单目标概率约束规划的微种群免疫优化算法

针对无先验随机分布信息的单目标概率约束规划，探讨了微种群免疫优化算法。算法设计中，受危险理论启发设计微种群免疫优化算法进化框架；借助估计值的误差幅度，提出2个方法分别估计概率值和目标值；依据个体间的优劣关系，划分群体为3个类型子群协同进化；构建生命周期模型，设计自适应的交叉与变异概率、变异策略，结合交叉算子促进子群信息有效交流，并沿不同方向协同进化。数值实验统计结果说明:所提算法拥有良好的搜索效率、搜索效果及降噪能力，具有一定的竞争力和应用潜力。 

Micro immune optimization algorithm for single objective probabilistic constrained programming

An immune optimization algorithm with a small population is proposed to solve a single objective probability constrained programming with no prior random distribution information. In the design of the algorithm, we develop an evolutionary framework with a micro population inspired by danger theory. Based on the amplitude of error of the estimated value, two approaches are proposed to estimate the individual’s objective values and each chance constraint’s probability respectively. According to the superior and inferior relationships among individuals, the population was divided into three types of sub-population for co-evolution. A version of individual life cycle is constructed, while adaptive crossover probability, adaptive mutation probability and adaptive mutation strategy as well as crossover strategy are designed to promote effective information exchange among the above sub-populations to co-evolve individuals in different directions. The results of numerical experiments show that the proposed algorithm has good search efficiency, search effect and noise reduction ability, and has certain competitiveness and application potential.