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 transfor med 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, th e calculating approaches for the base penalty and the formula f or the

base function of continuous mapping are carried out, and self-adaptive penalty factors based on these notions for handling cons traints

are presented. It is studied that a novel measure, termed as a　quasi re-averaging gene distance for a population, is employed t o　depict

the diversity of the population and chaotic immigration operato rs depending on this measure a nd the probability are implemented to

preserve the population diversity. Orientating constrained engineering optimizati