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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 mapping relation of decision variables, discrete constrained optimization problems in gearing design are transformed into Constrained non-negative integer programming problems (CNIPPs), and solved by Discrete Differential Evolution (DDE) algorithm The problem. In order to overcome the shortcomings of the basic DDE algorithm in solving discrete problems, it is easy to fall into the local optimal region. This paper introduces an average genetic distance index that quantitatively evaluates the population diversity and proposes an adaptive escape strategy using backward learning operator to generate new individuals. The escape strategy is integrated into the DDE algorithm. Combined with the rule-of-feasibility constraint processing technology, an Escape DDE (EDDE) algorithm for solving CNIPPs is formed. The EDDE algorithm is used to solve the optimization design examples of gear drive, and the relative comprehensive performance index for comparing various algorithms to optimize the performance is proposed. Through testing and analysis, the new algorithm has good robustness and reliability, and the comprehensive index is better than the contrast algorithm. The optimization result is obviously better than the optimal solution of the existing literature, and the gear quality is reduced by 27%.