Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s f...Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.展开更多
Component reallocation(CR)is receiving increasing attention in many engineering systems with functionally interchangeable and unbalanced degradation components.This paper studies a CR and system replacement maintenanc...Component reallocation(CR)is receiving increasing attention in many engineering systems with functionally interchangeable and unbalanced degradation components.This paper studies a CR and system replacement maintenance policy of series repairable systems,which undergoes minimal repairs for each emergency failure of components,and considers constant downtime and cost of minimal repair,CR and system replacement.Two binary mixed integer nonlinear programming models are respectively established to determine the assignment of CR,and the uptime right before CR and system replacement with the objective of minimizing the system average maintenance cost and maximizing the system availability.Further,we derive the optimal uptime right before system replacement with maximization of the system availability,and then give the relationship between the system availability and the component failure rate.Finally,numerical examples show that the CR and system replacement maintenance policy can effectively reduce the system average maintenance cost and improve the system availability,and further give the sensitivity analysis and insights of the CR and system replacement maintenance policy.展开更多
基金supported by the National Natural Science Fundation of China (60374063)
文摘Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.
基金supported by the National Natural Science Foundation of China(72101025,72271049)the Fundamental Research Funds for the Central Universities(FRF-TP-20-073A1)the China Postdoct oral Science Foundation(2021M690349)。
文摘Component reallocation(CR)is receiving increasing attention in many engineering systems with functionally interchangeable and unbalanced degradation components.This paper studies a CR and system replacement maintenance policy of series repairable systems,which undergoes minimal repairs for each emergency failure of components,and considers constant downtime and cost of minimal repair,CR and system replacement.Two binary mixed integer nonlinear programming models are respectively established to determine the assignment of CR,and the uptime right before CR and system replacement with the objective of minimizing the system average maintenance cost and maximizing the system availability.Further,we derive the optimal uptime right before system replacement with maximization of the system availability,and then give the relationship between the system availability and the component failure rate.Finally,numerical examples show that the CR and system replacement maintenance policy can effectively reduce the system average maintenance cost and improve the system availability,and further give the sensitivity analysis and insights of the CR and system replacement maintenance policy.
