Abstract: In order to improve the shortcomings of the?Imperialist Competitive Algorithm（ICA）, such as?premature convergence, low searching range, low precision and non-empire?interaction, this paper?puts forward?two kinds of innovated ICA?based on assimilation model and competition model. When the colonies move to empire directly, the searching range will be smaller. The paper introduces the difference factor to make the range wider. The lack of interaction between empires aren’t good to the optimal?value, so the paper employs loyalty operator to enhance the interaction between empires. The changed assimilation model will make the stronger empire get more support, so that every country looks different to the final optimal?value. Nash equilibrium is employed to the competition model. The algorithm sets up time node during iteration and selects the better relative competitive coefficient. The paper puts forward the prove in theory and experiment. The new algorithm compares to other ICA, and it makes a progress in searching precision and breadth.

Key words: Imperialist Competitive Algorithm（ICA）, assimilation model, competition model, convergence theorems, Nash equilibrium

摘要： 为了改善帝国竞争算法（Imperialist Competitive Algorithm，ICA）易早熟收敛，搜索范围低，精度小，帝国之间信息交互性不强等缺点，提出了两种基于同化模型和竞争模型的改进的ICA算法。针对殖民地在移动过程中由于过于直接的靠近统治者而造成的搜索范围过小以及容易陷入局部最优的情况在同化过程中引入了差异因子来增大搜索范围。针对帝国之间的交互性的缺失，引入了人忠诚度的算子来实现帝国交互以及同化机制的模型改变，较强的帝国统治者会因为忠诚度算子获得更多的支持，从而细致划分了一个帝国中的每个国家，利用纳什均衡和最大最小公平性引导帝国竞争进而使算法向最优解进行搜索。在竞争过程中设置时间节点动态划分迭代阶段，根据迭代的不同阶段特点选择最优竞争系数。对算法进行了理论证明，最后将算法应用于多个函数进行检测并与其他的改进ICA算法进行比较，在搜索精度和范围广度上有了一定的提高。

关键词: 帝国竞争算法, 同化模型, 竞争模型, 收敛性定理, 纳什均衡