Bilevel linear programming, which consists of the objective functions of the upper level and lower level, is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this pr...Bilevel linear programming, which consists of the objective functions of the upper level and lower level, is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this problem. Of all the algorithms, the ge- netic algorithm is an alternative to conventional approaches to find the solution of the bilevel linear programming. In this paper, we describe an adaptive genetic algorithm for solving the bilevel linear programming problem to overcome the difficulty of determining the probabilities of crossover and mutation. In addition, some techniques are adopted not only to deal with the difficulty that most of the chromosomes maybe infeasible in solving constrained optimization problem with genetic algorithm but also to improve the efficiency of the algorithm. The performance of this proposed algorithm is illustrated by the examples from references.展开更多
In this paper, we study sensitivity analysis of bilevel linear programming. Twocases of the leader’s objective function and the right-hand side of the constraints includingparameters are discussed separately. We pres...In this paper, we study sensitivity analysis of bilevel linear programming. Twocases of the leader’s objective function and the right-hand side of the constraints includingparameters are discussed separately. We presellt a necessary and sufficient optimalitycondition for an optimal solution to a bilevel linear programming problem and its equivalentexpression in nonconvex quadratic programming. The necessary and sufficient conditionsare proposed to guarantee that the current optimal solution or the corresponding basisremains optimal when the parameters vary. An algorithm is also proposed to determinethe set of the parameters which leaves the current optimal solution optimal or -optimal.展开更多
基金This paper was partly supported by National Outstanding Young Investigator Grant (70225005) of National Natural Science Foundation of China and Teaching & Research Award Program for Outstanding Young Teachers (2001) in Higher Education Institutions of Ministry of Education, China.
基金the National Natural Science Foundation of China(Nos.60574071 and70771080)
文摘Bilevel linear programming, which consists of the objective functions of the upper level and lower level, is a useful tool for modeling decentralized decision problems. Various methods are proposed for solving this problem. Of all the algorithms, the ge- netic algorithm is an alternative to conventional approaches to find the solution of the bilevel linear programming. In this paper, we describe an adaptive genetic algorithm for solving the bilevel linear programming problem to overcome the difficulty of determining the probabilities of crossover and mutation. In addition, some techniques are adopted not only to deal with the difficulty that most of the chromosomes maybe infeasible in solving constrained optimization problem with genetic algorithm but also to improve the efficiency of the algorithm. The performance of this proposed algorithm is illustrated by the examples from references.
文摘In this paper, we study sensitivity analysis of bilevel linear programming. Twocases of the leader’s objective function and the right-hand side of the constraints includingparameters are discussed separately. We presellt a necessary and sufficient optimalitycondition for an optimal solution to a bilevel linear programming problem and its equivalentexpression in nonconvex quadratic programming. The necessary and sufficient conditionsare proposed to guarantee that the current optimal solution or the corresponding basisremains optimal when the parameters vary. An algorithm is also proposed to determinethe set of the parameters which leaves the current optimal solution optimal or -optimal.
