拱坝体型的多目标博弈设计

MULTI-OBJECTIVE GAME DESIGN OF ARCH DAM SHAPE

提出基于博弈理论的多目标求解方法,给出多目标问题的博弈描述和各博弈方策略空间的计算方法,研究:1)利用Nash均衡模型求解无目标偏好的多目标竞争问题;2)利用Stackelberg寡头模型求解有目标偏好的多目标竞争问题;3)利用合作竞争模型求解关注整体得益的多目标设计问题;并给出相应的技术步骤.以白鹤滩拱坝体型的三目标博弈设计为例,取体积目标、坝体最大主拉应力目标和坝体应变能目标为博弈方,分别采用Nash均衡模型、Stackelberg寡头模型和合作竞争模型进行博弈求解,设计结果显示拱坝的体积方量、应力、应变能和位移等较初始体型的变化改善情况,实现了各博弈模型的设计目的,表明了多目标博弈设计方法的有效性.

For the economy and safety of hyperbolic arch dam under static loading, a mathematical multi-objective optimization design model of arch dam shape has been established and the solution to this model was studied. This paper set up a multi-objective solution based on game theory, as well as the game description of multi-objective problem and the calculation of each game player＇s strategy space. Our attentions are paid to the following points. （1） Using Nash equilibrium model to solve the no preference multi- objective competition problem. （2） Using Stackelberg oligarch model to solve the multi-objective competition problem with preference. （3） Using co-operation-competition model to solve the multi-objective problem which cares about all the players＇ payoff. Taking the triple-objective design of Baihetan arch dam shape for example, the game players are volume, maximum primary tensile stress of dam body and strain energy of dam. With the adoption of Nash equilibrium model, Stackelberg model and co-operation-competition model, the design results show that the indexes of stress, strain energy and displacement are improved, comparing with those of the virgin shape. It shows that the multi-objective game design is effective.