Most real-world optimization problems are hierarchical involving non-cooperative objectives. Many of these problems can be formulated in terms of the first（upper level） objective function being minimized over the so...Most real-world optimization problems are hierarchical involving non-cooperative objectives. Many of these problems can be formulated in terms of the first（upper level） objective function being minimized over the solution set mapping of the second（lower level） optimization problem. Often the upper level decision maker is risk-averse. The resulting class of problem is named weak bilevel programming problem. This paper presents a new algorithm which embeds a penalty function method into a branch and bound algorithm to deal with a weak linear bilevel programming problem. An example illustrates the feasibility of the proposed algorithm.展开更多
基金Supported by the National Natural Science Foundation of China(11501233)the Natural Science Research Project of Universities of Anhui Province(KJ2018A0390)
文摘Most real-world optimization problems are hierarchical involving non-cooperative objectives. Many of these problems can be formulated in terms of the first（upper level） objective function being minimized over the solution set mapping of the second（lower level） optimization problem. Often the upper level decision maker is risk-averse. The resulting class of problem is named weak bilevel programming problem. This paper presents a new algorithm which embeds a penalty function method into a branch and bound algorithm to deal with a weak linear bilevel programming problem. An example illustrates the feasibility of the proposed algorithm.
