中文摘要：

针对一种微种群免疫优化算法求解非线性区间数规划存在搜索效果不稳定、优化质量依赖于不确定参数所属区间的宽度等不足，基于免疫应答原理和区间分析，提出一种改进型免疫优化方法。通过引入小生境策略改善种群多样性，避免处理高维或多峰值区间数规划时算法陷入局部搜索；引入精英保留思想增强种群的进化能力，保证种群的收敛性，增强算法的稳定性；借助局部扰动劣质个体，增强全局搜索能力及提高寻优速度，获得可有效搜寻优化对象的最优值区间的快速优化算法。基于多种类型的标准测试问题和应用事例，比较性的数值仿真结果表明：该改进型优化算法在获得解的质量、收敛性方面均具有明显优势，算法稳定性好，对复杂区间数规划问题有较好应用潜力。

英文摘要：

For the drawbacks of effect instability and solution quality dependent on interval widths of uncertain parameters in a reported micro immune optimization algorithm,an improved immune optimization algorithm based on the immune response theory and interval a-nalysis is proposed to solve a class of nonlinear interval number programming problems. The phenomenon of getting into local search can be avoided when dealing with high-dimensional or multimodal interval number programming,depending on the niching strategy helpful for the diversity of population. The elitism strategy,capable of enhancing the evolving ability of population,is adopted to guarantee the convergence of population and the high stability of the algorithm. The ability of global search can be achieved by locally disturbing low-quality individuals. These make that one such algorithm can effectively seek the optimal-valued intervals of optimization problems solving with high efficiency. Relying upon multiple kinds of benchmark problems and an engineering example,comparative stimulation results il-lustrate that the approach has the prominent advantages of optimized quality,search stability and convergence as well as the potential use for complex interval number programming problems.