圆柱齿轮传动多目标优化的差分进化算法

Differential Evolution Algorithm of Multiobjective Optimization for Cylindrical Gear Transmission

针对单级斜齿圆柱齿轮传动机构优化设计问题,建立以体积最小化和重合度最大化为目标的约束多目标优化模型。为提高Pareto前沿的分布均匀性和分布广度,将网格Pareto占优技术与约束多目标差分进化算法结合,设计网格占优约束多目标差分进化算法(ε-CMODE)。根据工程实践需要,将离散约束多目标优化模型映射为约束非负整数规划问题,再改进ε-CMODE算法以求解该模型。最后,给出优化设计实例。结果表明,ε-CMODE算法能有效求解齿轮机构多目标优化问题,得到均匀分布的Pareto前沿,可为设计人员提供多组备选解。

A constrained multiobjective optimization （CMOP） model is constructed to formulate the optimal design problem on the minimum volume and maximum contact ratio for a single - stage helical cylindrical gear transmission mechanism. To enhance the distribution uniformity and spread of Pareto fronts, an ε - grid domination based con- strained multiobjective differential evolution （ε - CMODE） algorithm which integrates the grid- based Pareto dominat- ed technique and the constrained multiobjective differential evolution algorithm is presented to form a hybrid algorithm. The constrained discrete multiobjective optimization model is transformed into a constrained non - negativeinteger pro- gramming （CNIP） problem which is satisfied with requires of engineering practice. Furthermore, the s - CMODE algo- rithm is improved to solve the CNIP problem. Finally, a real case of optimization design is employed to indicate that this algorithm is able to solve the CMOP problem of gear mechanism and to obtain Pareto fronts with uniform distribution. And the corresponding Pareto optimal solutions may be decided by designers as alternative solutions.