ISSN 1000-1239 CN 11-1777/TP

• 人工智能 •

### 求解非线性区间数规划的微免疫优化算法研究

1. 1(贵州大学大数据与信息工程学院信息与通信工程系 贵阳 550025);2(贵州大学理学院系统科学及信息技术研究所 贵阳 550025) (sci.zhzhang@gzu.edu.cn)
• 出版日期: 2014-12-01
• 基金资助:
基金项目：国家自然科学基金项目(61065010)；教育部高等学校博士学科点专项科研基金项目(20125201110003)

### Micro-Immune Optimization Approach Solving Nonlinear Interval Number Programming

Zhang Zhuhong1, Tao Juan2

1. 1(Department of Information and Communication Engineering, College of Big Data and Information Engineering, Guizhou University, Guiyang 550025); 2(Institute of System Science & Information Technology, College of Science, Guizhou University, Guiyang 550025)
• Online: 2014-12-01

Abstract: Based on interval analysis and immune principles, some properties of solutions on nonlinear interval number programming are investigated, and an immune optimization approach as well as its theoretical foundations are explored. Firstly, the concept of optimal solution for such nonlinear programming is developed based on the version of optimal-valued interval. Some properties of efficient solutions on interval-valued programming are found, while an inherent solution relation is obtained between such nonlinear programming and interval natural extension programming. This derives an efficient pathway to find the optimal solution in terms of sufficient conditions acquired. Secondly, based on simplified metaphors of the immune response, a micro-immune optimization approach is proposed with the characteristics of small populations, few adjustable parameters, simple and non-master-slave structures. It is also proven to be convergent with low computational complexity. Comparatively numerical results show that such an efficient and effective approach is potential to nonlinear interval number programming problems with low or somewhat high dimensions.