Although supplying extensive design space,the curse of dimensionality restricts the widespread application of largescale topology optimization in practical engineering.Various acceleration techniques have been integra...Although supplying extensive design space,the curse of dimensionality restricts the widespread application of largescale topology optimization in practical engineering.Various acceleration techniques have been integrated with topology optimization,achieving significant attention and progress in large-scale problems.This work aims to investigate how much benefit can be obtained by combining parallel computing and machine learning techniques to enhance the efficiency of large-scale topology optimization algorithms.Accordingly,a parallel problem independent machine learning(PIML)-enhanced topology optimization method is proposed.The PIML model substantially reduces the dimension of the condensed stiffness matrix and its computational cost,and parallel computing reduces the workload per process and enables the application of a parallel multigrid solver.Besides,several techniques,such as matrix-free implementation,direct condensation of uniform coarse elements,and adjusting computational resource limits,have been developed to enhance computational efficiency.The weak scaling efficiency,strong scaling speedup,and maximum achievable efficiency of the proposed method are validated across multiple numerical examples,showing significant improvement in the tractable problem size and solution efficiency compared to traditional topology optimization algorithms.展开更多
To address the critical requirements for collaborative delivery of multiple tasks within each order in personalized mass customization,this paper develops a dynamic parallel machine scheduling model that accounts for ...To address the critical requirements for collaborative delivery of multiple tasks within each order in personalized mass customization,this paper develops a dynamic parallel machine scheduling model that accounts for stochastic machine failures and order priorities,thereby more accurately reflecting the uncertainties and complexities of real-world production environments.A dual-objective optimization framework is adopted to minimize both the makespan(maximum task completion time)and the variance of task completion times,aiming to improve the coordination and reliability of intra-order task delivery.An adaptive weighted reward function is designed to balance overall scheduling efficiency with consistency among tasks during reinforcement learning training.To tackle the challenges posed by partially observable Markov decision processes(POMDP)induced by unexpected machine breakdowns,a Gated Recurrent Unit(GRU)-embedded Proximal Policy Optimization(PPO)intelligent scheduling algorithm is proposed.The algorithm incorporates an Action Masking mechanism to prevent invalid scheduling actions,while the GRU module captures historical state sequences to enhance perception of dynamic production environments.Extensive validation on benchmark datasets,along with comparisons against traditional heuristic algorithms,metaheuristic algorithms,and other deep reinforcement learning methods,demonstrates that the proposed approach achieves robust convergence,high resilience,and strong generalization across both static and dynamic scenarios,significantly improving coordinated delivery performance of order tasks.Overall,the proposed method not only provides an efficient and scalable real-time decision-making solution for Parallel Machine Scheduling Problems(PMSP)but also offers new theoretical and practical insights for optimizing complex production scheduling in intelligent manufacturing systems.展开更多
Parallel machining robot is a new type of robotized equipment for high-efficiency machining structural com-ponents with complex geometries.Terminal rigidity is of great importance index for such type of equipment,whic...Parallel machining robot is a new type of robotized equipment for high-efficiency machining structural com-ponents with complex geometries.Terminal rigidity is of great importance index for such type of equipment,which affects their load capacity and working accuracy.Before a parallel machining robot can be used for heavy-load and high-efficiency machining,its terminal rigidity should be evaluated systematically.The present study is to quantitatively reveal the stiffness properties of a previously invented Z4 redundantly actuated parallel ma-chining robot(RAPMR).For this purpose,two critical issues,i.e.,stiffness modelling and index construction,are clarified to carry out stiffness evaluation of the Z4 RAPMR.Firstly,drawing on the screw theory,a semi-analytic stiffness model of the proposed RAPMR is established at a component level.Secondly,a set of virtual work-based stiffness indices is constructed to evaluate the terminal rigidity of parallel robots.Those indices have a consistent physical unit in describing linear and angular terminal rigidity.With these indices,the local and the global stiffness performance of the Z4 RAPMR are predicted.Thirdly,a laboratory prototype of the proposed RAPMR is fabricated.And the experimental test is performed to verify the correctness of the established stiffness model.The present work is expected to provide fundamental information for further light-weight design and rigidity enhancement.展开更多
As a complicated optimization problem,parallel batch processing machines scheduling problem(PBPMSP)exists in many real-life manufacturing industries such as textiles and semiconductors.Machine eligibility means that a...As a complicated optimization problem,parallel batch processing machines scheduling problem(PBPMSP)exists in many real-life manufacturing industries such as textiles and semiconductors.Machine eligibility means that at least one machine is not eligible for at least one job.PBPMSP and scheduling problems with machine eligibility are frequently considered;however,PBPMSP with machine eligibility is seldom explored.This study investigates PBPMSP with machine eligibility in fabric dyeing and presents a novel shuffled frog-leaping algorithm with competition(CSFLA)to minimize makespan.In CSFLA,the initial population is produced in a heuristic and random way,and the competitive search of memeplexes comprises two phases.Competition between any two memeplexes is done in the first phase,then iteration times are adjusted based on competition,and search strategies are adjusted adaptively based on the evolution quality of memeplexes in the second phase.An adaptive population shuffling is given.Computational experiments are conducted on 100 instances.The computational results showed that the new strategies of CSFLA are effective and that CSFLA has promising advantages in solving the considered PBPMSP.展开更多
Fabric dyeing is a critical production process in the clothing industry and heavily relies on batch processing machines(BPM).In this study,the parallel BPM scheduling problem with machine eligibility in fabric dyeing ...Fabric dyeing is a critical production process in the clothing industry and heavily relies on batch processing machines(BPM).In this study,the parallel BPM scheduling problem with machine eligibility in fabric dyeing is considered,and an adaptive cooperated shuffled frog-leaping algorithm(ACSFLA)is proposed to minimize makespan and total tardiness simultaneously.ACSFLA determines the search times for each memeplex based on its quality,with more searches in high-quality memeplexes.An adaptive cooperated and diversified search mechanism is applied,dynamically adjusting search strategies for each memeplex based on their dominance relationships and quality.During the cooperated search,ACSFLA uses a segmented and dynamic targeted search approach,while in non-cooperated scenarios,the search focuses on local search around superior solutions to improve efficiency.Furthermore,ACSFLA employs adaptive population division and partial population shuffling strategies.Through these strategies,memeplexes with low evolutionary potential are selected for reconstruction in the next generation,while thosewithhighevolutionarypotential are retained to continue their evolution.Toevaluate the performance of ACSFLA,comparative experiments were conducted using ACSFLA,SFLA,ASFLA,MOABC,and NSGA-CC in 90 instances.The computational results reveal that ACSFLA outperforms the other algorithms in 78 of the 90 test cases,highlighting its advantages in solving the parallel BPM scheduling problem with machine eligibility.展开更多
Unifying the models for topology design and kinematic analysis has long been a desire for the research of parallel kinematic machines(PKMs). This requires that analytical description, formulation and operation for bot...Unifying the models for topology design and kinematic analysis has long been a desire for the research of parallel kinematic machines(PKMs). This requires that analytical description, formulation and operation for both finite and instantaneous motions are performed by the same mathematical tool. Based upon finite and instantaneous screw theory, a unified and systematic approach for topology design and kinematic analysis of PKMs is proposed in this paper. Using the derivative mapping between finite and instantaneous screws built in the authors’ previous work, the finite and instantaneous motions of PKMs are analytically described by the simple and non?redundant screws in quasi?vector and vector forms. And topological and parametric models of PKMs are algebraically formulated and related. These related topological and parametric models are ready to do type synthesis and kinematic analysis of PKMs under the unified framework of screw theory. In order to show the validity of the proposed approach, a kind of two?translational and three?rotational(2T3R)5?axis PKMs is taken as example. Numerous new structures of the 2T3R PKMs are synthe?sized as the results of topology design, and their Jacobian matrix is obtained easily for parameter optimization and performance evaluation. Some of the synthesized PKMs have outstanding capabilities in terms of large workspaces and flexible orientations, and have great potential for industrial applications of machining and manufacture. Among them, METROM PKM is a typical example which has attracted a lot of attention from global companies and already been developed as commercial products. The approach is a general and unified approach that can be used in the innovative design of different kinds of PKMs.展开更多
The compliance modeling and rigidity performance evaluation for the lower mobility parallel manipulators are still to be remained as two overwhelming challenges in the stage of conceptual design due to their geometric...The compliance modeling and rigidity performance evaluation for the lower mobility parallel manipulators are still to be remained as two overwhelming challenges in the stage of conceptual design due to their geometric complexities. By using the screw theory, this paper explores the compliance modeling and eigencompliance evaluation of a newly patented 1T2R spindle head whose topological architecture is a 3-RPS parallel mechanism. The kinematic definitions and inverse position analysis are briefly addressed in the first place to provide necessary information for compliance modeling. By considering the 3-RPS parallel kinematic machine(PKM) as a typical compliant parallel device, whose three limb assemblages have bending, extending and torsional deflections, an analytical compliance model for the spindle head is established with screw theory and the analytical stiffness matrix of the platform is formulated. Based on the eigenscrew decomposition, the eigencompliance and corresponding eigenscrews are analyzed and the platform's compliance properties are physically interpreted as the suspension of six screw springs. The distributions of stiffness constants of the six screw springs throughout the workspace are predicted in a quick manner with a piece-by-piece calculation algorithm. The numerical simulation reveals a strong dependency of platform's compliance on its configuration in that they are axially symmetric due to structural features. At the last stage, the effects of some design variables such as structural, configurational and dimensional parameters on system rigidity characteristics are investigated with the purpose of providing useful information for the structural design and performance improvement of the PKM. Compared with previous efforts in compliance analysis of PKMs, the present methodology is more intuitive and universal thus can be easily applied to evaluate the overall rigidity performance of other PKMs with high efficiency.展开更多
As a newly invented parallel kinematic machine(PKM), Exechon has found its potential application in machining and assembling industries due to high rigidity and high dynamics. To guarantee the overall performance, t...As a newly invented parallel kinematic machine(PKM), Exechon has found its potential application in machining and assembling industries due to high rigidity and high dynamics. To guarantee the overall performance, the loading conditions and deflections of the key components must be revealed to provide basic mechanic data for component design. For this purpose, a kinetostatic model is proposed with substructure synthesis technique. The Exechon is divided into a platform subsystem, a fixed base subsystem and three limb subsystems according to its structure. By modeling the limb assemblage as a spatial beam constrained by two sets of lumped virtual springs representing the compliances of revolute joint, universal joint and spherical joint, the equilibrium equations of limb subsystems are derived with finite element method(FEM). The equilibrium equations of the platform are derived with Newton's 2nd law. By introducing deformation compatibility conditions between the platform and limb, the governing equilibrium equations of the system are derived to formulate an analytical expression for system's deflections. The platform's elastic displacements and joint reactions caused by the gravity are investigated to show a strong position-dependency and axis-symmetry due to its kinematic and structure features. The proposed kinetostatic model is a trade-off between the accuracy of FEM and concision of analytical method, thus can predict the kinetostatics throughout the workspace in a quick and succinct manner. The proposed modeling methodology and kinetostatic analysis can be further expanded to other PKMs with necessary modifications, providing useful information for kinematic calibration as well as component strength calculations.展开更多
Production scheduling has a major impact on the productivity of the manufacturing process. Recently, scheduling problems with deteriorating jobs have attracted increasing attentions from researchers. In many practical...Production scheduling has a major impact on the productivity of the manufacturing process. Recently, scheduling problems with deteriorating jobs have attracted increasing attentions from researchers. In many practical situations,it is found that some jobs fail to be processed prior to the pre-specified thresholds,and they often consume extra deteriorating time for successful accomplishment. Their processing times can be characterized by a step-wise function. Such kinds of jobs are called step-deteriorating jobs. In this paper,parallel machine scheduling problem with stepdeteriorating jobs( PMSD) is considered. Due to its intractability,four different mixed integer programming( MIP) models are formulated for solving the problem under consideration. The study aims to investigate the performance of these models and find promising optimization formulation to solve the largest possible problem instances. The proposed four models are solved by commercial software CPLEX. Moreover,the near-optimal solutions can be obtained by black-box local-search solver LocalS olver with the fourth one. The computational results show that the efficiencies of different MIP models depend on the distribution intervals of deteriorating thresholds, and the performance of LocalS olver is clearly better than that of CPLEX in terms of the quality of the solutions and the computational time.展开更多
Parallel kinematic machines have drawn considerable attention and have been widely used in some special fields.However,high precision is still one of the challenges when they are used for advanced machine tools.One of...Parallel kinematic machines have drawn considerable attention and have been widely used in some special fields.However,high precision is still one of the challenges when they are used for advanced machine tools.One of the main reasons is that the kinematic chains of parallel kinematic machines are composed of elongated links that can easily suffer deformations,especially at high speeds and under heavy loads.A 3-RRR parallel kinematic machine is taken as a study object for investigating its accuracy with the consideration of the deformations of its links during the motion process.Based on the dynamic model constructed by the Newton-Euler method,all the inertia loads and constraint forces of the links are computed and their deformations are derived.Then the kinematic errors of the machine are derived with the consideration of the deformations of the links.Through further derivation,the accuracy of the machine is given in a simple explicit expression,which will be helpful to increase the calculating speed.The accuracy of this machine when following a selected circle path is simulated.The influences of magnitude of the maximum acceleration and external loads on the running accuracy of the machine are investigated.The results show that the external loads will deteriorate the accuracy of the machine tremendously when their direction coincides with the direction of the worst stiffness of the machine.The proposed method provides a solution for predicting the running accuracy of the parallel kinematic machines and can also be used in their design optimization as well as selection of suitable running parameters.展开更多
A self-adaptive large neighborhood search method for scheduling n jobs on m non-identical parallel machines with mul- tiple time windows is presented. The problems' another feature lies in oversubscription, namely no...A self-adaptive large neighborhood search method for scheduling n jobs on m non-identical parallel machines with mul- tiple time windows is presented. The problems' another feature lies in oversubscription, namely not all jobs can be scheduled within specified scheduling horizons due to the limited machine capacity. The objective is thus to maximize the overall profits of processed jobs while respecting machine constraints. A first-in- first-out heuristic is applied to find an initial solution, and then a large neighborhood search procedure is employed to relax and re- optimize cumbersome solutions. A machine learning mechanism is also introduced to converge on the most efficient neighborhoods for the problem. Extensive computational results are presented based on data from an application involving the daily observation scheduling of a fleet of earth observing satellites. The method rapidly solves most problem instances to optimal or near optimal and shows a robust performance in sensitive analysis.展开更多
Accurate kinematic calibration is the very foundation for robots'application in industry demanding high precision such as machining.Considering the complex error characteristic and severe ill-posed identification ...Accurate kinematic calibration is the very foundation for robots'application in industry demanding high precision such as machining.Considering the complex error characteristic and severe ill-posed identification issues of a 5-DoF parallel machining robot,this paper proposes an adaptive and weighted identification method to achieve high-precision kinematic calibration while maintaining reliable stability.First,a kinematic error propagation mechanism model considering the non-ideal constraints and the screw self-rotation is formulated by incorporating the intricate structure of multiple chains and a unique driven screw arrangement of the robot.To address the challenge of accurately identifying such a sophisticated error model,a novel adaptive and weighted identification method based on generalized cross validation(GCV)is proposed.Specifically,this approach innovatively introduces Gauss-Markov estimation into the GCV algorithm and utilizes prior physical information to construct both a weighted identification model and a weighted cross-validation function,thus eliminating the inaccuracy caused by significant differences in dimensional magnitudes of pose errors and achieving accurate identification with flexible numerical stability.Finally,the kinematic calibration experiment is conducted.The comparative experimental results demonstrate that the presented approach is effective and has enhanced accuracy performance over typical least squares methods,with maximum position and orientation errors reduced from 2.279 mm to 0.028 mm and from 0.206°to 0.017°,respectively.展开更多
Robustly stable multi-step-ahead model predictive control (MPC) based on parallel support vector machines (SVMs) with linear kernel was proposed. First, an analytical solution of optimal control laws of parallel SVMs ...Robustly stable multi-step-ahead model predictive control (MPC) based on parallel support vector machines (SVMs) with linear kernel was proposed. First, an analytical solution of optimal control laws of parallel SVMs based MPC was derived, and then the necessary and sufficient stability condition for MPC closed loop was given according to SVM model, and finally a method of judging the discrepancy between SVM model and the actual plant was presented, and consequently the constraint sets, which can guarantee that the stability condition is still robust for model/plant mismatch within some given bounds, were obtained by applying small-gain theorem. Simulation experiments show the proposed stability condition and robust constraint sets can provide a convenient way of adjusting controller parameters to ensure a closed-loop with larger stable margin.展开更多
In this paper,we study a model on joint decisions of scheduling and subcontracting, in which jobs(orders) can be either processed by parallel machines at the manufacturer in-house or subcontracted to a subcontractor.T...In this paper,we study a model on joint decisions of scheduling and subcontracting, in which jobs(orders) can be either processed by parallel machines at the manufacturer in-house or subcontracted to a subcontractor.The manufacturer needs to determine which jobs should be produced in-house and which jobs should be subcontracted.Furthermore,it needs to determine a production schedule for jobs to be produced in-house.We discuss five classical scheduling objectives as production costs.For each problem with different objective functions,we give optimality conditions and propose dynamic programming algorithms.展开更多
Returning home is the most important process of a parallel kinematic machine(PKM)with incremental encoders.Currently,most corresponding articles focus on the accuracy of homing process,and there lacks the investigatio...Returning home is the most important process of a parallel kinematic machine(PKM)with incremental encoders.Currently,most corresponding articles focus on the accuracy of homing process,and there lacks the investigation of the operation's safety.For a 4RRR PKM,all servoaxes would be independently driven to their zero positions at the same time based on the traditional homing mode,and that can bring serious interfere of the kinematic chains.This paper systemically investigates this 4RRR PKM's safety of homing process.A homing strategy usually contains three parts which are the home switches'locations,the platform's initial moving space,and each links'homing direction,and all of them can influence the safety of homing operation.For the purpose of evaluating and describing the safety of the homing strategy,some important parameters are introduced as follows:Safely homing ratio(SHR)is used to evaluate the probability of a machine's successfully returning home from an initial moving space;Synchronal rotational angle(SRA)is the four links'largest synchronal rotational angle with given directions from a given pose.Whether a machine can safely return home from a given pose can be judged by comparing the SRA with all four home switches'mounting angles.By meshing the initial moving space and checking the safeties of returning home from all the initial poses on the nodes,the SHR of this initial moving space can be calculate.For the sake of convenience,the platform's initial moving space should be as large as possible,and in this 4RRR PKM,a square zone in the center of the workspace with a giving initial rotation range is selected as the platform's initial moving space.The forward direction is selected as each link's homing direction according to custom,and the platform's initial rotational angle is selected as larger than 0°based on this 4RRR PKM's kinematic characteristics.The platform's initial moving space can be defined only by the side length of the initial moving square.By setting a probable searching step and calculating the SHR of the initial moving square,an optimal procedure of searching for the largest side length of the platform's initial moving square is proposed.The homing strategy proposed is based on a systemic research on the safety of homing process for PKM,and the two new indexes SHR and SRA can clearly describe the safety of homing operation.The homing operation based on this strategy is fast and safe,and the method can also be used in other PKMs with the situation of serious components'interference.展开更多
A new three dimensional simulation method is introduced to study the workspace of a 6 PSS (P denotes a prismatic kinematic pair, S denotes a spherical kinematic pair) parallel machine tool. This algorithm adopts the m...A new three dimensional simulation method is introduced to study the workspace of a 6 PSS (P denotes a prismatic kinematic pair, S denotes a spherical kinematic pair) parallel machine tool. This algorithm adopts the method of numerical analysis to investigate the boundary points in a series of sections which form the surface of the workspace. That is, to study such points that have the largest polar radius on a certain section in a system of polar coordinates according to conditions of constraint. The constraint conditions considered in the article include the maximum and minimum displacements of each dieblock, the maximum and minimum angles of oscillation in each hinge. By converting the constraint inequalities into constraint equations, the largest polar radius corresponding to every constraint condition can be evaluated and the minimum one is used to decide the boundary point. This algorithm greatly simplifies the computational process and can be used to analyze any section of the workspace. It provides a theoretical basis for the structural design of such a machine tool.展开更多
A 3-degree-of-freedom(3-DOF)parallel machine tool based on a tripod mechanism is developed and studied.The kinematics analysis is performed,the workspace is derived,and an analysis on the number of conditions of the J...A 3-degree-of-freedom(3-DOF)parallel machine tool based on a tripod mechanism is developed and studied.The kinematics analysis is performed,the workspace is derived,and an analysis on the number of conditions of the Jacobian matrix and manipulability is carried out.A method for error analysis and manipulability is introduced.Hence,the manipulability analysis of the parallel machine tool is accomplished.展开更多
This paper considers the uniform parallel machine scheduling problem with unequal release dates and delivery times to minimize the maximum completion time.For this NP-hard problem,the largest sum of release date,proce...This paper considers the uniform parallel machine scheduling problem with unequal release dates and delivery times to minimize the maximum completion time.For this NP-hard problem,the largest sum of release date,processing time and delivery time first rule is designed to determine a certain machine for each job,and the largest difference between delivery time and release date first rule is designed to sequence the jobs scheduled on the same machine,and then a novel algorithm for the scheduling problem is built.To evaluate the performance of the proposed algorithm,a lower bound for the problem is proposed.The accuracy of the proposed algorithm is tested based on the data with problem size varying from 200 jobs to 600 jobs.The computational results indicate that the average relative error between the proposed algorithm and the lower bound is only 0.667%,therefore the solutions obtained by the proposed algorithm are very accurate.展开更多
The scheduling efficiency of the tracking and data relay satellite system(TDRSS)is strictly limited by the scheduling degrees of freedom(DoF),including time DoF defined by jobs' flexible time windows and spatial ...The scheduling efficiency of the tracking and data relay satellite system(TDRSS)is strictly limited by the scheduling degrees of freedom(DoF),including time DoF defined by jobs' flexible time windows and spatial DoF brought by multiple servable tracking and data relay satellites(TDRSs).In this paper,ageneralized multiple time windows(GMTW)model is proposed to fully exploit the time and spatial DoF.Then,the improvements of service capability and job-completion probability based on the GMTW are theoretically proved.Further,an asymmetric path-relinking(APR)based heuristic job scheduling framework is presented to maximize the usage of DoF provided by the GMTW.Simulation results show that by using our proposal 11%improvement of average jobcompletion probability can be obtained.Meanwhile,the computing time of the time-to-target can be shorten to 1/9 of the GRASP.展开更多
This paper considers a hybrid two-stage flow-shop scheduling problem with m identical parallel machines on one stage and a batch processor on the other stage. The processing time of job Jj on any of m identical parall...This paper considers a hybrid two-stage flow-shop scheduling problem with m identical parallel machines on one stage and a batch processor on the other stage. The processing time of job Jj on any of m identical parallel machines is aj≡a (j∈N), and the processing time of job Jj is bj(j∈N) on a batch processorM. We take makespan (Cmax) as our minimization objective. In this paper, for the problem of FSMP-BI (m identical parallel machines on the first stage and a batch processor on the second stage), based on the algorithm given by Sung and Choung for the problem of 1 |ri, BI|Cmax under the constraint of the given processing sequence, we develop an optimal dynamic programming Algorithm H1 for it in max {O(nlogn), O(nB)} time. A max {O(nlogn) , O(nB)}time symmetric Algorithm H2 is given then for the problem of BI-FSMP (a batch processor on the first stage and m identical parallel machines on the second stage).展开更多
基金supported by the National Key Research and Development Program of China(Grant No.2023YFB3309104)the National Natural Science Foundation of China(Grant Nos.11821202 and 123721222)+1 种基金the Science Technology Plan of Liaoning Province(Grant No.2023JH2/101600044)the 111 Project of China(Grant No.B14013).
摘要Although supplying extensive design space,the curse of dimensionality restricts the widespread application of largescale topology optimization in practical engineering.Various acceleration techniques have been integrated with topology optimization,achieving significant attention and progress in large-scale problems.This work aims to investigate how much benefit can be obtained by combining parallel computing and machine learning techniques to enhance the efficiency of large-scale topology optimization algorithms.Accordingly,a parallel problem independent machine learning(PIML)-enhanced topology optimization method is proposed.The PIML model substantially reduces the dimension of the condensed stiffness matrix and its computational cost,and parallel computing reduces the workload per process and enables the application of a parallel multigrid solver.Besides,several techniques,such as matrix-free implementation,direct condensation of uniform coarse elements,and adjusting computational resource limits,have been developed to enhance computational efficiency.The weak scaling efficiency,strong scaling speedup,and maximum achievable efficiency of the proposed method are validated across multiple numerical examples,showing significant improvement in the tractable problem size and solution efficiency compared to traditional topology optimization algorithms.
摘要To address the critical requirements for collaborative delivery of multiple tasks within each order in personalized mass customization,this paper develops a dynamic parallel machine scheduling model that accounts for stochastic machine failures and order priorities,thereby more accurately reflecting the uncertainties and complexities of real-world production environments.A dual-objective optimization framework is adopted to minimize both the makespan(maximum task completion time)and the variance of task completion times,aiming to improve the coordination and reliability of intra-order task delivery.An adaptive weighted reward function is designed to balance overall scheduling efficiency with consistency among tasks during reinforcement learning training.To tackle the challenges posed by partially observable Markov decision processes(POMDP)induced by unexpected machine breakdowns,a Gated Recurrent Unit(GRU)-embedded Proximal Policy Optimization(PPO)intelligent scheduling algorithm is proposed.The algorithm incorporates an Action Masking mechanism to prevent invalid scheduling actions,while the GRU module captures historical state sequences to enhance perception of dynamic production environments.Extensive validation on benchmark datasets,along with comparisons against traditional heuristic algorithms,metaheuristic algorithms,and other deep reinforcement learning methods,demonstrates that the proposed approach achieves robust convergence,high resilience,and strong generalization across both static and dynamic scenarios,significantly improving coordinated delivery performance of order tasks.Overall,the proposed method not only provides an efficient and scalable real-time decision-making solution for Parallel Machine Scheduling Problems(PMSP)but also offers new theoretical and practical insights for optimizing complex production scheduling in intelligent manufacturing systems.
基金Supported by National Natural Science Foundation of China(Grant No.52375009)Fujian Provincial Young and Middle-Aged Teacher Education Research Project of China(Grant No.JAT220029).
摘要Parallel machining robot is a new type of robotized equipment for high-efficiency machining structural com-ponents with complex geometries.Terminal rigidity is of great importance index for such type of equipment,which affects their load capacity and working accuracy.Before a parallel machining robot can be used for heavy-load and high-efficiency machining,its terminal rigidity should be evaluated systematically.The present study is to quantitatively reveal the stiffness properties of a previously invented Z4 redundantly actuated parallel ma-chining robot(RAPMR).For this purpose,two critical issues,i.e.,stiffness modelling and index construction,are clarified to carry out stiffness evaluation of the Z4 RAPMR.Firstly,drawing on the screw theory,a semi-analytic stiffness model of the proposed RAPMR is established at a component level.Secondly,a set of virtual work-based stiffness indices is constructed to evaluate the terminal rigidity of parallel robots.Those indices have a consistent physical unit in describing linear and angular terminal rigidity.With these indices,the local and the global stiffness performance of the Z4 RAPMR are predicted.Thirdly,a laboratory prototype of the proposed RAPMR is fabricated.And the experimental test is performed to verify the correctness of the established stiffness model.The present work is expected to provide fundamental information for further light-weight design and rigidity enhancement.
基金supported by the National Natural Science Foundation of China(Grant Number 61573264).
摘要As a complicated optimization problem,parallel batch processing machines scheduling problem(PBPMSP)exists in many real-life manufacturing industries such as textiles and semiconductors.Machine eligibility means that at least one machine is not eligible for at least one job.PBPMSP and scheduling problems with machine eligibility are frequently considered;however,PBPMSP with machine eligibility is seldom explored.This study investigates PBPMSP with machine eligibility in fabric dyeing and presents a novel shuffled frog-leaping algorithm with competition(CSFLA)to minimize makespan.In CSFLA,the initial population is produced in a heuristic and random way,and the competitive search of memeplexes comprises two phases.Competition between any two memeplexes is done in the first phase,then iteration times are adjusted based on competition,and search strategies are adjusted adaptively based on the evolution quality of memeplexes in the second phase.An adaptive population shuffling is given.Computational experiments are conducted on 100 instances.The computational results showed that the new strategies of CSFLA are effective and that CSFLA has promising advantages in solving the considered PBPMSP.
摘要Fabric dyeing is a critical production process in the clothing industry and heavily relies on batch processing machines(BPM).In this study,the parallel BPM scheduling problem with machine eligibility in fabric dyeing is considered,and an adaptive cooperated shuffled frog-leaping algorithm(ACSFLA)is proposed to minimize makespan and total tardiness simultaneously.ACSFLA determines the search times for each memeplex based on its quality,with more searches in high-quality memeplexes.An adaptive cooperated and diversified search mechanism is applied,dynamically adjusting search strategies for each memeplex based on their dominance relationships and quality.During the cooperated search,ACSFLA uses a segmented and dynamic targeted search approach,while in non-cooperated scenarios,the search focuses on local search around superior solutions to improve efficiency.Furthermore,ACSFLA employs adaptive population division and partial population shuffling strategies.Through these strategies,memeplexes with low evolutionary potential are selected for reconstruction in the next generation,while thosewithhighevolutionarypotential are retained to continue their evolution.Toevaluate the performance of ACSFLA,comparative experiments were conducted using ACSFLA,SFLA,ASFLA,MOABC,and NSGA-CC in 90 instances.The computational results reveal that ACSFLA outperforms the other algorithms in 78 of the 90 test cases,highlighting its advantages in solving the parallel BPM scheduling problem with machine eligibility.
基金Supported by National Natural Science Foundation of China(Grant No.51675366)Tianjin Research Program of Application Foundation and Advanced Technology(Grant Nos.16JCYBJC19300,15JCZDJC38900)
摘要Unifying the models for topology design and kinematic analysis has long been a desire for the research of parallel kinematic machines(PKMs). This requires that analytical description, formulation and operation for both finite and instantaneous motions are performed by the same mathematical tool. Based upon finite and instantaneous screw theory, a unified and systematic approach for topology design and kinematic analysis of PKMs is proposed in this paper. Using the derivative mapping between finite and instantaneous screws built in the authors’ previous work, the finite and instantaneous motions of PKMs are analytically described by the simple and non?redundant screws in quasi?vector and vector forms. And topological and parametric models of PKMs are algebraically formulated and related. These related topological and parametric models are ready to do type synthesis and kinematic analysis of PKMs under the unified framework of screw theory. In order to show the validity of the proposed approach, a kind of two?translational and three?rotational(2T3R)5?axis PKMs is taken as example. Numerous new structures of the 2T3R PKMs are synthe?sized as the results of topology design, and their Jacobian matrix is obtained easily for parameter optimization and performance evaluation. Some of the synthesized PKMs have outstanding capabilities in terms of large workspaces and flexible orientations, and have great potential for industrial applications of machining and manufacture. Among them, METROM PKM is a typical example which has attracted a lot of attention from global companies and already been developed as commercial products. The approach is a general and unified approach that can be used in the innovative design of different kinds of PKMs.
基金Supported by National Natural Science Foundation of China(Grant No.51375013)Anhui Provincial Natural Science Foundation of China(Grant No.1208085ME64)Open Research Fund of Key Laboratory of High Performance Complex Manufacturing,Central South University(Grant No.Kfkt2013-12)
摘要The compliance modeling and rigidity performance evaluation for the lower mobility parallel manipulators are still to be remained as two overwhelming challenges in the stage of conceptual design due to their geometric complexities. By using the screw theory, this paper explores the compliance modeling and eigencompliance evaluation of a newly patented 1T2R spindle head whose topological architecture is a 3-RPS parallel mechanism. The kinematic definitions and inverse position analysis are briefly addressed in the first place to provide necessary information for compliance modeling. By considering the 3-RPS parallel kinematic machine(PKM) as a typical compliant parallel device, whose three limb assemblages have bending, extending and torsional deflections, an analytical compliance model for the spindle head is established with screw theory and the analytical stiffness matrix of the platform is formulated. Based on the eigenscrew decomposition, the eigencompliance and corresponding eigenscrews are analyzed and the platform's compliance properties are physically interpreted as the suspension of six screw springs. The distributions of stiffness constants of the six screw springs throughout the workspace are predicted in a quick manner with a piece-by-piece calculation algorithm. The numerical simulation reveals a strong dependency of platform's compliance on its configuration in that they are axially symmetric due to structural features. At the last stage, the effects of some design variables such as structural, configurational and dimensional parameters on system rigidity characteristics are investigated with the purpose of providing useful information for the structural design and performance improvement of the PKM. Compared with previous efforts in compliance analysis of PKMs, the present methodology is more intuitive and universal thus can be easily applied to evaluate the overall rigidity performance of other PKMs with high efficiency.
基金Supported by State Key Laboratory for Manufacturing Systems Engineering,Xi’an Jiaotong University(Grant No.sklms2015004)Open Research Fund of Key Laboratory of High Performance Complex Manufacturing,Central South University(Grant No.Kfkt2013-12)+2 种基金Open Fund of Shanghai Key Laboratory of Digital Manufacture for Thin-walled Structures(Grant No.2014001)Innovation Research Fund for Postgraduates of Anhui University of Technology(Grant No.2014054)Engineering and Physical Science Research Council in the United Kingdom(Grant No.EP/K004964/1)
摘要As a newly invented parallel kinematic machine(PKM), Exechon has found its potential application in machining and assembling industries due to high rigidity and high dynamics. To guarantee the overall performance, the loading conditions and deflections of the key components must be revealed to provide basic mechanic data for component design. For this purpose, a kinetostatic model is proposed with substructure synthesis technique. The Exechon is divided into a platform subsystem, a fixed base subsystem and three limb subsystems according to its structure. By modeling the limb assemblage as a spatial beam constrained by two sets of lumped virtual springs representing the compliances of revolute joint, universal joint and spherical joint, the equilibrium equations of limb subsystems are derived with finite element method(FEM). The equilibrium equations of the platform are derived with Newton's 2nd law. By introducing deformation compatibility conditions between the platform and limb, the governing equilibrium equations of the system are derived to formulate an analytical expression for system's deflections. The platform's elastic displacements and joint reactions caused by the gravity are investigated to show a strong position-dependency and axis-symmetry due to its kinematic and structure features. The proposed kinetostatic model is a trade-off between the accuracy of FEM and concision of analytical method, thus can predict the kinetostatics throughout the workspace in a quick and succinct manner. The proposed modeling methodology and kinetostatic analysis can be further expanded to other PKMs with necessary modifications, providing useful information for kinematic calibration as well as component strength calculations.
基金National Natural Science Foundation of China(No.51405403)the Fundamental Research Funds for the Central Universities,China(No.2682014BR019)the Scientific Research Program of Education Bureau of Sichuan Province,China(No.12ZB322)
摘要Production scheduling has a major impact on the productivity of the manufacturing process. Recently, scheduling problems with deteriorating jobs have attracted increasing attentions from researchers. In many practical situations,it is found that some jobs fail to be processed prior to the pre-specified thresholds,and they often consume extra deteriorating time for successful accomplishment. Their processing times can be characterized by a step-wise function. Such kinds of jobs are called step-deteriorating jobs. In this paper,parallel machine scheduling problem with stepdeteriorating jobs( PMSD) is considered. Due to its intractability,four different mixed integer programming( MIP) models are formulated for solving the problem under consideration. The study aims to investigate the performance of these models and find promising optimization formulation to solve the largest possible problem instances. The proposed four models are solved by commercial software CPLEX. Moreover,the near-optimal solutions can be obtained by black-box local-search solver LocalS olver with the fourth one. The computational results show that the efficiencies of different MIP models depend on the distribution intervals of deteriorating thresholds, and the performance of LocalS olver is clearly better than that of CPLEX in terms of the quality of the solutions and the computational time.
基金Supported by National Natural Science Foundation of China(Grant No.51272560)National Basic Research Program of China(973 Program,Grant No.2011CB302404)National Science Foundation for Distinguished Young Scholars of China(Grant No.51225503)
摘要Parallel kinematic machines have drawn considerable attention and have been widely used in some special fields.However,high precision is still one of the challenges when they are used for advanced machine tools.One of the main reasons is that the kinematic chains of parallel kinematic machines are composed of elongated links that can easily suffer deformations,especially at high speeds and under heavy loads.A 3-RRR parallel kinematic machine is taken as a study object for investigating its accuracy with the consideration of the deformations of its links during the motion process.Based on the dynamic model constructed by the Newton-Euler method,all the inertia loads and constraint forces of the links are computed and their deformations are derived.Then the kinematic errors of the machine are derived with the consideration of the deformations of the links.Through further derivation,the accuracy of the machine is given in a simple explicit expression,which will be helpful to increase the calculating speed.The accuracy of this machine when following a selected circle path is simulated.The influences of magnitude of the maximum acceleration and external loads on the running accuracy of the machine are investigated.The results show that the external loads will deteriorate the accuracy of the machine tremendously when their direction coincides with the direction of the worst stiffness of the machine.The proposed method provides a solution for predicting the running accuracy of the parallel kinematic machines and can also be used in their design optimization as well as selection of suitable running parameters.
基金supported by the National Natural Science Foundation of China (7060103570801062)
摘要A self-adaptive large neighborhood search method for scheduling n jobs on m non-identical parallel machines with mul- tiple time windows is presented. The problems' another feature lies in oversubscription, namely not all jobs can be scheduled within specified scheduling horizons due to the limited machine capacity. The objective is thus to maximize the overall profits of processed jobs while respecting machine constraints. A first-in- first-out heuristic is applied to find an initial solution, and then a large neighborhood search procedure is employed to relax and re- optimize cumbersome solutions. A machine learning mechanism is also introduced to converge on the most efficient neighborhoods for the problem. Extensive computational results are presented based on data from an application involving the daily observation scheduling of a fleet of earth observing satellites. The method rapidly solves most problem instances to optimal or near optimal and shows a robust performance in sensitive analysis.
基金Supported by National Key R&D Program of China(Grant No.2022YFB3404101)National Natural Science Foundation of China(Grant Nos.52375018,92148301)。
摘要Accurate kinematic calibration is the very foundation for robots'application in industry demanding high precision such as machining.Considering the complex error characteristic and severe ill-posed identification issues of a 5-DoF parallel machining robot,this paper proposes an adaptive and weighted identification method to achieve high-precision kinematic calibration while maintaining reliable stability.First,a kinematic error propagation mechanism model considering the non-ideal constraints and the screw self-rotation is formulated by incorporating the intricate structure of multiple chains and a unique driven screw arrangement of the robot.To address the challenge of accurately identifying such a sophisticated error model,a novel adaptive and weighted identification method based on generalized cross validation(GCV)is proposed.Specifically,this approach innovatively introduces Gauss-Markov estimation into the GCV algorithm and utilizes prior physical information to construct both a weighted identification model and a weighted cross-validation function,thus eliminating the inaccuracy caused by significant differences in dimensional magnitudes of pose errors and achieving accurate identification with flexible numerical stability.Finally,the kinematic calibration experiment is conducted.The comparative experimental results demonstrate that the presented approach is effective and has enhanced accuracy performance over typical least squares methods,with maximum position and orientation errors reduced from 2.279 mm to 0.028 mm and from 0.206°to 0.017°,respectively.
基金Project(2002CB312200) supported by the National Key Fundamental Research and Development Program of China project(60574019) supported by the National Natural Science Foundation of China
摘要Robustly stable multi-step-ahead model predictive control (MPC) based on parallel support vector machines (SVMs) with linear kernel was proposed. First, an analytical solution of optimal control laws of parallel SVMs based MPC was derived, and then the necessary and sufficient stability condition for MPC closed loop was given according to SVM model, and finally a method of judging the discrepancy between SVM model and the actual plant was presented, and consequently the constraint sets, which can guarantee that the stability condition is still robust for model/plant mismatch within some given bounds, were obtained by applying small-gain theorem. Simulation experiments show the proposed stability condition and robust constraint sets can provide a convenient way of adjusting controller parameters to ensure a closed-loop with larger stable margin.
基金Supported by the National Natural Science Foundation of China(70731160015)Supported the National Natural Science Foundation of Jiangsu Province(yw06037)
摘要In this paper,we study a model on joint decisions of scheduling and subcontracting, in which jobs(orders) can be either processed by parallel machines at the manufacturer in-house or subcontracted to a subcontractor.The manufacturer needs to determine which jobs should be produced in-house and which jobs should be subcontracted.Furthermore,it needs to determine a production schedule for jobs to be produced in-house.We discuss five classical scheduling objectives as production costs.For each problem with different objective functions,we give optimality conditions and propose dynamic programming algorithms.
基金supported by National Natural Science Foundation of China(Grant No.50775125,and No.50775117)National Hi-tech Research and Development Program of China(863 Program,Grant No.2007AA041901)National Basic Research Program of China(973 Program,Grant No.2004CB318007)
摘要Returning home is the most important process of a parallel kinematic machine(PKM)with incremental encoders.Currently,most corresponding articles focus on the accuracy of homing process,and there lacks the investigation of the operation's safety.For a 4RRR PKM,all servoaxes would be independently driven to their zero positions at the same time based on the traditional homing mode,and that can bring serious interfere of the kinematic chains.This paper systemically investigates this 4RRR PKM's safety of homing process.A homing strategy usually contains three parts which are the home switches'locations,the platform's initial moving space,and each links'homing direction,and all of them can influence the safety of homing operation.For the purpose of evaluating and describing the safety of the homing strategy,some important parameters are introduced as follows:Safely homing ratio(SHR)is used to evaluate the probability of a machine's successfully returning home from an initial moving space;Synchronal rotational angle(SRA)is the four links'largest synchronal rotational angle with given directions from a given pose.Whether a machine can safely return home from a given pose can be judged by comparing the SRA with all four home switches'mounting angles.By meshing the initial moving space and checking the safeties of returning home from all the initial poses on the nodes,the SHR of this initial moving space can be calculate.For the sake of convenience,the platform's initial moving space should be as large as possible,and in this 4RRR PKM,a square zone in the center of the workspace with a giving initial rotation range is selected as the platform's initial moving space.The forward direction is selected as each link's homing direction according to custom,and the platform's initial rotational angle is selected as larger than 0°based on this 4RRR PKM's kinematic characteristics.The platform's initial moving space can be defined only by the side length of the initial moving square.By setting a probable searching step and calculating the SHR of the initial moving square,an optimal procedure of searching for the largest side length of the platform's initial moving square is proposed.The homing strategy proposed is based on a systemic research on the safety of homing process for PKM,and the two new indexes SHR and SRA can clearly describe the safety of homing operation.The homing operation based on this strategy is fast and safe,and the method can also be used in other PKMs with the situation of serious components'interference.
基金Ministerial Level Foundation(96J185 .1BQ0150) Fund for Reasearch on Doctoral Programs in Institutions of Higher Learning(1997000716)
摘要A new three dimensional simulation method is introduced to study the workspace of a 6 PSS (P denotes a prismatic kinematic pair, S denotes a spherical kinematic pair) parallel machine tool. This algorithm adopts the method of numerical analysis to investigate the boundary points in a series of sections which form the surface of the workspace. That is, to study such points that have the largest polar radius on a certain section in a system of polar coordinates according to conditions of constraint. The constraint conditions considered in the article include the maximum and minimum displacements of each dieblock, the maximum and minimum angles of oscillation in each hinge. By converting the constraint inequalities into constraint equations, the largest polar radius corresponding to every constraint condition can be evaluated and the minimum one is used to decide the boundary point. This algorithm greatly simplifies the computational process and can be used to analyze any section of the workspace. It provides a theoretical basis for the structural design of such a machine tool.
基金supported by University Key Laboratory Foundation of Liaoning Province of China(No.2008S094)
摘要A 3-degree-of-freedom(3-DOF)parallel machine tool based on a tripod mechanism is developed and studied.The kinematics analysis is performed,the workspace is derived,and an analysis on the number of conditions of the Jacobian matrix and manipulability is carried out.A method for error analysis and manipulability is introduced.Hence,the manipulability analysis of the parallel machine tool is accomplished.
基金supported by the National Natural Science Foundation of China (7087103290924021+2 种基金70971035)the National High Technology Research and Development Program of China (863 Program) (2008AA042901)Anhui Provincial Natural Science Foundation (11040606Q27)
摘要This paper considers the uniform parallel machine scheduling problem with unequal release dates and delivery times to minimize the maximum completion time.For this NP-hard problem,the largest sum of release date,processing time and delivery time first rule is designed to determine a certain machine for each job,and the largest difference between delivery time and release date first rule is designed to sequence the jobs scheduled on the same machine,and then a novel algorithm for the scheduling problem is built.To evaluate the performance of the proposed algorithm,a lower bound for the problem is proposed.The accuracy of the proposed algorithm is tested based on the data with problem size varying from 200 jobs to 600 jobs.The computational results indicate that the average relative error between the proposed algorithm and the lower bound is only 0.667%,therefore the solutions obtained by the proposed algorithm are very accurate.
基金Supported by the National Natural Science Foundation of China(91338101,91338108,61132002,6132106)Research Fund of Tsinghua University(2011Z05117)Co-innovation Laboratory of Aerospace Broadband Network Technology
摘要The scheduling efficiency of the tracking and data relay satellite system(TDRSS)is strictly limited by the scheduling degrees of freedom(DoF),including time DoF defined by jobs' flexible time windows and spatial DoF brought by multiple servable tracking and data relay satellites(TDRSs).In this paper,ageneralized multiple time windows(GMTW)model is proposed to fully exploit the time and spatial DoF.Then,the improvements of service capability and job-completion probability based on the GMTW are theoretically proved.Further,an asymmetric path-relinking(APR)based heuristic job scheduling framework is presented to maximize the usage of DoF provided by the GMTW.Simulation results show that by using our proposal 11%improvement of average jobcompletion probability can be obtained.Meanwhile,the computing time of the time-to-target can be shorten to 1/9 of the GRASP.
基金Sponsored by the Innovation Foundation of Shanghai University(Grant No.A.10-0101-07 -406)NNSF of China(Grant No.60874039)
摘要This paper considers a hybrid two-stage flow-shop scheduling problem with m identical parallel machines on one stage and a batch processor on the other stage. The processing time of job Jj on any of m identical parallel machines is aj≡a (j∈N), and the processing time of job Jj is bj(j∈N) on a batch processorM. We take makespan (Cmax) as our minimization objective. In this paper, for the problem of FSMP-BI (m identical parallel machines on the first stage and a batch processor on the second stage), based on the algorithm given by Sung and Choung for the problem of 1 |ri, BI|Cmax under the constraint of the given processing sequence, we develop an optimal dynamic programming Algorithm H1 for it in max {O(nlogn), O(nB)} time. A max {O(nlogn) , O(nB)}time symmetric Algorithm H2 is given then for the problem of BI-FSMP (a batch processor on the first stage and m identical parallel machines on the second stage).