非线性多目标概率约束规划免疫优化算法

针对噪声信息未知的一般非线性多目标概率约束规划（MOPCP）问题，探讨基于危险理论的多目标免疫优化算法（MOIOA）。算法设计中，借助自适应采样方法估计机会约束的概率和目标值；借助危险理论蕴含的应答模式分割进化种群为已感染、易感染和未感染子群；借助二进制交叉、自适应变异概率、多项式变异策略平衡种群的全局与局部搜索能力。与7种算法相比较获得的数值结果表明，所提算法的搜索效率有明显优势且搜索效果有一定的优越性，同时对复杂工程问题有应用潜力。 

Immune optimization algorithm for nonlinear multi-objective probabilistic constrained programming

This paper investigates a Multi-Objective Immune Optimization Algorithm (MOIOA) based on danger theory to solve the problem of nonlinear Multi-Objective Probabilistic Constrained Programming (MOPCP) with unknown noise information. In the design of the algorithm, adaptive sampling methods are used to estimate each chance constraint's probability and objective values, while each evolving population is divided into infected, susceptible and uninfected sub-populations in terms of one specific immune response mechanism contained by danger theory. The capability of global and local search can be enhanced, relying upon simulated binary crossover, adaptive mutation probability and polynomial mutation strategy. Numerical experiment results show that the proposed multi-objective algorithm has high efficiency and has some advantages over seven comparative methods with regard to solution quality. It has application potential to complex engineering problems.