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
The objective of this work was to determine the location of emergency material warehouses. For the site selection problem of emergency material warehouses, the triangular fuzzy numbers are respectively demand of the d...The objective of this work was to determine the location of emergency material warehouses. For the site selection problem of emergency material warehouses, the triangular fuzzy numbers are respectively demand of the demand node, the distance between the warehouse and demand node and the cost of the warehouse, a bi-objective programming model was established with minimum total cost of the system and minimum distance between the selected emergency material warehouses and the demand node. Using the theories of fuzzy numbers, the fuzzy programming model was transformed into a determinate bi-objective mixed integer programming model and a heuristic algorithm for this model was designed. Then, the algorithm was proven to be feasible and effective through a numerical example. Analysis results show that the location of emergency material warehouse depends heavily on the values of degree a and weight wl. Accurate information of a certain emergency activity should be collected before making the decision.展开更多
This paper investigates the maximum network through- put for resource-constrained space networks based on the delay and disruption-tolerant networking （DTN） architecture. Specifically, this paper proposes a methodol...This paper investigates the maximum network through- put for resource-constrained space networks based on the delay and disruption-tolerant networking （DTN） architecture. Specifically, this paper proposes a methodology for calculating the maximum network throughput of multiple transmission tasks under storage and delay constraints over a space network. A mixed-integer linear programming （MILP） is formulated to solve this problem. Simula- tions results show that the proposed methodology can successfully calculate the optimal throughput of a space network under storage and delay constraints, as well as a clear, monotonic relationship between end-to-end delay and the maximum network throughput under storage constraints. At the same time, the optimization re- sults shine light on the routing and transport protocol design in space communication, which can be used to obtain the optimal network throughput.展开更多
Many difficult engineering problems cannot be solved by the conventional optimization techniques in practice. Direct searches that need no recourse to explicit derivatives are revived and become popular since the new ...Many difficult engineering problems cannot be solved by the conventional optimization techniques in practice. Direct searches that need no recourse to explicit derivatives are revived and become popular since the new century. In order to get a deep insight into this field, some notes on the direct searches for non-smooth optimization problems are made. The global convergence vs. local convergence and their influences on expected solutions for simulation-based stochastic optimization are pointed out. The sufficient and simple decrease criteria for step acceptance are analyzed, and why simple decrease is enough for globalization in direct searches is identified. The reason to introduce the positive spanning set and its usage in direct searches is explained. Other topics such as the generalization of direct searches to bound, linear and non-linear constraints are also briefly discussed.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Project(71071162)supported by the National Natural Science Foundation of China
文摘The objective of this work was to determine the location of emergency material warehouses. For the site selection problem of emergency material warehouses, the triangular fuzzy numbers are respectively demand of the demand node, the distance between the warehouse and demand node and the cost of the warehouse, a bi-objective programming model was established with minimum total cost of the system and minimum distance between the selected emergency material warehouses and the demand node. Using the theories of fuzzy numbers, the fuzzy programming model was transformed into a determinate bi-objective mixed integer programming model and a heuristic algorithm for this model was designed. Then, the algorithm was proven to be feasible and effective through a numerical example. Analysis results show that the location of emergency material warehouse depends heavily on the values of degree a and weight wl. Accurate information of a certain emergency activity should be collected before making the decision.
基金supported by the National Natural Sciences Foundation of China(6113200261321061+3 种基金6123101161201183)the National Basic Research Program of China(2014CB340206)the Tsinghua University Initiative Scientific Research Program(2011Z05117)
文摘This paper investigates the maximum network through- put for resource-constrained space networks based on the delay and disruption-tolerant networking （DTN） architecture. Specifically, this paper proposes a methodology for calculating the maximum network throughput of multiple transmission tasks under storage and delay constraints over a space network. A mixed-integer linear programming （MILP） is formulated to solve this problem. Simula- tions results show that the proposed methodology can successfully calculate the optimal throughput of a space network under storage and delay constraints, as well as a clear, monotonic relationship between end-to-end delay and the maximum network throughput under storage constraints. At the same time, the optimization re- sults shine light on the routing and transport protocol design in space communication, which can be used to obtain the optimal network throughput.
基金supported by the Key Foundation of Southwest University for Nationalities(09NZD001).
文摘Many difficult engineering problems cannot be solved by the conventional optimization techniques in practice. Direct searches that need no recourse to explicit derivatives are revived and become popular since the new century. In order to get a deep insight into this field, some notes on the direct searches for non-smooth optimization problems are made. The global convergence vs. local convergence and their influences on expected solutions for simulation-based stochastic optimization are pointed out. The sufficient and simple decrease criteria for step acceptance are analyzed, and why simple decrease is enough for globalization in direct searches is identified. The reason to introduce the positive spanning set and its usage in direct searches is explained. Other topics such as the generalization of direct searches to bound, linear and non-linear constraints are also briefly discussed.
