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求解概率优化问题的微种群免疫优化算法
张著洪1 , 张仁崇2     
1. 贵州大学 大数据与信息工程学院, 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
摘要: 针对未知随机变量分布环境下的非线性概率优化模型,探讨微种群免疫优化算法。算法设计中,基于危险理论的应答模式,设计隐并行优化结构;经由自适应采样方法辨析优质和劣质个体;通过动态调整个体的危险半径确定危险区域和不同类型子群;利用多种变异策略指导个体展开多方位局部和全局搜索。该算法的计算复杂度依赖于迭代数、变量维数和群体规模,其具有进化种群规模小、可调参数少和结构简单等优点。借助理论测试例子和公交车调度问题,比较性的数值实验显示,此算法在寻优效率、搜索效果等方面均有一定的优势,对复杂概率优化模型有较好潜力。
关键词: 单目标P-模型     免疫优化     危险理论     自适应采样     微种群    
Micro-immune optimization algorithm for solving probabilistic optimization problems
ZHANG Zhuhong1 , ZHANG Renchong2     
1. College of Big Data & Information Engineering, Guizhou University, Guiyang 550025, China ;
2. Institute of System Science and Information Technology, College of Science, Guizhou University, Guiyang 550025, China
Received: 2015-09-01; Accepted: 2015-10-18; Published online: 2016-03-15
Foundation item: National Natural Science Foundation of China (61563009); Doctoral Fund of Ministry of Education of China (20125201110003); Graduate Innovation Fund of Guizhou University (2015057)
Corresponding author. Tel.:0851-83629086,E-mail:zhzhang@gzu.edu.cn
Abstract: This paper investigates a micro-immune optimization algorithm for the problem of nonlinear probabilistic optimization with unknown random variable distribution. In the design of algorithm, an implicit parallel optimization structure is developed based on the danger theory, while individuals can be identified through a proposed adaptive sampling method. Those danger regions and subpopulations can be decided dynamically through regulating danger radiuses, and meanwhile multiple kinds of mutation strategies are used to guide individuals to move towards multiple directions. Such algorithm has the merits of small population, few adjustable parameters, structural simplicity and so forth; the computational complexity depends on iteration number, variable dimension and population size. Based on the theoretical test examples and a bus scheduling problem, numerically comparative experiments show that the proposed algorithm possesses some advantages of search efficiency and optimized effect, and has potential for solving complex probabilistic optimization problems.
Key words: single-objective P-model     immune optimization     danger theory     adaptive sampling     micro population    

机会约束规划 (Chance-Constrained Programming,CCP)[1]是一类含机会约束或概率不等式的随机规划。依据目标函数表现形式的不同,CCP包含两类模型,即目标函数是期望值函数的E-模型和目标函数满足概率不等式的P-模型 (即概率优化模型)。大量实际优化问题