中文摘要：

以坝体体积、最大主拉应力和整体应变能作为目标函数，建立拱坝体形多目标优化设计模型，提出基于无私合作博弈模型的多目标求解方法。将3个设计目标视为3个博弈方，通过计算设计变量对目标函数的影响因子和模糊聚类，将设计变量分解为各博弈方拥有的策略空间。采用合作约束力协议，建立博弈得益函数与目标函数之间的映射关系。各博弈方分别以自身博弈得益函数为目标，在各自的策略空间中进行单目标优化，获得本博弈方对其余博弈方的最佳对策，所有博弈方的最佳对策形成一轮博弈的策略组合，并根据收敛判别，通过多轮博弈，获得最终的博弈解。以白鹤滩拱坝为例，设计结果显示体积方量减少了27．7万m^3，最大主拉应力降低了0．58MPa，应变能下降了0．057GJ，体现了无私合作博弈解法的有效性。

英文摘要：

Taking the volume, maximum tensile principal stress and integral strain energy of dam as the design objective functions, a multi-objective optimization model of arch dam shape design is presented. The unselfish cooperation game is used to solve this optimization model with three objective functions taken as the game players. By calculating the affecting factors of the design variables to objective functions and fuzzy clustering, the design variables are divided into different strategic spaces owned by each player. With the cooperative agreement, a mapping relationship between the game players＇ payoff and the objective functions is proposed. Each game player takes its payoff as singular objective to optimize its own strategic spaces and obtains the best strategy to deal with the others. All the best strategies are combined as a game strategy set. By multi-gaming, the final solution meeting given convergence of criterion is obtained. The method has been applied in the shape optimization of the Baihetan arch dam, the optimization results in a decrease of the dam volume by 277 ×103 m^3 , a decrease of the maximum tensile principal stress by 0.58MPa and a decrease of strain energy of dam by 0.057GJ, reflecting the effectiveness of the unselfish cooperation game.