工程约束优化的自适应罚函数混合离散差分进化算法

Hybrid Discrete Differential Evolution with a Self-adaptive Penalty Function for Constrained Engineering Optimization

将离散约束优化问题转化为非负整数约束规划问题,开发求解该问题的离散差分进化算法。该算法采用基于混沌映射的种群初始化、双版本变异和带随机扰动项的取整运算等新策略。针对非线性约束条件,给出惩罚基数的计算方法和连续映射基函数的表达式,在此基础上设计处理非线性约束的自适应惩罚因子。提出一种刻画种群多样性的新测度——种群二次平均基因距离及基于新测度的依概率混沌移民算子。将自适应罚函数法、依概率混沌移民操作与离散差分进化算法有机融合,构造面向工程约束优化的混合离散差分进化算法。对3个离散约束优化实例进行验证,结果表明,混合算法具有良好的鲁棒性且优于离散粒子群算法。应用混合算法求解斜齿圆柱齿轮传动优化设计问题,结果优于遗传算法及其改进算法、离散粒子群算法,目标函数值较遗传算法及其改进算法分别下降41%和10%。

The constrained discrete optimization（CDO） is transformed into a nonlinear constrained non-negative integer programming（CNIP） which can be solved by the proposed discrete differential evolution（DDE） algorithm that adopts several improvements such as the chaotic initialization of a population,the double-scheme mutation,and the integrating operator with stochastic perturbation.Aiming at the nonlinear constraints,the calculating approaches for the base penalty and the formula for the base function of continuous mapping are carried out,and self-adaptive penalty factors based on these notions for handling constraints are presented.It is studied that a novel measure,termed as a quasi re-averaging gene distance for a population,is employed to depict the diversity of the population and chaotic immigration operators depending on this measure and the probability are implemented to preserve the population diversity.Orientating constrained engineering optimizations,it proposes a novel hybrid DDE（HDDE） in which a self-adaptive method and a chaotic immigration strategy are dynamically incorporated in the DDE algorithm to improve its performance.Furthermore,three benchmark functions in CDO fields are utilized to test this HDDE algorithm and the results show that the new approach is robust and efficient,and is more optimal in objective functions than the discrete particle swarm optimization（DPSO） algorithm.Finally,this work also uses the proposed algorithm to optimize the transmission design of helical gear reducers and its objective value is better than those obtained by genetic algorithm（GA）,improved GA（IGA）,and DPSO,etc.,and has decreased by 41% and 10% compared with GA and IGA,respectively.