The single machine scheduling problem which involves uncertain job due dates is one of the most important issues in the real make-to-order environment. To deal with the uncertainty, this paper establishes a robust opt...The single machine scheduling problem which involves uncertain job due dates is one of the most important issues in the real make-to-order environment. To deal with the uncertainty, this paper establishes a robust optimization model by minimizing the maximum tardiness in the worst case scenario over all jobs. Unlike the traditional stochastic programming model which requires exact distributions, our model only needs the information of due date intervals. The worst case scenario for a given sequence that belongs to a set containing only n scenarios is proved, where n is the number of jobs. Then, the model is simplified and reformulated as an equivalent mixed 0-1 integer linear programming(MILP) problem. To solve the MILP problems efficiently, a heuristic approach is proposed based on a robust dominance rule. The experimental results show that the proposed method has the advantages of robustness and high calculating efficiency, and it is feasible for large-scale problems.展开更多
Heavy-load transfer robots are widely used in automobile production and machinery manufacturing to improve production efficiency.In order to meet the needs of large billet transfer,a 4-DOF transfer robot is designed i...Heavy-load transfer robots are widely used in automobile production and machinery manufacturing to improve production efficiency.In order to meet the needs of large billet transfer,a 4-DOF transfer robot is designed in this paper,which consists of parallel four-bar mechanisms.The Jacobian matrix referring to the mapping matrix from the joint velocity to the operating space velocity of the transfer robot can be solved by the differential-vector method.The mean value of the Jacobian matrix condition number in the workspace is used as the global performance index of the robot velocity and the optimization goal.The constraint condition is established based on the actual working condition.Then the linkage length optimization is carried out to decrease the length of the linkage and to increase the global performance index of velocity.The total length of robot rods is reduced by 6.12%.The global performance index of velocity is improved by 45.15%.Taking the optimized rod length as the mechanism parameter,the distribution of the motion space of the transfer robot is obtained.Finally,the results show that the proposed method for establishing the Jacobian matrix of the lower-mobility robot and for the optimization of the rods based on the velocity global performance index is accurate and effective.The workspace distribution of the robot meets the design requirements.展开更多
基金supported by the National Natural Science Foundation of China(61503211,U1660202)。
文摘The single machine scheduling problem which involves uncertain job due dates is one of the most important issues in the real make-to-order environment. To deal with the uncertainty, this paper establishes a robust optimization model by minimizing the maximum tardiness in the worst case scenario over all jobs. Unlike the traditional stochastic programming model which requires exact distributions, our model only needs the information of due date intervals. The worst case scenario for a given sequence that belongs to a set containing only n scenarios is proved, where n is the number of jobs. Then, the model is simplified and reformulated as an equivalent mixed 0-1 integer linear programming(MILP) problem. To solve the MILP problems efficiently, a heuristic approach is proposed based on a robust dominance rule. The experimental results show that the proposed method has the advantages of robustness and high calculating efficiency, and it is feasible for large-scale problems.
基金supported by the National Key R&D Program of China(No.2018YFB1307900)the Natural Science Foundation of Shanxi Province(Nos.201901D211009,201901D211010)the Technology In⁃novation Foundation of Shanxi University(No.2019L 0177).
文摘Heavy-load transfer robots are widely used in automobile production and machinery manufacturing to improve production efficiency.In order to meet the needs of large billet transfer,a 4-DOF transfer robot is designed in this paper,which consists of parallel four-bar mechanisms.The Jacobian matrix referring to the mapping matrix from the joint velocity to the operating space velocity of the transfer robot can be solved by the differential-vector method.The mean value of the Jacobian matrix condition number in the workspace is used as the global performance index of the robot velocity and the optimization goal.The constraint condition is established based on the actual working condition.Then the linkage length optimization is carried out to decrease the length of the linkage and to increase the global performance index of velocity.The total length of robot rods is reduced by 6.12%.The global performance index of velocity is improved by 45.15%.Taking the optimized rod length as the mechanism parameter,the distribution of the motion space of the transfer robot is obtained.Finally,the results show that the proposed method for establishing the Jacobian matrix of the lower-mobility robot and for the optimization of the rods based on the velocity global performance index is accurate and effective.The workspace distribution of the robot meets the design requirements.
