不适定线性二层规划问题的一种新的激励模型

针对不适定线性二层规划问题,考虑将部分合作模型中参数合作度更改为变量激励份额,由上层决策者适当分配激励份额给下层决策者,从而使得下层决策者心甘情愿与其合作.首先给出对应的激励模型,并给出与之相对应的罚问题.然后,证明了解的存在性,并设计相应算法来获得原二层规划问题的最优解.最后,数值实验不仅验证了该方法的可行性,并且结果显示,该文激励模型的最优值要优于部分合作模型的结果.

A new coordination model for ill-posed bilevel programming problem

For ill-posed linear bilevel programming problem, how the leader motivate the follower to maximize its own profit is studied. Firstly, a coordination model is presented with its corresponding penalty problem given. Then, under some conditions, the result on the existence of a solution is established and an algorithm is developed to obtain a coordination solution to the original bilevel programming problem. Finally, numerical results show that the proposed method is feasible.