CNN-DC).ResultsThe results showed that SVM, ANN, and CNN-DC could discriminate well between maize seeds with different vigor levels, and their accuracy rate was over 70%. The SPA algorithm showed that the RMSE value achieved a minimum of 0.3406, while the number of variables was 49. The CNN-DC model outperformed the other models, which reached the highest accuracy of 92.06%. This study demonstrates that DL combined with HSI has excellent potential for identifying seed vigor.ConclusionsThis study shows that the proposed method has excellent results for hyperspectral image data processing and can accurately identify maize seed vigor.

The effect of the flipped row strategy on a number of kinematic variables in the Performance art and achievement of some basic skills in volleyball

This research aims at revealing the impact of flipped classroom strategy on a number of kinematic variables in the art of performance and achievement of some basic skills in volleyball; recognizing the differences between pre-tests and post-tests for both experimental and control groups، detecting the differences between both experimental and control groups in post hoc tests of the researched variables. Furthermore، the researchers applied the experimental curriculum in order to adapt it to the nature of the research. The research community consists of (160) students (males and females) from the Faculty of Physical Education، and the research sample reached (40) students of the second stage. The sample was then divided into experimental and control groups، randomly putting 20 students in each group; and the tested sample consists of (12) students due to the lack of commitment of some of them to apply the curriculum and the absence of many others. The two researchers then conducted the processes of homogenization and parity of the two groups، all of which show a value greater than 0.05. In addition، the sample ratio reached15%، and the two researchers in this study arrived at the conclusion that there was a difference in measuring skillful performance between accurate measurements (tests) and the measurement of art of performance by the residents. Moreover، the strategy of flipped classroom has the effect of improving some of the kinematic variables (working angles) of some of the basic skills in volleyball. Besides، there are kinematic variables of the human body that have much to do with the stage of learning skills (handling، receiving transmissions)، compared to variables that have little to do with the learning process when emphasized by the instructor.

The Impact of Right to Health Under Legal Public Health Care System in India

An individual's right to health is fundamental to a decent life, hence it is important to examine the several aspects that support this right from different perspectives. Furthermore, since modern health care includes a larger social component in addition to an individualistic demand, this right must be examined in the context of the individual's personal and social life. Discrimination against members of society's most vulnerable groups women, children, the economically disadvantaged, the elderly, individuals with disabilities, including those who are mentally retarded means that people's right to health is violated. Additionally, this right is threatened by a number of other variables, including harmful working conditions and settings, natural disasters and wars, food and nutrition, housing and living situations, and forced population displacement. Therefore, in order to achieve the aim of "Health for All," this work advocated a right to health by assessing the impact of these several previously mentioned elements.

Effects of soil heating changes on soil hydraulic properties in Central Chile

Wildfires are natural phenomena for most ecosystems on Earth. Many soil properties are impacted by fire, including soil hydraulic properties. We used a laboratory experiment to replicate the temperatures reached by a natural wildfire and documented the effects on soil hydraulic properties. This study hypothesizes that the impact of heating on soil hydrological properties can be explained by the interaction of a number of variables especially organic matter content (OM), cation exchange capacity (CEC), texture, pH, and electrical conductivity (EC). The main objective of this study is to explore the interconnections between soil hydraulic, chemical, and physical properties, focusing on understanding how these relationships change across different ecoregions and temperatures. Sixteen soils were collected across 16 sites susceptible to forest fires in the Central Zone of Chile and heated to 100 °C and 300 °C for two hours. These sites were representative of two distinct ecoregions: the Chilean Matorral (CM) and the Valdivian Temperate Forests (VTF). Chemical, physical, and hydraulic soil properties were measured before and after heating. At 100 °C, there were no significant changes in chemical, physical, or hydraulic soil properties. At 300 °C, significant changes were observed in most soil properties in soils from both ecoregions. The OM content and CEC decreased, whereas pH and electrical conductivity increased. In addition, clay content and water aggregate stability (WSA) decreased, while all hydraulic properties increased their values. The aforementioned results demonstrate that infiltration increased after the soil was heated. This can be attributed primarily to decreases in clay content. At the same time, the water repellency (R) index decreased, allowing water to more easily wet the soil particles. Correlations revealed that CEC and clay are the main factors ruling soil hydraulic properties at all temperatures. Clay mineralogy also contributes to the soil hydraulic behavior observed. Nonlinear models were developed to estimate hydraulic properties at 100 °C and 300 °C, using the main soil properties. The models illustrated that the soils of the CM ecoregion, which are characterized by lower OM and influence of clay/CEC ratio, would be less affected by fire compared to the soils of VTF. The water holding capacity would decrease in both ecoregions. However, due to the greater changes in OM and clay in VTF, the impact would be greater than in CM.11Ca2+ = Calcium cations (meq/ 100g); CEC = Cation exchange capacity (meq/ 100g); CM = Chilean Matorral; EC = Electrical conductivity (μS/cm); I = Cumulative infiltration (cm); K = Unsaturated hydraulic conductivity (mm/h); K+ = Potassium cations (meq/ 100g); Ks = Saturated hydraulic conductivity (mm/h); Mg2+ = Magnesium cations (meq/100g); Na+ = Sodium cations (meq/100g); OM = Organic matter (g/100g); R index = Water repellency index; Se = Ethanol sorptivity (cm/s05); Sw = Water sorptivity (cm/s05); VTF = Valdivian Temperate Forest; WSA = Water-stable aggregates (%).

Automated damage assessment of prestressed concrete bridge beam based on sagging

The appropriate bridge maintenance strategy cannot be determined unless the damage is identified, localized, and quantified correctly. Damage assessment can be performed based on model updating, where material properties of a numerical model are modified to represent the damaged state as accurately as possible. However, this approach may become tedious for complex structures such as bridges due to the high number of unknown variables. This study replaces the time-consuming Finite Element (FE) simulations with Artificial Neural Network (ANN) as a surrogate model to reduce the required computational time. The implementation of ANN enables automating the existing manual damage assessment of a prestressed concrete bridge beam. In this paper, the objective is to minimize the difference between the simulated and measured sagging, which is the irreversible downward movement of the bridge due to its weight. The minimization is performed with the Simulated Annealing (SA) algorithm, and the optimization process is repeated with 100 different starting points to ensure robustness. The results indicate that the automated approach performs similarly to the manual approach while being faster and enabling wider exploration in the search space without compromising accuracy. The proposed approach serves as a practical tool for real-world problems by offering an efficient damage assessment.

Can Psychedelic Use Benefit Meditation Practice? Examining Individual, Psychedelic, and Meditation-Related Factors.

Meditation practice and psychedelic use have attracted increasing attention in the public sphere and scientific research. Both methods induce non-ordinary states of consciousness that may have significant therapeutic benefits. Thus, there is growing scientific interest in potential synergies between psychedelic use and meditation practice with some research suggesting that psychedelics may benefit meditation practice. The present study examined individual, psychedelic-related, and meditation-related factors to determine under what conditions meditators perceive psychedelic use as beneficial for their meditation practice. Participants (N = 863) who had reported psychedelic use and a regular meditation practice (at least 3 times per week during the last 12 months) were included in the study. To accommodate a large number of variables, machine learning (i.e., elastic net, random forest) was used to analyze the data. Most participants (n = 634, 73.5%) found psychedelic use to have a positive influence on their quality of meditation. Twenty-eight variables showed significant zero-order associations with perceived benefits even following a correction. Elastic net had the best performance (R2 = .266) and was used to identify the most important features. Across 53 variables, the model found that greater use of psychedelics, intention setting during psychedelic use, agreeableness, and exposure to N,N-Dimethyltryptamine (N,N-DMT) were most likely to be associated with the perception that psychedelics benefit meditation practice. The results were consistent across several different approaches used to identify the most important variables (i.e., Shapley values, feature ablation). Results suggest that most meditators found psychedelic use to have a positive influence on their meditation practice, with: 1) regularity of psychedelic use, 2) the setting of intentions for psychedelic use, 3) having an agreeable personality, and 4) reported use of N,N-DMT being the most likely predictors of perceiving psychedelic use as beneficial. Longitudinal designs and randomized trials manipulating psychedelic use are needed to establish causality.

Implementation of the World Health Organization Minimum Dataset for Emergency Medical Teams to Create Disaster Profiles for the Indonesian SATUSEHAT Platform Using Fast Healthcare Interoperability Resources: Development and Validation Study.

The National Disaster Management Agency (Badan Nasional Penanggulangan Bencana) handles disaster management in Indonesia as a health cluster by collecting, storing, and reporting information on the state of survivors and their health from various sources during disasters. Data were collected on paper and transferred to Microsoft Excel spreadsheets. These activities are challenging because there are no standards for data collection. The World Health Organization (WHO) introduced a standard for health data collection during disasters for emergency medical teams (EMTs) in the form of a minimum dataset (MDS). Meanwhile, the Ministry of Health of Indonesia launched the SATUSEHAT platform to integrate all electronic medical records in Indonesia based on Fast Healthcare Interoperability Resources (FHIR). This study aims to implement the WHO EMT MDS to create a disaster profile for the SATUSEHAT platform using FHIR. We extracted variables from 2 EMT MDS medical records-the WHO and Association of Southeast Asian Nations (ASEAN) versions-and the daily reporting form. We then performed a mapping process to match these variables with the FHIR resources and analyzed the gaps between the variables and base resources. Next, we conducted profiling to see if there were any changes in the selected resources and created extensions to fill the gap using the Forge application. Subsequently, the profile was implemented using an open-source FHIR server. The total numbers of variables extracted from the WHO EMT MDS, ASEAN EMT MDS, and daily reporting forms were 30, 32, and 46, with the percentage of variables matching FHIR resources being 100% (30/30), 97% (31/32), and 85% (39/46), respectively. From the 40 resources available in the FHIR ID core, we used 10, 14, and 9 for the WHO EMT MDS, ASEAN EMT MDS, and daily reporting form, respectively. Based on the gap analysis, we found 4 variables in the daily reporting form that were not covered by the resources. Thus, we created extensions to address this gap. We successfully created a disaster profile that can be used as a disaster case for the SATUSEHAT platform. This profile may standardize health data collection during disasters.

A Robust High-Dimensional Test for Two-Sample Comparisons

The Hotelling T2 statistic is used to compare the mean vectors of two independent multivariate Gaussian distributions. Nevertheless, this statistic is highly sensitive to outliers and is not suitable for high-dimensional datasets where the number of variables exceeds the sample size. This study introduces a robust permutation test based on the minimum regularized covariance determinant (MRCD) estimator to address these limitations of the two-sample Hotelling T2 statistic. Simulation studies were performed to evaluate the proposed test’s empirical size, power, and robustness. Additionally, the test was applied to both uncontaminated and contaminated Alzheimer’s Disease datasets. The findings from the simulations and real data examples provide clues that the proposed test can be effectively used with high-dimensional data without being impacted by outliers. Finally, an R function within the “MVTests” package was developed to implement the proposed test statistic on real-world data.

Optimizing Rule Weights to Improve FRBS Clustering in Wireless Sensor Networks.

Wireless sensor networks (WSNs) are usually composed of tens or hundreds of nodes powered by batteries that need efficient resource management to achieve the WSN's goals. One of the techniques used to manage WSN resources is clustering, where nodes are grouped into clusters around a cluster head (CH), which must be chosen carefully. In this article, a new centralized clustering algorithm is presented based on a Type-1 fuzzy logic controller that infers the probability of each node becoming a CH. The main novelty presented is that the fuzzy logic controller employs three different knowledge bases (KBs) during the lifetime of the WSN. The first KB is used from the beginning to the instant when the first node depletes its battery, the second KB is then applied from that moment to the instant when half of the nodes are dead, and the last KB is loaded from that point until the last node runs out of power. These three KBs are obtained from the original KB designed by the authors after an optimization process. It is based on a particle swarm optimization algorithm that maximizes the lifetime of the WSN in the three periods by adjusting each rule in the KBs through the assignment of a weight value ranging from 0 to 1. This optimization process is used to obtain better results in complex systems where the number of variables or rules could make them unaffordable. The results of the presented optimized approach significantly improved upon those from other authors with similar methods. Finally, the paper presents an analysis of why some rule weights change more than others, in order to design more suitable controllers in the future.

CMA-ES-based topology optimization accelerated by spectral level-set-boundary modeling

Topology optimization commonly encounters several challenges, such as ill-posedness, grayscale issues, interdependencies among design variables, multimodality, and the curse of dimensionality. Furthermore, addressing the latter two concurrently presents considerable difficulty. In this study, we introduce a framework aimed at mitigating all the above obstacles simultaneously. The objective is to achieve optimal configurations in a notably reduced timeframe eliminating the need for the initial trial-and-error iterations. The topology optimization approach we propose is implemented via precise structural boundary modeling utilizing a body-fitted mesh generated using a Fourier series expanded level-set method. This methodology expedites the exploration of optimal solutions. We employ the covariance matrix adaptation-evolution strategy to address multimodality, thereby enhancing the optimization process. The implementation of the Fourier-series-expanded level-set method reduces the number of design variables while maintaining accuracy in finite-element analyses by replacing design variables from discretized level-set functions with the coefficients of the Fourier series expansion. To facilitate the exploration of optimal solutions, a method is also introduced for handling box constraints through an adaptive penalty function. To demonstrate the effectiveness of the proposed scheme, we address three distinct problems: mean compliance minimization, heat flux manipulation, and the control of electromagnetic wave scattering. Despite each system being governed by different equations, topology optimization method consistently yields notable acceleration in computational efficiency across all scenarios, and remarkably without requiring initial guesses.

When can we identify the students at risk of failure in the national medical licensure examination in Japan using the predictive pass rate?

ContextFailure of students to pass the National Medical Licensure Examination (NMLE) is a major problem for universities and the health system in Japan. To assist students at risk for NMLE failure as early as possible after admission, this study investigated the time points (from the time of admission to graduation) at which predictive pass rate (PPR) can be used to identify students at risk of failing the NMLE.MethodsSeven consecutive cohorts of medical students between 2012 and 2018 (n = 637) at the Gifu University Graduate School of Medicine were investigated. Using 7 variables before admission to medical school and 10 variables after admission, a prediction model to obtain the PPR for the NMLE was developed using logistic regression analysis at five time points, i.e., at admission and the end of the 1st, 2nd, 4th, and 6th grades. All students were divided into high (PPR < 95%) and low (PPR ≥ 95%) risk groups for failing the NMLE at the five time points, respectively, and the movement between the groups during 6 years in school was simulated.ResultsMedical students who passed the NMLE had statistically significant factors at each of the 5 time points, and the number of significant variables increased as their grade in school advanced. In addition, two factors extracted at admission were also selected as significant variables at all other time points. Especially, age at entry had a consistent and significant effect during medical school.ConclusionsRisk analysis based on multiple variables, such as PPR, can inform more effective intervention compared to a single variable, such as performance in the mock exam. A longer prospective study is required to confirm the validity of PPR.

Thermodynamic modelling of gas hydrate dissociation conditions in porous medium in the presence of NaCl/methanol aqueous solution

AbstractDue to the growing significance of the existence of gas hydrates in natural media like the ocean floor/permafrost regions and the extraction of natural gas from hydrate reservoirs using thermodynamic hydrate inhibitors, investigating the dissociation of gas hydrates in porous media in the presence of inhibitors is crucial. This work examines a broad range of laboratory data on the dissociation conditions of gas hydrates in the porous mediums when salt/alcohol aqueous solutions are present. The temperature of gas hydrate dissociation in the presence of pure water is calculated using the van der Waals–Platteeuw solid solution theory. The water activity in the porous medium is then calculated by taking into account a number of variables, including the radius of the porous medium, molar volume, shape factor, wetting angle, and surface tension. The Pitzer and Margules activity coefficient models are used to determine the water activity in the presence of salt and alcohol, respectively. Lastly, the gas hydrate dissociation temperature in a porous medium in the presence of salt and/or alcohol aqueous solution is determined by combining Piereon's model with an enthalpy‐based correlation that was proposed by Azimi et al. The selected package can consistently correlate the gas hydrate dissociation conditions in a porous medium in the presence of alcohol or salt aqueous solution. The average absolute deviation (AAD) of 0.67 K for the whole data bank (90 experimental data points) shows the precision of the model.

Comparative Analysis of Financial Forecasting Techniques in Machine Learning for Netflix Stock Price Prediction

Abstract - In the stock market, predicting the price of stocks is still a hot research issue. One of the most challenging tasks in the field of computation is prediction of the stock market. The prediction depends on a number of variables, including physiological vs. Physical elements, rational vs. irrational investor behavior, investor attitude, market rumors, etc. All these factors work together to make stock values unpredictable and very challenging to predict accurately. Supervised Machine Learning (SML) algorithms is used to predict future value by using past stock price data. ML approaches have the ability to reveal trends and knowledge that hadn't previously noticed, and they can be used to predict that are incredibly accurate. The primary objective of this project is to predict stock prices of Netflix for analyzing profit on day closing. Data was gathered between the years of 2002 and 2022, and separated into two parts: training set and testing set. Only the testing portion is to be used for the final forecast. Four machine learning algorithms such as linear regression, decision tree, MLP, and KNN are used to forecast the close value of the Netflix stock price. This project's output adds to the body of knowledge on predicting stock prices and offers investors some new information for accurate prediction of stock prices.

How dairy food affects prostate cancer - a literature overview

Introduction: Prostate cancer is one of the most common type of tumors. Potential factors influencing this neoplasm are subject of many scientific studies as a scarce number of risk variables have been well-established so far. Purpose of the work: The objective of this review is to collect and interpret recent findings regarding dairy food and its influence on prostate cancer. Materials and method: A systematic research was conducted using the PubMed database. Articles in English published from 2015 to 2024 were selected using keywords: dairy products, dairy, milk, prostate cancer. State of knowledge: There is an overall positive association between total dairy products, milk and prostate cancer risk. Although whole milk is not considered as a risk factor, it has been reported that high-fat milk has a positive association with fatality rate and recurrence. Several studies presented a new potential pathomechanisms of dairy’s influence on prostate tumors. Casein, IGF-1 and exosomes are labeled as mediators between high dairy food intake and prostate cancer occurrence. Summary: As of now, there is not strong enough evidence to limit dairy food intake in the whole population. Further research is needed to explore the relationship between dairy consumption and prostate cancer. Men with diagnosed prostate tumors are suggested to eat food according to the Mediterranean diet as it has been reported that it decreases cancer-specific and overall mortality.

Weighted Variable Optimization-Based Method for Estimating Soil Salinity Using Multi-Source Remote Sensing Data: A Case Study in the Weiku Oasis, Xinjiang, China

Soil salinization is a significant global threat to sustainable agricultural development, with soil salinity serving as a crucial indicator for evaluating soil salinization. Remote sensing technology enables large-scale inversion of soil salinity, facilitating the monitoring and assessment of soil salinization levels, thus supporting the prevention and management of soil salinization. This study employs multi-source remote sensing data, selecting 8 radar polarization combinations, 10 spectral indices, and 3 topographic factors to form a feature variable dataset. By applying a normalized weighted variable optimization method, highly important feature variables are identified. AdaBoost, LightGBM, and CatBoost machine learning methods are then used to develop soil salinity inversion models and evaluate their performance. The results indicate the following: (1) There is generally a strong correlation between radar polarization combinations and vegetation indices, and a very high correlation between various vegetation indices and the salinity index S3. (2) The top five feature variables, in order of importance, are Aspect, VH2, Normalized Difference Moisture Index (NDMI), VH, and Vegetation Moisture Index (VMI). (3) The method of normalized weighted importance scoring effectively screens important variables, reducing the number of input feature variables while enhancing the model’s inversion accuracy. (4) Among the three machine learning models, CatBoost performs best overall in soil salt content (SSC) prediction. Combined with the top five feature variables, CatBoost achieves the highest prediction accuracy (R2 = 0.831, RMSE = 2.653, MAE = 1.034) in the prediction phase. This study provides insights for the further development and application of methods for collaborative inversion of soil salinity using multi-source remote sensing data.

Multi-UAV Path Planning Based on Cooperative Co-Evolutionary Algorithms with Adaptive Decision Variable Selection

When dealing with UAV path planning problems, evolutionary algorithms demonstrate strong flexibility and global search capabilities. However, as the number of UAVs increases, the scale of the path planning problem grows exponentially, leading to a significant rise in computational complexity. The Cooperative Co-Evolutionary Algorithm (CCEA) effectively addresses this issue through its divide-and-conquer strategy. Nonetheless, the CCEA needs to find a balance between computational efficiency and algorithmic performance while also resolving convergence difficulties arising from the increased number of decision variables. Moreover, the complex interrelationships between the decision variables of each UAV add to the challenge of selecting appropriate decision variables. To tackle this problem, we propose a novel collaborative algorithm called CCEA-ADVS. This algorithm reduces the difficulty of the problem by decomposing high-dimensional variables into sub-variables for collaborative optimization. To improve the efficiency of decision variable selection in the collaborative algorithm and to accelerate the convergence speed, an adaptive decision variable selection strategy is introduced. This strategy selects decision variables according to the order of solving single-UAV constraints and multi-UAV constraints, reducing the cost of the optimization objective. Furthermore, to improve computational efficiency, a two-stage evolutionary optimization process from coarse to fine is adopted.Specifically, the Adaptive Differential Evolution with Optional External Archive algorithm (JADE) is first used to optimize the waypoints of the UAVs to generate a basic path, and then, the Dubins algorithm is combined to optimize the trajectory, yielding the final flight path. The experimental results show that in four different scenarios involving 40 UAVs, the CCEA-ADVS algorithm significantly outperforms the Grey Wolf Optimizer (GWO), Particle Swarm Optimization (PSO), Artificial Bee Colony (ABC), and JADE algorithms in terms of path performance, running time, computational efficiency, and convergence speed. In addition, in large-scale experiments involving 500 UAVs, the algorithm also demonstrates good adaptability, stability, and scalability.

Proximity guarantees of a lift-and-project approach for the cardinality-constrained Boolean quadric polytope

We consider a lift-and-project approach for the cardinality-constrained Boolean quadric polytope. Some upper bounds for the distance between the polytope and its linear approximation are derived. Unsurprisingly, the distance converges to 0 when the number of variables increases sufficiently.

Optimal recharge sequencing in multi-AGV systems: A mixed ILP approach

Battery level is a critical issue in AGV transportation systems, as AGVs cannot run out of power while operating. Hence, at some point they will be forced to stop and recharge at any of the charging stations available in the warehouse. The question that immediately arises is where, and when, to recharge in an optimal way. Assuming that an AGV has already been assigned a task sequence consisting of visiting a number of working stations, stops at charging stations should be optimally inserted. Here, we do so by minimizing the total tour time, including recharges. Recently, this problem was cast as a mixed integer nonlinear program that also included linear and nonlinear constraints. We recast this problem into a mixed integer linear program under linear constraints, which allows to find an exact solution. Moreover, we derive a procedure to reduce the number of variables of the problem. We also show that, when a charging station is visited, bringing the level of charge to the maximum allowed is optimal except for the case where the tour can be completed without other stops. Finally, we present a stochastic formulation of the problem to consider the presence of multiple AGVs in the layout, which may affect the time spent by AGVs at charging stations due to queuing and, consequently, the optimal solution. Interestingly, the linear formulation of the problem allows to fully characterize the optimal solution as a function of the expected occupancies of the charging stations.