Abstract: Aiming at the constrained discrete optimization of a gear train featuring a large solution space with a narrow feasible region，two new strategies based on Particle Swarm Optimizer （PSO） are introduced to deal with constraints and discrete variables.In order to reduce the number of algorithm parameters，the formula of updating particle’s velocity in normal PSO is also modified.Then，the algorithm is applied to the discrete optimization problem.Compared with the approaches in the relative literature，the success rate of the algorithm to find feasible solutions is higher，and at the same time it obtained better “best” solutions and mean result without either requiring transformation of the problem or reliance on the designer’s interaction.The results show that the algorithm is simple and easy to implement yet effective，and it have an important reference value to the solving of similar optimal design problems.

Key words: Particle Swarm Optimizer（PSO）, discrete variable, feasible region, optimal design, gear train

摘要： 针对一个离散变量齿轮系优化设计问题搜索空间大、可行域狭小的特点，基于粒子群算法提出了新的约束与离散变量处理策略。另外，修改粒子群算法的速度更新公式以减少算法参数数目。与有关文献相比，所采用的算法应用于该优化问题时，不但发现可行解的成功率高，而且获得了更好的“最优”可行解和平均结果。与此同时，该算法不要求对该问题进行任何转化，也不依赖于人机交互。结果表明，该算法简单、易行、有效，对于类似优化设计问题的求解很有参考价值。

关键词: 粒子群算法, 离散变量, 可行域, 优化设计, 齿轮系