The integrated systems of unmanned surface vehicles(USVs) and remotely operated vehicles(ROVs) have been extensively applied in marine exploration and seabed coverage. However, the simultaneous navigation of USV-ROV s...The integrated systems of unmanned surface vehicles(USVs) and remotely operated vehicles(ROVs) have been extensively applied in marine exploration and seabed coverage. However, the simultaneous navigation of USV-ROV systems is frequently limited by strong disturbances induced by waves or currents. This paper develops a novel rigidflexible coupling multibody dynamic model that incorporates disturbances of variable-length marine cables with geometrically nonlinear motion. A hybrid Lagrangian-Eulerian absolute nodal coordinate formulation(ANCF) element is developed to accurately model subsea cables which undergo significant overall motion, substantial deformation,and mass flow during the deployment of underwater equipment. Furthermore, the governing equations of the coupled USV-umbilical-ROV system are derived, considering wave-induced forces and current disturbances. A numerical solver based on the Newmark-beta method is proposed, along with an adaptive meshing technique near the release point. After validating three experimental cases, the cable disturbances at both the USV and ROV ends—caused by ocean currents, heave motion, and simultaneous navigation—are comprehensively compared and evaluated. Finally,it is demonstrated that a PD controller with disturbance compensation can enhance the simultaneous navigation performance of USV-ROV systems.展开更多
An axially variable-length solid element with eight nodes is proposed by integrating the arbitrary Lagrangian-Eulerian (ALE) formulation and the absolute nodal coordinate formulation (ANCF). In addition to the nodal p...An axially variable-length solid element with eight nodes is proposed by integrating the arbitrary Lagrangian-Eulerian (ALE) formulation and the absolute nodal coordinate formulation (ANCF). In addition to the nodal positions and slopes of eight nodes, two material coordinates in the axial direction are used as the generalized coordinates. As a consequence, the nodes in the ALE-ANCF are not associated with any specific material points and the axial length of the solid element can be varied over time. These two material coordinates give rise to a variable mass matrix and an additional inertial force vector. Computationally efficient formulae of the additional inertial forces and elastic forces, as well as their Jacobians, are also derived. The dynamic equation of a flexible multibody system (FMBS) with variable-length bodies is presented. The maximum and minimum lengths of the boundary elements of an FMBS have to be appropriately defined to ensure accuracy and non-singularity when solving the dynamic equation. Three numerical examples of static and dynamic problems are given to validate the variable-length solid elements of ALE-ANCF and show their capability.展开更多
MPEG-4 High-Efficiency Advanced Audio Coding (HE-AAC) is designed for low bit rate applications, such as audio streaming in mobile communications. The HE-AAC audio codec offers a better coding efficiency since variabl...MPEG-4 High-Efficiency Advanced Audio Coding (HE-AAC) is designed for low bit rate applications, such as audio streaming in mobile communications. The HE-AAC audio codec offers a better coding efficiency since variable-length codes (VLCs) are adopted. However, HE-AAC has originally been designed for storage and error-free transmission conditions. For the transmission over bit error-prone channels, error propagation is a serious problem for the VLCs. Therefore, a robust HE-AAC decoder is desired, especially for mobile communications. In contrast to traditional hard-decision decoding, utilizing bit-wise channel reliability information, softdecision (SD) decoding has been known to offer better audio quality. In HE-AAC, the global gain parameter is coded with fixedlength codes (FLCs), while the scale factors and quantized spectral coefficients are coded with VLCs. In this work, we apply FL/SD decoding to the global gain parameter, VL/SD decoding to the parameters scale factors and quantized spectral coefficients. Especially, in order to apply VL/SD decoding to the quantized spectral coefficients, a new modified trellis representation in VL/SD decoding is proposed. An improved HE-AAC performance is clearly observed, with the support of both instrumental measurements and a subjective listening test.展开更多
Anomaly detection has been an active research topic in the field of network intrusion detection for many years. A novel method is presented for anomaly detection based on system calls into the kernels of Unix or Linux...Anomaly detection has been an active research topic in the field of network intrusion detection for many years. A novel method is presented for anomaly detection based on system calls into the kernels of Unix or Linux systems. The method uses the data mining technique to model the normal behavior of a privileged program and uses a variable-length pattern matching algorithm to perform the comparison of the current behavior and historic normal behavior, which is more suitable for this problem than the fixed-length pattern matching algorithm proposed by Forrest et al. At the detection stage, the particularity of the audit data is taken into account, and two alternative schemes could be used to distinguish between normalities and intrusions. The method gives attention to both computational efficiency and detection accuracy and is especially applicable for on-line detection. The performance of the method is evaluated using the typical testing data set, and the results show that it is significantly better than the anomaly detection method based on hidden Markov models proposed by Yan et al. and the method based on fixed-length patterns proposed by Forrest and Hofmeyr. The novel method has been applied to practical hosted-based intrusion detection systems and achieved high detection performance.展开更多
High-speed real-time digital frequency analysis is one major field of Fast Fourier Transform(FFT)application,such as Synthetic Aperture Radar(SAR)processing and medical imaging.In SAR processing,the image size could b...High-speed real-time digital frequency analysis is one major field of Fast Fourier Transform(FFT)application,such as Synthetic Aperture Radar(SAR)processing and medical imaging.In SAR processing,the image size could be 4 k×4 k in normal and it has become larger over the years.In the view of real-time,extensibility and reusable characteristics,an Field Programmable Gate Array(FPGA)based multi-channel variable-length FFT architecture which adopts radix-2 butterfly algorithm is proposed in this paper.The hardware implementation of FFT is partially reconfigurable architecture.Firstly,the proposed architecture in the paper has flexibility in terms of chip area,speed,resource utilization and power consumption.Secondly,the proposed architecture combines serial and parallel methods in its butterfly computations.Furthermore,on system-level issue,the proposed architecture takes advantage of state processing in serial mode and data processing in parallel mode.In case of sufficient FPGA resources,state processing of serial mode mentioned above is converted to pipeline mode.State processing of pipeline mode achieves high throughput.展开更多
Most of multimedia schemes employ variable-length codes （VLCs） like Huffman code as core components in obtaining high compression rates. However VLC methods are very sensitive to channel noise. The goal of this pape...Most of multimedia schemes employ variable-length codes （VLCs） like Huffman code as core components in obtaining high compression rates. However VLC methods are very sensitive to channel noise. The goal of this paper is to salvage as many data from the damaged packets as possible for higher audiovisual quality. This paper proposes an integrated joint source-channel decoder （I-JSCD） at a symbol-level using three-dimensional （3-D） trellis representation for first-order Markov sources encoded with VLC source code and convolutional channel code. This method combines source code and channel code state-spaces and bit-lengths to construct a two-dimensional （2-D） state-space, and then develops a 3-D trellis and a maximum a-posterior （MAP） algorithm to estimate the source sequence symbol by symbol. Experiment results demonstrate that our method results in significant improvement in decoding performance, it can salvage at least half of （50%） data in any channel error rate, and can provide additional error resilience to VLC stream like image, audio, video stream over high error rate links.展开更多
A new dynamic model of a variable-length rope,which could be used for the transient analysis of a buoy-rope-generator(BRG)wave energy system,was proposed in this paper.The model started from the basic dynamic equation...A new dynamic model of a variable-length rope,which could be used for the transient analysis of a buoy-rope-generator(BRG)wave energy system,was proposed in this paper.The model started from the basic dynamic equations of variable mass system,and took into account the physical properties such as axial force,shear and bending.According to the principle of D'Alembert-Lagrange,the equivalent integral weak formulation was firstly obtained,and through consistent linearization and isoparametric discretization,the finite element model of the variable-length rope was then derived.The Bathe scheme was employed to solve the model numerically,based on its excellent performance in solving nonlinear dynamic problems,and an automatic time step size algorithm was designed according to the number of iterations of the two substeps of Bathe scheme.The procedures of rope mesh regeneration were also put forward,where only one variable-length element was always located at the top end of the rope,and the rest were all fixed-length elements.The proposed variable-length rope model and solution schemes were verified through comparison with the results of a tank experiment.Finally,the transient dynamics of a kind of BRG system was analyzed and discussed.展开更多
A novel Variable-Length Code (VLC), called Alternate VLC (AVLC), is proposed in this letter, which employs two types of VLC to encode source symbols alternately. Its advantage is that it can not only stop the symbol e...A novel Variable-Length Code (VLC), called Alternate VLC (AVLC), is proposed in this letter, which employs two types of VLC to encode source symbols alternately. Its advantage is that it can not only stop the symbol error propagation effect, but also correct symbol insertion errors and avoid symbol deletion er-rors, so the original sequence number of symbols can be kept correctly, which is very important in video com-munication.展开更多
In order to solve the problem that traditional signature-based malware detection systems are inefficacious in detecting new malware,a practical malware detection system is constructed to find out new malware. Applicat...In order to solve the problem that traditional signature-based malware detection systems are inefficacious in detecting new malware,a practical malware detection system is constructed to find out new malware. Application programming interface( API) call sequence is introduced to capture activities of a program in this system. After that,based on variable-length n-gram,API call order can be extracted from API call sequence as the malicious behavior feature of a software. Compared with traditional methods,which use fixed-length n-gram,the solution can find more new malware. The experimental results show that the presented approach improves the accuracy of malware detection.展开更多
Flammable gas leakage in a semi-enclosed scenario can lead to catastrophic consequences,such as vapor cloud explosions.To reduce casualties and environmental damage,predicting the consequences based on the initial con...Flammable gas leakage in a semi-enclosed scenario can lead to catastrophic consequences,such as vapor cloud explosions.To reduce casualties and environmental damage,predicting the consequences based on the initial concentration time series monitored by sensors is of paramount importance.This paper proposes a consequence prediction model based on deep learning using variable-length concentration time series.Incomplete concentration values are padded and then passed through a masking layer,enabling the network to focus exclusively on valid data.The temporal correlations are extracted using a long short-term memory(LSTM)network,and the final prediction results are obtained by passing these features into a feedforward neural network(FNN).Computational fluid dynamics(CFD)software was used to simulate the leakage of hydrogen-mixed natural gas.Experiments were carried out for nine distinct prediction targets,derived from combinations of the mass and centroid coordinates of vapor clouds formed by various gases.These prediction targets were modeled using both fixed-length and variable-length input sequences.The high accuracy of the experimental results validates the effectiveness of the proposed method.展开更多
Reusable and flexible capturing of space debris is highly required in future aerospace technologies.A tendon-actuated flexible robotic arm is therefore proposed for capturing floating targets in this paper.Firstly,an ...Reusable and flexible capturing of space debris is highly required in future aerospace technologies.A tendon-actuated flexible robotic arm is therefore proposed for capturing floating targets in this paper.Firstly,an accurate dynamic model of the flexible robotic arm is established by using the absolute nodal coordinate formulation(ANCF)in the framework of the arbitrary Lagrangian-Eulerian(ALE)description and the natural coordinate formulation(NCF).The contact and self-contact dynamics of the flexible robotic arm when bending and grasping an object are considered via a fast contact detection approach.Then,the dynamic simulations of the flexible robotic arm for capturing floating targets are carried out to study the influence of the position,size,and mass of the target object on the grasping performance.Finally,a principle prototype of the tendon-actuated flexible robotic arm is manufactured to validate the dynamic model.The corresponding grasping experiments for objects of various shapes are also conducted to illustrate the excellent performance of the flexible robotic arm.展开更多
This paper proposes an integrated joint source-channel decoder （I-JSCD） using Max-Log-MAP method for sources encoded with exp-Golomb codes and convolutional codes, and proposes a system applying this method to decod...This paper proposes an integrated joint source-channel decoder （I-JSCD） using Max-Log-MAP method for sources encoded with exp-Golomb codes and convolutional codes, and proposes a system applying this method to decoding the VLC data, e.g. motion vector differences （MVDs）, of H.264 across an AWGN channel. This method combines the source code state-space and the channel code state-space together to construct a joint state-space, develops a 3-D trellis and a maximum a-posterior （MAP） algorithm to estimate the source sequence symbol by symbol, and then uses max-log approximation to simplify the algorithm. Experiments indicate that the proposed system gives significant improvements on peak signal-to-noise ratio （PSNR） （maximum about 15 dB） than a separate scheme. This also leads to a higher visual quality of video stream over a highly noisy channel.展开更多
This paper presents an integrated methodology for the modelling and optimisation of precedence-constrained production sequencing and scheduling for multiple production lines based on Genetic Algorithms （GA）. The pro...This paper presents an integrated methodology for the modelling and optimisation of precedence-constrained production sequencing and scheduling for multiple production lines based on Genetic Algorithms （GA）. The problems in this class are NP-hard combinatorial problems, requiring a triple optimisation at the same time： allocation of resources to each line, production sequencing and production scheduling within each production line. They are ubiquitous to production and manufacturing environments. Due to nature of constraints, the length of solutions for the problem can be variable. To cope with this variability, new strategies for encoding chromosomes, crossover and mutation operations have been developed. Robustness of the proposed GA is demonstrated by a complex and realistic case study.展开更多
基金financially supported in part by the General Program of the National Natural Science Foundation of China (Grant No.12272221)the State Key Laboratory of Ocean Engineering (Shanghai Jiao Tong University)(Grant No. GKZD010087)。
文摘The integrated systems of unmanned surface vehicles(USVs) and remotely operated vehicles(ROVs) have been extensively applied in marine exploration and seabed coverage. However, the simultaneous navigation of USV-ROV systems is frequently limited by strong disturbances induced by waves or currents. This paper develops a novel rigidflexible coupling multibody dynamic model that incorporates disturbances of variable-length marine cables with geometrically nonlinear motion. A hybrid Lagrangian-Eulerian absolute nodal coordinate formulation(ANCF) element is developed to accurately model subsea cables which undergo significant overall motion, substantial deformation,and mass flow during the deployment of underwater equipment. Furthermore, the governing equations of the coupled USV-umbilical-ROV system are derived, considering wave-induced forces and current disturbances. A numerical solver based on the Newmark-beta method is proposed, along with an adaptive meshing technique near the release point. After validating three experimental cases, the cable disturbances at both the USV and ROV ends—caused by ocean currents, heave motion, and simultaneous navigation—are comprehensively compared and evaluated. Finally,it is demonstrated that a PD controller with disturbance compensation can enhance the simultaneous navigation performance of USV-ROV systems.
基金the National Natural Science Foundation of China (Grants 11521062, 11722216)the 111 China Project (Grant B16003)+1 种基金Postgraduate Research and Practice Innovation Program of Jiangsu Province (Grant KYCX17_0226)China Scholarship Council.
文摘An axially variable-length solid element with eight nodes is proposed by integrating the arbitrary Lagrangian-Eulerian (ALE) formulation and the absolute nodal coordinate formulation (ANCF). In addition to the nodal positions and slopes of eight nodes, two material coordinates in the axial direction are used as the generalized coordinates. As a consequence, the nodes in the ALE-ANCF are not associated with any specific material points and the axial length of the solid element can be varied over time. These two material coordinates give rise to a variable mass matrix and an additional inertial force vector. Computationally efficient formulae of the additional inertial forces and elastic forces, as well as their Jacobians, are also derived. The dynamic equation of a flexible multibody system (FMBS) with variable-length bodies is presented. The maximum and minimum lengths of the boundary elements of an FMBS have to be appropriately defined to ensure accuracy and non-singularity when solving the dynamic equation. Three numerical examples of static and dynamic problems are given to validate the variable-length solid elements of ALE-ANCF and show their capability.
文摘MPEG-4 High-Efficiency Advanced Audio Coding (HE-AAC) is designed for low bit rate applications, such as audio streaming in mobile communications. The HE-AAC audio codec offers a better coding efficiency since variable-length codes (VLCs) are adopted. However, HE-AAC has originally been designed for storage and error-free transmission conditions. For the transmission over bit error-prone channels, error propagation is a serious problem for the VLCs. Therefore, a robust HE-AAC decoder is desired, especially for mobile communications. In contrast to traditional hard-decision decoding, utilizing bit-wise channel reliability information, softdecision (SD) decoding has been known to offer better audio quality. In HE-AAC, the global gain parameter is coded with fixedlength codes (FLCs), while the scale factors and quantized spectral coefficients are coded with VLCs. In this work, we apply FL/SD decoding to the global gain parameter, VL/SD decoding to the parameters scale factors and quantized spectral coefficients. Especially, in order to apply VL/SD decoding to the quantized spectral coefficients, a new modified trellis representation in VL/SD decoding is proposed. An improved HE-AAC performance is clearly observed, with the support of both instrumental measurements and a subjective listening test.
基金supported by the National Grand Fundamental Research "973" Program of China (2004CB318109)the National High-Technology Research and Development Plan of China (2006AA01Z452)the National Information Security "242"Program of China (2005C39).
文摘Anomaly detection has been an active research topic in the field of network intrusion detection for many years. A novel method is presented for anomaly detection based on system calls into the kernels of Unix or Linux systems. The method uses the data mining technique to model the normal behavior of a privileged program and uses a variable-length pattern matching algorithm to perform the comparison of the current behavior and historic normal behavior, which is more suitable for this problem than the fixed-length pattern matching algorithm proposed by Forrest et al. At the detection stage, the particularity of the audit data is taken into account, and two alternative schemes could be used to distinguish between normalities and intrusions. The method gives attention to both computational efficiency and detection accuracy and is especially applicable for on-line detection. The performance of the method is evaluated using the typical testing data set, and the results show that it is significantly better than the anomaly detection method based on hidden Markov models proposed by Yan et al. and the method based on fixed-length patterns proposed by Forrest and Hofmeyr. The novel method has been applied to practical hosted-based intrusion detection systems and achieved high detection performance.
基金The work was supported by National Natural Science Foundation of China(61271149)and by Beijing Natural Science Foundation(4144093)
文摘High-speed real-time digital frequency analysis is one major field of Fast Fourier Transform(FFT)application,such as Synthetic Aperture Radar(SAR)processing and medical imaging.In SAR processing,the image size could be 4 k×4 k in normal and it has become larger over the years.In the view of real-time,extensibility and reusable characteristics,an Field Programmable Gate Array(FPGA)based multi-channel variable-length FFT architecture which adopts radix-2 butterfly algorithm is proposed in this paper.The hardware implementation of FFT is partially reconfigurable architecture.Firstly,the proposed architecture in the paper has flexibility in terms of chip area,speed,resource utilization and power consumption.Secondly,the proposed architecture combines serial and parallel methods in its butterfly computations.Furthermore,on system-level issue,the proposed architecture takes advantage of state processing in serial mode and data processing in parallel mode.In case of sufficient FPGA resources,state processing of serial mode mentioned above is converted to pipeline mode.State processing of pipeline mode achieves high throughput.
基金Supported by the Foundation of Ministry of Education of China (211CERS10)
文摘Most of multimedia schemes employ variable-length codes （VLCs） like Huffman code as core components in obtaining high compression rates. However VLC methods are very sensitive to channel noise. The goal of this paper is to salvage as many data from the damaged packets as possible for higher audiovisual quality. This paper proposes an integrated joint source-channel decoder （I-JSCD） at a symbol-level using three-dimensional （3-D） trellis representation for first-order Markov sources encoded with VLC source code and convolutional channel code. This method combines source code and channel code state-spaces and bit-lengths to construct a two-dimensional （2-D） state-space, and then develops a 3-D trellis and a maximum a-posterior （MAP） algorithm to estimate the source sequence symbol by symbol. Experiment results demonstrate that our method results in significant improvement in decoding performance, it can salvage at least half of （50%） data in any channel error rate, and can provide additional error resilience to VLC stream like image, audio, video stream over high error rate links.
基金This work was funded by the National Natural Science Foundation of China(Grant No.51709102)the Natural Science Foundation of Hunan Province(Grant No.2019JJ50166)the Scientific Research Fund of Hunan Provincial Education Department(Grant No.19B184).
文摘A new dynamic model of a variable-length rope,which could be used for the transient analysis of a buoy-rope-generator(BRG)wave energy system,was proposed in this paper.The model started from the basic dynamic equations of variable mass system,and took into account the physical properties such as axial force,shear and bending.According to the principle of D'Alembert-Lagrange,the equivalent integral weak formulation was firstly obtained,and through consistent linearization and isoparametric discretization,the finite element model of the variable-length rope was then derived.The Bathe scheme was employed to solve the model numerically,based on its excellent performance in solving nonlinear dynamic problems,and an automatic time step size algorithm was designed according to the number of iterations of the two substeps of Bathe scheme.The procedures of rope mesh regeneration were also put forward,where only one variable-length element was always located at the top end of the rope,and the rest were all fixed-length elements.The proposed variable-length rope model and solution schemes were verified through comparison with the results of a tank experiment.Finally,the transient dynamics of a kind of BRG system was analyzed and discussed.
文摘A novel Variable-Length Code (VLC), called Alternate VLC (AVLC), is proposed in this letter, which employs two types of VLC to encode source symbols alternately. Its advantage is that it can not only stop the symbol error propagation effect, but also correct symbol insertion errors and avoid symbol deletion er-rors, so the original sequence number of symbols can be kept correctly, which is very important in video com-munication.
基金Supported by the National High Technology Research and Development Programme of China(No.2013AA014702)the Fundamental Research Funds for the Central University(No.2014PTB-00-04)the China Next Generation Internet Project(No.CNGI-12-02-027)
文摘In order to solve the problem that traditional signature-based malware detection systems are inefficacious in detecting new malware,a practical malware detection system is constructed to find out new malware. Application programming interface( API) call sequence is introduced to capture activities of a program in this system. After that,based on variable-length n-gram,API call order can be extracted from API call sequence as the malicious behavior feature of a software. Compared with traditional methods,which use fixed-length n-gram,the solution can find more new malware. The experimental results show that the presented approach improves the accuracy of malware detection.
基金supported by the National Key Research and Development Program of China(2022YFB3305900)National Natural Science Foundation of China(62373153,62173147)+1 种基金the Programme of Introducing Talents of Discipline to Universities(the 111 Project)under Grant B17017Fundamental Research Funds for the Central Universities(222202517006)。
文摘Flammable gas leakage in a semi-enclosed scenario can lead to catastrophic consequences,such as vapor cloud explosions.To reduce casualties and environmental damage,predicting the consequences based on the initial concentration time series monitored by sensors is of paramount importance.This paper proposes a consequence prediction model based on deep learning using variable-length concentration time series.Incomplete concentration values are padded and then passed through a masking layer,enabling the network to focus exclusively on valid data.The temporal correlations are extracted using a long short-term memory(LSTM)network,and the final prediction results are obtained by passing these features into a feedforward neural network(FNN).Computational fluid dynamics(CFD)software was used to simulate the leakage of hydrogen-mixed natural gas.Experiments were carried out for nine distinct prediction targets,derived from combinations of the mass and centroid coordinates of vapor clouds formed by various gases.These prediction targets were modeled using both fixed-length and variable-length input sequences.The high accuracy of the experimental results validates the effectiveness of the proposed method.
基金funded by the"14th Five-Year Plan"Civil Aerospace Pre-research Project of China(Grant No.D010301).
文摘Reusable and flexible capturing of space debris is highly required in future aerospace technologies.A tendon-actuated flexible robotic arm is therefore proposed for capturing floating targets in this paper.Firstly,an accurate dynamic model of the flexible robotic arm is established by using the absolute nodal coordinate formulation(ANCF)in the framework of the arbitrary Lagrangian-Eulerian(ALE)description and the natural coordinate formulation(NCF).The contact and self-contact dynamics of the flexible robotic arm when bending and grasping an object are considered via a fast contact detection approach.Then,the dynamic simulations of the flexible robotic arm for capturing floating targets are carried out to study the influence of the position,size,and mass of the target object on the grasping performance.Finally,a principle prototype of the tendon-actuated flexible robotic arm is manufactured to validate the dynamic model.The corresponding grasping experiments for objects of various shapes are also conducted to illustrate the excellent performance of the flexible robotic arm.
基金Supported by the Foundation of Ministry of Education of China (211CERS10)
文摘This paper proposes an integrated joint source-channel decoder （I-JSCD） using Max-Log-MAP method for sources encoded with exp-Golomb codes and convolutional codes, and proposes a system applying this method to decoding the VLC data, e.g. motion vector differences （MVDs）, of H.264 across an AWGN channel. This method combines the source code state-space and the channel code state-space together to construct a joint state-space, develops a 3-D trellis and a maximum a-posterior （MAP） algorithm to estimate the source sequence symbol by symbol, and then uses max-log approximation to simplify the algorithm. Experiments indicate that the proposed system gives significant improvements on peak signal-to-noise ratio （PSNR） （maximum about 15 dB） than a separate scheme. This also leads to a higher visual quality of video stream over a highly noisy channel.
文摘This paper presents an integrated methodology for the modelling and optimisation of precedence-constrained production sequencing and scheduling for multiple production lines based on Genetic Algorithms （GA）. The problems in this class are NP-hard combinatorial problems, requiring a triple optimisation at the same time： allocation of resources to each line, production sequencing and production scheduling within each production line. They are ubiquitous to production and manufacturing environments. Due to nature of constraints, the length of solutions for the problem can be variable. To cope with this variability, new strategies for encoding chromosomes, crossover and mutation operations have been developed. Robustness of the proposed GA is demonstrated by a complex and realistic case study.
