• CN：11-2187/TH
  • ISSN：0577-6686
机械工程学报

机械工程学报 ›› 2016, Vol. 52 ›› Issue (21): 44-55.doi: 10.3901/JME.2016.21.044

• 机械学及机器人 • 上一篇    下一篇

多样性保持离散差分进化算法及齿轮传动优化应用*

车林仙1,2   

  1. 1. 重庆工商大学制造装备机构设计与控制重庆市重点实验室 重庆 400067;
    2. 重庆工程职业技术学院机械工程学院 重庆 402260
  • 出版日期:2016-11-05 发布日期:2016-11-05
  • 作者简介:车林仙(通信作者)，男，1971年出生，博士，教授。主要研究方向为机构数值分析与综合、并联机器人机构学、机械优化设计及计算智能等。

    E-mail：lx.che@163.com

  • 基金资助:
    * 重庆市教育委员会科学技术研究计划(KJ1403201)、制造装备机构设计与控制重庆市重点实验室(重庆工商大学)开放基金(611115006)和重庆市基础科学与前沿技术研究专项(cstc2015jcyjA70006)资助项目; 20151110收到初稿，20160630收到修改稿;

Discrete Differential Evolution with Diversity Maintenance Strategies and Its Application in Optimization Design for Gear Transmission

CHE Linxian1,2   

  1. 1. Chongqing Municipal Key Laboratory of Mechanism Design and Control for Manufacturing Equipment， Chongqing Technology and Business University， Chongqing 400067;
    2. School of Mechanical Engineering， Chongqing Vocational Institute of Engineering， Chongqing 402260
  • Online:2016-11-05 Published:2016-11-05

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摘要：

将离散约束优化问题转化为等效约束整数规划问题(Constrained integer programming problem， CIPP)，并应用离散差分进化(Discrete differential evolution， DDE)算法求解这类问题。提出DDE算法种群维分量一致的概念，并揭示种群维分量呈现一致状态将导致进化停滞的缺陷，数值算例仿真结果验证了理论分析的正确性。在引入定量刻画DDE算法种群多样性指标——种群多样度Γ的基础上，提出一种基于种群连续进化停滞代数和Γ监测的种群多样性保持策略，以克服种群维分量一致进化缺陷，进而增强算法全局优化能力。将多样性保持策略嵌入DDE算法，并结合可行性规则约束处理技术，形成求解CIPP的多样性保持离散差分进化算法(DDE algorithm with diversity maintenance strategies， DMDDE)。建立某刮板输送机所用二级斜齿圆柱齿轮传动体积最小化设计的离散约束优化模型，再采用DMDDE算法求解该问题。数值试验表明，DMDDE算法的鲁棒性和收敛精度优于4种对比算法。优化结果明显好于原设计方案，齿轮体积较原设计下降40.8%。

关键词: 差分进化算法, 多样性保持策略, 圆柱齿轮传动, 种群多样度, 离散约束优化

Abstract: A constrained discrete optimization problem is transformed into an equivalent constrained integer programming problem (CIPP) and a discrete differential evolution (DDE) algorithm is employed to solve this problem. The concept of component consistency at the dimensional level is proposed to analysis a population of DDE algorithm. It is revealed that if components at the dimensional level in a population are in a consistent status, it will cause evolutionary stagnation of the population. The simulation results of numerical examples confirm the validity of theoretical analysis. The diversity metricΓ of a population is introduced to depict quantitatively the diversity for a population of DDE algorithm. On this basis, the study presents a maintenance strategy for population diversity based on monitoring the continuous generations of evolutionary stagnation and diversity metricΓ to overcome the stagnant evolutionary defect of a population caused by a component consistency at the dimensional level, and furthermore to enhance the global optimization performance of the algorithm. Thus this work embeds the diversity maintenance strategies in DDE algorithm, adopts feasibility rules to handle constraints, and forms to a DDE algorithm with the diversity maintenance strategy (DMDDE) for solving CIPPs. A constrained discrete optimization model is constructed to formulate the optimal design problem on the minimum volume for a two-stage helical cylindrical gear transmission in a flight conveyer, and DMDDE algorithm is utilized to approach this problem. Numerical experiments indicate that DMDDE algorithm has better performance than four compared algorithms in terms of the robustness and convergence accuracy. Moreover, the obtained result is better than one of the original design scheme and the corresponding volume has decreased by 40.8% compared with that scheme.

Key words: cylindrical gear transmission, differential evolution algorithm, diversity maintenance strategy, population diversity metric, constrained discrete optimization

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