中文摘要：

基于区间分析和免疫学原理,探讨非线性区间数规划问题解的概念和性质,以及求解的免疫优化方法和算法的理论基础.首先,基于该问题的最优值区间,给予最优解概念;研究区间值优化问题有效解的性质,探讨区间自然扩张规划与区间数规划的解之间联系,获得有效解是最优解的充分条件以及寻优的有效途径.其次,基于免疫应答的简化机制,设计具有群体规模小、可调参数少、结构简单等特点的非主从结构微免疫优化算法,并获证该算法具有收敛性和低计算复杂度.通过扩展标准测试函数和应用事例,比较性的数值实验结果显示,此算法执行效率高、搜索效果好,对低、偏高维非线性区间数规划具有较好应用潜力.

英文摘要：

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 nonmaster-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.