中文摘要：

针对遗传算法群体多样性保持能力不足，易陷入局部最优等缺点，提出了一种改进的免疫算法（ImprovedArtificialImmuneAlgorithm，IAIA），并将其与函数优化相结合，用于解决多模函数优化问题．用个体的实数值根据欧式距离进行适当的聚类分析，认为类内个体均具有相同的浓度值，用个体的二进制编码计算类的平均信息熵，进而得到浓度值，用以取代了标准人工免疫算法（ArtificialImmuneAlgorithm，AIA）中计算任意两个体间信息熵的算法；根据个体适应值和浓度控制个体的繁殖率，该算法在保持与AIA相近的多样性和收敛性的同时，达到减少算法的时间复杂性，提高计算效率的目的．测试实验表明，对单模和多模函数优化问题，以及在高维的情况下，IAIA有较高的解质量及较短的运算时间，显示出良好的性能．

英文摘要：

To improve the efficiency of basic artificial immune algorithm （ AIA）, this paper presents an improved artificial immune algorithm （IAIA） for multimodal function optimization. Appropriate cluster analysis was conducted on real values of individuals with Euclidean distance measure, then all individuals within a cluster were considered as a group with the same concentration value. The average entropy on the whole group was calculated with binary encoding of individuals, which replaced the conventionally calculation of entropy between two individuals in AIA. To maintain high diversity, the fitness of each individual and concentration were taken into account in determining reproduction probability. Two benchmark functions were used to demonstrate the validity of IAIA and the role of each design of IAIA. Numerical experiments show that IAIA can reduce the complexity of computation, and then increases the efficiency of AIA with the maintenance of diversity and convergence in optimizing muhimodal functions.