中文摘要：

以坝体体积、最大主应力、高应力区范围为目标函数，建立了拱坝体形多目标优化模型．根据多目标优化设计问题与经济学中博弈问题之间的相似性，将多目标优化中的各分目标函数看成博弈方，所有可行解就是博弈策略集，从而提出了拱坝体形多目标优化设计问题的合作博弈方法．白鹤滩拱坝体形优化设计结果表明，该方法比传统的多目标优化方法（如线性加权法和理想点法）更能综合反映各优化目标的要求，优化结果更加合理，并具有较高的计算效率．

英文摘要：

A multi-objective optimization model for shape design of arch dams was developed with the dam volume,maximal principal stresses and maximal relative depth of large tensile stress region taken as objective functions. Based on the similarity between multi-objective optimization and game problems in economics, each objective function was taken as a game player, and all the feasible solutions constituted the game strategy set. Consequently, a cooperative game method for multi-objective optimization of the shape of arch dams was worked out. A case study of shape optimization of the Baihetan arch dam demonstrates that, compared with other multi-objective optimization methods, including the linear weighting method and utopia point method, the present method is of high efficiency of calculation and can comprehensively reflect the requirement of each objective to be optimized, and that the optimized result is reasonable.