Human intrusion detection for high-speed railway perimeter under all-weather condition

Purpose – The paper aims to solve the problem of personnel intrusion identification within the limits of highspeed railways. It adopts the fusion method of millimeter wave radar and camera to improve the accuracy ofobject recognition in dark and harsh weather conditions.Design/methodology/approach – This paper adopts the fusion strategy of radar and camera linkage toachieve focus amplification of long-distance targets and solves the problem of low illumination by laser lightfilling of the focus point. In order to improve the recognition effect, this paper adopts the YOLOv8 algorithm formulti-scale target recognition. In addition, for the image distortion caused by bad weather, this paper proposesa linkage and tracking fusion strategy to output the correct alarm results.Findings – Simulated intrusion tests show that the proposed method can effectively detect human intrusionwithin 0–200 m during the day and night in sunny weather and can achieve more than 80% recognitionaccuracy for extreme severe weather conditions.Originality/value – (1) The authors propose a personnel intrusion monitoring scheme based on the fusion ofmillimeter wave radar and camera, achieving all-weather intrusion monitoring;(2) The authors propose a newmulti-level fusion algorithm based on linkage and tracking to achieve intrusion target monitoring underadverse weather conditions;(3) The authors have conducted a large number of innovative simulationexperiments to verify the effectiveness of the method proposed in this article.

YOLO-O2E:A Variant YOLO Model for Anomalous Rail Fastening Detection

Rail fasteners are a crucial component of the railway transportation safety system.These fasteners,distinguished by their high length-to-width ratio,frequently encounter elevated failure rates,necessitating manual inspection and maintenance.Manual inspection not only consumes time but also poses the risk of potential oversights.With the advancement of deep learning technology in rail fasteners,challenges such as the complex background of rail fasteners and the similarity in their states are addressed.We have proposed an efficient and high-precision rail fastener detection algorithm,named YOLO-O2E(you only look once-O2E).Firstly,we propose the EFOV(Enhanced Field of View)structure,aiming to adjust the effective receptive field size of convolutional kernels to enhance insensitivity to small spatial variations.Additionally,The OD_MP(ODConv and MP_2)and EMA(EfficientMulti-Scale Attention)modules mentioned in the algorithm can acquire a wider spectrum of contextual information,enhancing the model’s ability to recognize and locate objectives.Additionally,we collected and prepared the GKA dataset,sourced from real train tracks.Through testing on the GKA dataset and the publicly available NUE-DET dataset,our method outperforms general-purpose object detection algorithms.On the GKA dataset,our model achieved a mAP 0.5 value of 97.6%and a mAP 0.5:0.95 value of 83.9%,demonstrating excellent inference speed.YOLO-O2E is an algorithm for detecting anomalies in railway fasteners that is applicable in practical industrial settings,addressing the industry gap in rail fastener detection.

Kinematic-mapping-model-guided analysis and optimization of 2-PSS&1-RR circular-rail parallel mechanism for fully steerable phased array antennas

This paper presents a systematic methodology for analyzing and optimizing an innovative antenna mount designed for phased array antennas, implemented through a novel 2-PSS&1-RR circular-rail parallel mechanism. Initially, a comparative motion analysis between the 3D model of the mount and its full-scale prototype is conducted to validate effectiveness. Given the inherent complexity, a kinematic mapping model is established between the mount and the crank-slider linkage, providing a guiding framework for subsequent analysis and optimization. Guided by this model, feasible inverse and forward solutions are derived, enabling precise identification of stiffness singularities. The concept of singularity distance is thus introduced to reflect the structural stiffness of the mount. Subsequently, also guided by the mapping model, a heuristic algorithm incorporating two backtracking procedures is developed to reduce the mount's mass. Additionally, a parametric finite-element model is employed to explore the relation between singularity distance and structural stiffness. The results indicate a significant reduction(about 16%) in the antenna mount's mass through the developed algorithm, while highlighting the singularity distance as an effective stiffness indicator for this type of antenna mount.

Understanding the Resilience of Urban Rail Transit:Concepts,Reviews,and Trends

As the scale of urban rail transit(URT)networks expands,the study of URT resilience is essential for safe and efficient operations.This paper presents a comprehensive review of URT resilience and highlights potential trends and directions for future research.First,URT resilience is defined by three primary abilities:absorption,resistance,and recovery,and four properties:robustness,vulnerability,rapidity,and redundancy.Then,the metrics and assessment approaches for URT resilience were summarized.The metrics are divided into three categories:topology-based,characteristic-based,and performance-based,and the assessment methods are divided into four categories:topological,simulation,optimization,and datadriven.Comparisons of various metrics and assessment approaches revealed that the current research trend in URT resilience is increasingly favoring the integration of traditional methods,such as conventional complex network analysis and operations optimization theory,with new techniques like big data and intelligent computing technology,to accurately assess URT resilience.Finally,five potential trends and directions for future research were identified:analyzing resilience based on multisource data,optimizing train diagram in multiple scenarios,accurate response to passenger demand through new technologies,coupling and optimizing passenger and traffic flows,and optimal line design.

An internal ballistic model of electromagnetic railgun based on PFN coupled with multi-physical field and experimental validation

To accelerate the practicality of electromagnetic railguns,it is necessary to use a combination of threedimensional numerical simulation and experiments to study the mechanism of bore damage.In this paper,a three-dimensional numerical model of the augmented railgun with four parallel unconventional rails is introduced to simulate the internal ballistic process and realize the multi-physics field coupling calculation of the rail gun,and a test experiment of a medium-caliber electromagnetic launcher powered by pulse formation network(PFN)is carried out.Various test methods such as spectrometer,fiber grating and high-speed camera are used to test several parameters such as muzzle initial velocity,transient magnetic field strength and stress-strain of rail.Combining the simulation results and experimental data,the damage condition of the contact surface is analyzed.

On the Polygonal Wear Evolution of Heavy-Haul Locomotive Wheels due to Wheel/Rail Flexibility and Its Mitigation Measures

Wheel polygonal wear can immensely worsen wheel/rail interactions and vibration performances of the train and track,and ultimately,lead to the shortening of service life of railway components.At present,wheel/rail medium-or high-frequency frictional interactions are perceived as an essential reason of the high-order polygonal wear of railway wheels,which are potentially resulted by the flexible deformations of the train/track system or other external excitations.In this work,the effect of wheel/rail flexibility on polygonal wear evolution of heavy-haul locomotive wheels is explored with aid of the long-term wheel polygonal wear evolution simulations,in which different flexible modeling of the heavy-haul wheel/rail coupled system is implemented.Further,the mitigation measures for the polygonal wear of heavy-haul locomotive wheels are discussed.The results point out that the evolution of polygonal wear of heavy-haul locomotive wheels can be veritably simulated with consideration of the flexible effect of both wheelset and rails.Execution of mixed-line operation of heavy-haul trains and application of multicut wheel re-profiling can effectively reduce the development of wheel polygonal wear.This research can provide a deep-going understanding of polygonal wear evolution mechanism of heavy-haul locomotive wheels and its mitigation measures.

Physics Guided Deep Learning-Based Model for Short-Term Origin–Destination Demand Prediction in Urban Rail Transit Systems Under Pandemic

Accurate origin–destination(OD)demand prediction is crucial for the efficient operation and management of urban rail transit(URT)systems,particularly during a pandemic.However,this task faces several limitations,including real-time availability,sparsity,and high-dimensionality issues,and the impact of the pandemic.Consequently,this study proposes a unified framework called the physics-guided adaptive graph spatial–temporal attention network(PAG-STAN)for metro OD demand prediction under pandemic conditions.Specifically,PAG-STAN introduces a real-time OD estimation module to estimate real-time complete OD demand matrices.Subsequently,a novel dynamic OD demand matrix compression module is proposed to generate dense real-time OD demand matrices.Thereafter,PAG-STAN leverages various heterogeneous data to learn the evolutionary trend of future OD ridership during the pandemic.Finally,a masked physics-guided loss function(MPG-loss function)incorporates the physical quantity information between the OD demand and inbound flow into the loss function to enhance model interpretability.PAG-STAN demonstrated favorable performance on two real-world metro OD demand datasets under the pandemic and conventional scenarios,highlighting its robustness and sensitivity for metro OD demand prediction.A series of ablation studies were conducted to verify the indispensability of each module in PAG-STAN.

Effect of deformation parameters on the austenite dynamic recrystallization behavior of a eutectoid pearlite rail steel

Understandings of the effect of hot deformation parameters close to the practical production line on grain refinement are crucial for enhancing both the strength and toughness of future rail steels.In this work,the austenite dynamic recrystallization(DRX)behaviors of a eutectoid pearlite rail steel were studied using a thermo-mechanical simulator with hot deformation parameters frequently employed in rail production lines.The single-pass hot deformation results reveal that the prior austenite grain sizes(PAGSs)for samples with different deformation reductions decrease initially with an increase in deformation temperature.However,once the deformation temperature is beyond a certain threshold,the PAGSs start to increase.It can be attributed to the rise in DRX volume fraction and the increase of DRX grain with deformation temperature,respectively.Three-pass hot deformation results show that the accumulated strain generated in the first and second deformation passes can increase the extent of DRX.In the case of complete DRX,PAGS is predominantly determined by the deformation temperature of the final pass.It suggests a strategic approach during industrial production where part of the deformation reduction in low temperature range can be shifted to the medium temperature range to release rolling mill loads.

Research and design of an expert diagnosis system for rail vehicle driven by data mechanism models

Purpose-The aim of this work is to research and design an expert diagnosis system for rail vehicle driven by data mechanism models.Design/methodology/approach-The expert diagnosis system utilizes statistical and deep learning methods to model the real-time status and historical data features of rail vehicle.Based on data mechanism models,it predicts the lifespan of key components,evaluates the health status of the vehicle and achieves intelligent monitoring and diagnosis of rail vehicle.Findings-The actual operation effect of this system shows that it has improved the intelligent level of the rail vehicle monitoring system,which helps operators to monitor the operation of vehicle online,predict potential risks and faults of vehicle and ensure the smooth and safe operation of vehicle.Originality/value-This system improves the efficiency of rail vehicle operation,scheduling and maintenance through intelligent monitoring and diagnosis of rail vehicle.

Design and verification of an improved experimental platform for stray current in urban rail transit

With the rapid development of urban rail transit,there have been an urgent problem of excessive stray current.Because the stray current distribution is random and difficult to verify in the field,we designed an improved stray current experimental platform by replacing the simulated aqueous solution with a real soil environment and by calculating the transition resistance by measuring the soil resistivity,which makes up for the defects in the previous references.Firstly,the mathematical models of rail-drainage net and rail-drainage netground were established,and the analytical expressions of current and voltage of rail,drainage net and other structures were derived.In addition,the simulation model was built,and the mathematical analysis results were compared with the simulation results.Secondly,the accuracy of the improved stray current experimental platform was verified by comparing the measured and simulation results.Finally,based on the experimental results,the influence factors of stray current were analyzed.The relevant conclusions provide experimental data and theoretical reference for the study of stray current in urban rail transit.

Parametric investigation of railway fastenings into the formation and mitigation of short pitch corrugation

Short pitch corrugation has been a problem for railways worldwide over one century.In this paper,a parametric investigation of fastenings is conducted to understand the corrugation formation mechanism and gain insights into corrugation mitigation.A three-dimensional finite element vehicle-track dynamic interaction model is employed,which considers the coupling between the structural dynamics and the contact mechanics,while the damage mechanism is assumed to be differential wear.Various fastening models with different configurations,boundary conditions,and parameters of stiffness and damping are built up and analysed.These models may represent different service stages of fastenings in the field.Besides,the effect of train speeds on corrugation features is studied.The results indicate:(1)Fastening parameters and modelling play an important role in corrugation formation.(2)The fastening longitudinal constraint to the rail is the major factor that determines the corrugation formation.The fastening vertical and lateral constraints influence corrugation features in terms of spatial distribution and wavelength components.(3)The strengthening of fastening constraints in the longitudinal dimension helps to mitigate corrugation.Meanwhile,the inner fastening constraint in the lateral direction is necessary for corrugation alleviation.(4)The increase in fastening longitudinal stiffness and damping can reduce the vibration amplitudes of longitudinal compression modes and thus reduce the track corrugation propensity.The simulation in this work can well explain the field corrugation in terms of the occurrence possibility and major wavelength components.It can also explain the field data with respect to the small variation between the corrugation wavelength and train speed,which is caused by frequency selection and jump between rail longitudinal compression modes.

KL-SG High-Speed Rail-a catalyst for national economic development Sri Viknesh Permalu and Karthigesu Nagarajoo

Purpose-In an increasingly interconnected world,transportation infrastructure has emerged as a critical determinant of economic growth and global competitiveness.High-speed rail(HSR),characterized by its exceptional speed and efficiency,has garnered widespread attention as a transformative mode of transportation that transcends borders and fosters economic development.The Kuala Lumpur-Singapore(KL-SG)HSR project stands as a prominent exemplar of this paradigm,symbolizing the potential of HSR to serve as a catalyst for national economic advancement.Design/methodologylapproach-This paper is prepared to provide an insight into the benefits and advantages of HSR based on proven case studies and references from global HSRs,including China,Spain,France and Japan.Findings-The findings that have been obtained focus on enhanced connectivity and accessibility,attracting foreign direct investment,revitalizing regional economies,urban development and city regeneration,boosting tourism and cultural exchange,human capital development,regionai integration and environmental and sustainability benefits.Originality/value-The KL-SG HSR,linking Kuala Lumpur and Singapore,epitomizes the potential for HSR to be a transformative agent in the realm of economic development.This project encapsulates the aspirations of two dynamic Southeast Asian economies,united in their pursuit of sustainable growth,enhanced connectivity and global competitiveness.By scrutinizing the KLSG High-Speed Rail through the lens of economic benchmarking,a deeper understanding emerges of how such projects can drive progress in areas such as cross-border trade,tourism,urban development and technological innovation.

Current status and prospects of research on safety situation awareness of high speed railway operation environment

Purpose–The safety of high-speed rail operation environments is an important guarantee for the safe operation of high-speed rail.The operating environment of the high-speed rail is complex,and the main factors affecting the safety of high-speed rail operating environment include meteorological disasters,perimeter intrusion and external environmental hazards.The purpose of the paper is to elaborate on the current research status and team research progress on the perception of safety situation in high-speed rail operation environment and to propose directions for further research in the future.Design/methodology/approach–In terms of the mechanism and spatio-temporal evolution law of the main influencing factors on the safety of high-speed rail operation environments,the research status is elaborated,and the latest research progress and achievements of the team are introduced.This paper elaborates on the research status and introduces the latest research progress and achievements of the team in terms of meteorological,perimeter and external environmental situation perception methods for high-speed rail operation.Findings–Based on the technical route of“situational awareness evaluation warning active control,”a technical system for monitoring the safety of high-speed train operation environments has been formed.Relevant theoretical and technical research and application have been carried out around the impact of meteorological disasters,perimeter intrusion and the external environment on high-speed rail safety.These works strongly support the improvement of China’s railway environmental safety guarantee technology.Originality/value–With the operation of CR450 high-speed trains with a speed of 400 kmper hour and the application of high-speed train autonomous driving technology in the future,new and higher requirements have been put forward for the safety of high-speed rail operation environments.The following five aspects of work are urgently needed:(1)Research the single factor disaster mechanism of wind,rain,snow,lightning,etc.for high-speed railways with a speed of 400 kms per hour,and based on this,study the evolution characteristics of multiple safety factors and the correlation between the high-speed driving safety environment,revealing the coupling disastermechanism ofmultiple influencing factors;(2)Research covers multi-source data fusion methods and associated features such as disaster monitoring data,meteorological information,route characteristics and terrain and landforms,studying the spatio-temporal evolution laws of meteorological disasters,perimeter intrusions and external environmental hazards;(3)In terms of meteorological disaster situation awareness,research high-precision prediction methods for meteorological information time series along high-speed rail lines and study the realization of small-scale real-time dynamic and accurate prediction of meteorological disasters along high-speed rail lines;(4)In terms of perimeter intrusion,research amulti-modal fusion perception method for typical scenarios of high-speed rail operation in all time,all weather and all coverage and combine artificial intelligence technology to achieve comprehensive and accurate perception of perimeter security risks along the high-speed rail line and(5)In terms of external environment,based on the existing general network framework for change detection,we will carry out research on change detection and algorithms in the surrounding environment of highspeed rail.

High-speed railway and safety: Insights from a bibliometric approach

High-Speed Rail(HSR)systems represent a significant advancement in modern transportation.They offer rapid,efficient,and environmentally friendly alternatives to traditional rail,air travel and road transportation.Even if highspeed trains appeared approximately in the middle of the previous century,several aspects concerning safety remain.This study aims to comprehensively review the scientific literature related to the safety issues of high-speed railways.A bibliometric analysis was carried out utilizing 2358 publications from the last two decades(2004-2023)to understand better the existing research on HSR and safety.Future trends and thematic areas of research are identified and analyzed.Chinese researchers and universities have led the total number of current publications related to the context of HSR safety.While most of the publications come from Chinese institutions,a significant international collaboration can be identified.The main areas of research on HSR and safety can be classified into four main clusters based on the keywords co-occurrence analysis and are related to risk management,structural dynamics and resilience in railway systems,geotechnical engineering and tunnelling and maintenance technologies.Researchers and policymakers can use the results of this study to better understand the dynamics of scientific research in the field of highspeed railways and safety and make decisions about future directions and funding priorities.

Research on the strain gauge mounting scheme of track wheel force measurement system based on high-speed wheel/rail relationship test rig

Purpose-This paper aims to analyze the stress and strain distribution on the track wheel web surface and study the optimal strain gauge location for force measurement system of the track wheel.Design/methodology/approach-Finite element method was employed to analyze the stress and strain distribution on the track wheel web surface under varying wheel-rail forces.Locations with minimal coupling interference between vertical and lateral forces were identified as suitable for strain gauge installation.Findings-The results show that due to the track wheel web’s unique curved shape and wheel-rail force loading mechanism,both tensile and compressive states exit on the surface of the web.When vertical force is applied,Mises stress and strain are relatively high near the inner radius of 710 mm and the outer radius of 1110mmof the web.Under lateral force,high Mises stress and strain are observed near the radius of 670mmon the inner and outer sides of the web.As the wheel-rail force application point shifts laterally toward the outer side,the Mises stress and strain near the inner radius of 710 mm of the web gradually decrease under vertical force while gradually increasing near the outer radius of 1110 mm of the web.Under lateral force,the Mises stress and strain on the surface of the web remain relatively unchanged regardless of the wheel-rail force application point.Based on the analysis of stress and strain on the surface of the web under different wheel-rail forces,the inner radius of 870 mm is recommended as the optimal mounting location of strain gauges for measuring vertical force,while the inner radius of 1143 mm is suitable for measuring lateral force.Originality/value-The research findings provide valuable insights for determining optimal strain gauge locations and designing an effective track wheel force measurement system.

A critical review of wheel/rail high frequency vibration-induced vibration fatigue of railway bogie in China

Purpose–This review aims to give a critical view of the wheel/rail high frequency vibration-induced vibration fatigue in railway bogie.Design/methodology/approach–Vibration fatigue of railway bogie arising from the wheel/rail high frequency vibration has become the main concern of railway operators.Previous reviews usually focused on the formation mechanism of wheel/rail high frequency vibration.This paper thus gives a critical review of the vibration fatigue of railway bogie owing to the short-pitch irregularities-induced high frequency vibration,including a brief introduction of short-pitch irregularities,associated high frequency vibration in railway bogie,typical vibration fatigue failure cases of railway bogie and methodologies used for the assessment of vibration fatigue and research gaps.Findings–The results showed that the resulting excitation frequencies of short-pitch irregularity vary substantially due to different track types and formation mechanisms.The axle box-mounted components are much more vulnerable to vibration fatigue compared with other components.The wheel polygonal wear and rail corrugation-induced high frequency vibration is the main driving force of fatigue failure,and the fatigue crack usually initiates from the defect of the weld seam.Vibration spectrum for attachments of railway bogie defined in the standard underestimates the vibration level arising from the short-pitch irregularities.The current investigations on vibration fatigue mainly focus on the methods to improve the accuracy of fatigue damage assessment,and a systematical design method for vibration fatigue remains a huge gap to improve the survival probability when the rail vehicle is subjected to vibration fatigue.Originality/value–The research can facilitate the development of a new methodology to improve the fatigue life of railway vehicles when subjected to wheel/rail high frequency vibration.

Comparison study on measurement of rail weld joint between inertial reference method and multi-point chord reference method

Purpose – Straightness measurement of rail weld joint is of essential importance to railway maintenance. Dueto the lack of efficient measurement equipment, there has been limited in-depth research on rail weld joint with a5-m wavelength range, leaving a significant knowledge gap in this field.Design/methodology/approach – In this study, the authors used the well-established inertial referencemethod (IR-method), and the state-of-the-art multi-point chord reference method (MCR-method). Two methodshave been applied in different types of rail straightness measurement trollies, respectively. These instrumentswere tested in a high-speed rail section within a certain region of China. The test results were ultimatelyvalidated through using traditional straightedge and feeler gauge methods as reference data to evaluate the railweld joint straightness within the 5-m wavelength range.Findings – The research reveals that IR-method and MCR-method produce reasonably similar measurementresults for wavelengths below 1 m. However, MCR-method outperforms IR-method in terms of accuracy forwavelengths exceeding 3 m. Furthermore, it was observed that IR-method, while operating at a slower speed,carries the risk of derailing and is incapable of detecting rail weld joints and low joints within the track.Originality/value – The research compare two methods’ measurement effects in a longer wavelength rangeand demonstrate the superiority of MCR-method.

Determining future high speed rail review topics through bibliometric analysis

As High Speed Rail(HSR)has proliferated globally,so has a related research field dedicated to exploring and addressing its unique issues.Yet,studies to understand and classify the HSR research domain are limited.This paper addresses the gap,using bibliometric analysis to identify future research areas and 20 candidate topics for literature review based on keyword analysis through VOSviewer.Article and review papers related to HSR published in the last 20 years(2003-2022)were retrieved from Scopus,and then analyzed to determine the split in knowledge between languages,the collaboration between countries and institutions,highly productive and cited journals,and research topics which have and have not been reviewed.Approximately 30%of the search results were published exclusively in Chinese,highlighting the importance of extending the evaluation to cover both languages.This is a novel aspect of the work,which has enabled the recognition of potential knowledge gaps.It is recommended that future reviews incorporate works in both languages,possibly through international collaboration.Institutions in China and other countries that are strong collaborators have been identified,as well as relevant,highly cited journals.

Research on fault time prediction method for high speed rail BTM unit based on multi method interactive validation

The Balise Transmission Module(BTM)unit of the on-board train control system is a crucial component.Due to its unique installation position and complex environment,this unit has a higher fault rate within the on-board train control system.To conduct fault prediction for the BTM unit based on actual fault data,this study proposes a prediction method combining reliability statistics and machine learning,and achieves the fusion of prediction results from different dimensions through multi-method interactive validation.Firstly,a method for predicting equipment fault time targeting batch equipment is introduced.This method utilizes reliability statistics to construct a model of the remaining faultless operating time distribution considering uncertainty,thereby predicting the remaining faultless operating probability of the BTM unit.Secondly,considering the complexity of the BTM unit’s fault mechanism,the small sample size of fault cases,and the potential presence of multiple fault features in fault text records,an individual-oriented fault prediction method based on Bayesian-optimized Gradient Boosting Regression Tree(Bayes-GBRT)is proposed.This method achieves better prediction results compared to linear regression algorithms and random forest regression algorithms,with an average absolute error of only 0.224 years for predicting the fault time of this type of equipment.Finally,a multi-method interactive validation approach is proposed,enabling the fusion and validation of multi-dimensional results.The results indicate that the predicted fault time and the actual fault time conform to a log-normal distribution,and the parameter estimation results are basically consistent,verifying the accuracy and effectiveness of the prediction results.The above research findings can provide technical support for the maintenance and modification of BTM units,effectively reducing maintenance costs and ensuring the safe operation of high-speed railway,thus having practical engineering value for preventive maintenance.

Optimal Scheduling of Multiple Rail Cranes in Rail Stations with Interference Crane Areas

In this paper,we consider a multi-crane scheduling problem in rail stations because their operations directly influence the throughput of the rail stations.In particular,the job is not only assigned to cranes but also the job sequencing is implemented for each crane to minimize the makespan of cranes.A dual cycle of cranes is used to minimize the number of working cycles of cranes.The rail crane scheduling problems in this study are based on the movement of containers.We consider not only the gantry moves,but also the trolley moves as well as the rehandle cases are also included.A mathematical model of multi-crane scheduling is developed.The traditional and parallel simulated annealing(SA)are adapted to determine the optimal scheduling solutions.Numerical examples are conducted to evaluate the applicability of the proposed algorithms.Verification of the proposed parallel SA is done by comparing it to existing previous works.Results of numerical computation highlighted that the parallel SA algorithm outperformed the SA and gave better solutions than other considered algorithms.