两层多目标规划的罚函数法
Penalty Function Method for Bilevel Multiobjective Programming
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摘要: 研究了一类非线性两层多目标规划问题.在下层多目标规划问题的目标函数是严格凸函 数、决策变量约束集是凸集的假设下,通过将两层多目标规划问题转化成一系列单层多目标规划 问题,建立了两层多目标规划的罚函数理论,并进行了收敛性分析.从而丰富了两层多目标规划的 理论,为解决实际中的两层多目标决策问题提供了有力的工具.Abstract: In this paper, a class of nonlinear bilevel multiobjective programming problems is studied. Under the assumptions that the objective functions are strictly convex and the constraint set of decision variables is convex, by transforming the bilevel multiobjective programming problem into a series of one-level multiobjective programming problems, the penalty function method for bilevel multiobjective programming is established, and the convergence of the method is proved. This method complements the theory of bilevel multiobjective programming and provides a powerful means to solve the practical bilevel multiobjective decision making problems.
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Key words:
- Bilevel programming /
- multiobjective programming /
- penalty function
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