逃逸离散差分进化算法在齿轮传动优化中的应用

Application of Escape Discrete Differential Evolution Algorithm in Optimal Design of Gear Transmission

根据决策变量映射关系,将齿轮传动设计中的离散约束优化问题转化为约束非负整数规划问题(Constrained non-negative integer programming problems,CNIPPs),并应用离散差分进化(Discrete differential evolution,DDE)算法求解该问题。引入定量评价种群多样性的平均基因距离指标,并据此提出一种采用反向学习算子生成新个体的自适应逃逸策略,以克服基本DDE算法求解离散问题易陷入局部最优区域的缺点。将逃逸策略融入DDE算法,并结合可行性规则约束处理技术,形成求解CNIPPs的逃逸离散差分进化(Escape DDE,EDDE)算法。应用EDDE算法求解齿轮传动优化设计实例,并提出用于比较多种算法优化性能的相对综合性能指标。通过测试与分析可知,新算法具有良好稳健性和可靠性,且综合指标优于对比算法。优化结果明显好于已有文献的最优解,齿轮质量下降了27%。

According to the equivalent mapping relation of decision variables, the constrained discrete optimization problems for gear transmission design are transformed into nonlinear constrained non - negative integer programming problems （CNIPPs） and a discrete differential evolution （DDE） algorithm is used to solve these problems. An index of average gene distance is introduced to evaluate quantitatively the population diver- sity. On this basis, this work presents an adaptive escape strategy in which an opposite -based learning opera- tor is employed to generate new individuals to overcome the drawback that the basic DDE algorithm easily traps into local optimal regions for solving discrete optimization problems. Thus this study embeds the escape strate- gies in DDE algorithm, adopts feasibility rules to handle constraints, and forms to an escape DDE （EDDE） algorithm for s01ving CNIPPs. The proposed EDDE algorithm is applied to approach a real case of gear transmis- sion optimization and an index of relative comprehensive performance is presented to compare several algorithms on optimization performances. The experimental and analytical results show that this novel algorithm has good robustness and reliability and is better than compared ones in term of the comprehensive index. Furthermore, the obtained result is better than one of the published literature and the corresponding gear mass is decreased by 27%.