基于仿生的多目标博弈算法及在拱坝体型优化中的应用

The multi-objective game algorithm is a heuristic method for solving the multi-objective optimization problem. It has been proposed in recent years. Its key technology is to estabilish the specific mapping relationships between the multi-objective optimization model and the model of the game. In the previous studies, our project team has proposed the bionic and the spatial mappings between the above two models. In this project, for the bionic mappings, the following four kinds of the game patterns, that is, the pure cooperation pattern, the master-slave pattern, the mixed pattern and the evolution pattern will be constructed. Besides, according to the behavior operator functions of competition, cooperation and self-adaption, the quantitative mapping relations between the payoff functions and the objective functions are established. Thus, the influence law that different game patterns and behavior operators have on the objective benefits is revealed. For the spatial mappings, the computation method that the space of the design variables is divided into the parallel subspace of the strategy variables owned by the corresponding players based on the K average clustering method in data mining will be studied. Moreover, the Baihetan arch dam is taken as a project example. Then, a multi-objective opitimization model is established and the game algorithm and the parallel calculation mode are designed. In addition, the theoretical method and the numerical approach are used to study the robustness and the Pareto optimality of the equilibrium solutions. Thus, the correlation and the dynamic changing rule between the arch dam shape and the objective functions are obtained. Moreover, the reasonable design suggestions and the scheme of the arch dam shape with the application value are proposed.

多目标博弈算法是近年提出的一种求解多目标优化问题的启发式算法，其技术关键是建立多目标优化模型和博弈模型之间的具体映射关系。项目组在前期研究中初步提出两个模型之间的仿生映射和空间映射。在本项目中，针对仿生映射，将构造纯合作格局、主从格局、混合格局和演化格局等4种博弈格局，并根据竞争、合作和自适应等行为算子作用，构建博弈得益函数与目标函数之间的定量映射关系，揭示不同博弈格局和行为算子对各目标利益的影响规律。针对空间映射，拟基于数据挖掘中的K平均聚类方法，研究将设计变量空间分割为各个目标博弈方拥有的策略变量并行子空间的计算方法。进而以白鹤滩高拱坝体型多目标优化设计作为工程算例，建立多目标优化模型，设计博弈求解算法和并行计算模式，采用理论方法和数值方法，研究博弈均衡解的鲁棒性和Pareto优性，获得拱坝体型特征与目标函数之间的关联与动态变化规律，提出合理的设计建议和具有工程应用价值的拱坝体型方案。

建立了系统的多目标博弈算法和计算机程序，提出了多目标优化模型和博弈模型之间的仿生映射及空间映射。针对仿生映射，构造了纯竞争格局、纯合作格局、主从格局、混合格局和演化格局等5种博弈格局，并根据竞争、合作和自适应等行为算子作用，构建了博弈得益函数与目标函数之间的定量映射关系，算例结果显示了不同博弈格局和行为算子对各目标利益的影响规律。针对空间映射，提出了策略变量子空间的模糊聚类方法和K-平均聚类方法，该方法自动化程度高，可有效促进多目标博弈算法的通用化；通过将设计变量空间分割为各博弈方拥有的策略变量子空间，揭示了各分目标与设计变量之间的关联性。进而以白鹤滩高拱坝体型多目标优化设计作为工程算例，建立多目标优化模型，设计了博弈求解算法和并行计算模式，获得拱坝体型特征与目标函数之间的关联与动态变化规律；同时，可根据设计人员的偏好和设计意图，给各设计目标赋予恰当的行为方式和构造合适的博弈格局，提出5种博弈格局共9种优化体型方案供决策参考。