可靠性优化问题中遗传算法适应值函数的建立  

Establishment of genetic algorithm fitness function in reliability-based structural optimization

作　　者：严心池[1] 华渊[1] 

机构地区：[1]江南大学环境与土木工程学院,无锡214122

出　　处：《计算力学学报》2009年第1期120-123,共4页Chinese Journal of Computational Mechanics

基　　金：国防科工委技术基础基金(Z192001A001)资助项目

摘　　要：应用遗传算法进行优化,约束的处理成为建立适应值函数和算法进行的关键。可靠性优化是以系统可靠性指标作为优化问题的约束条件。首先结合外罚函数法建立数学模型,处理约束的惩罚因子时根据种群情况自适应取值,构造适应值函数的映射公式。随后采用拉格朗日乘子法建立了新的约束与目标函数向适应值函数的映射公式,该公式可以避免因罚函数病态所导致的搜索终止,收敛更加快速,使遗传算法得以成功应用于可靠性优化问题中。分析计算结果表明乘子法具有更好地收敛效果,两个公式构造合理。The Reliability-based Structural Optimization （RBSO） in this paper includes system reliability index constraints, but it is difficult for genetic algorithm （GA） to solve the optimization issue with constraint, so in this process, how to handle the constraint become sixty-four-dollar question of establishing the fitness function and circulating this algorithm. Based on exterior penalty function method, mathematic model is made, penalty gene is get adaptively according to population＇s evolution, and mapping formula of objective function and constraint transformed fitness function is established. Subsequently laxity variable is introduced in primary mathematic model, based on Lagrange multiplier method, a new fitness function mapping formula is made, this method can avoid penalty function morbidity by means of adding a Lagrange multiplier, and has a more quick and stable convergence, genetic algorithm for numerical optimization for constrained problem is successfully solved. The calculation shows that the two equations＇ are reasonable, and the multiplier method has better convergence capability.

关 键 词：可靠性优化 遗传算法 约束 外罚函数法 乘子法 

分 类 号：O224[理学—运筹学与控制论]