中文摘要：

针对产品族设计中平台通用性与实例产品性能的平衡问题，在分析可调节平台产品开发特点的基础上，基于多平台产品族设计空间的二维染色体表达方式，提出了混合协同进化的产品族优化设计方法。将通用性与设计变量种群的进化分别放入主一附两个相关过程，主过程使用第二代非支配排序遗传算法求解平台通用性与产品性能的Pareto前沿，附过程使用粒子群优化算法，以并行方式搜索每个通用性等级下满足约束的产品族优化方案，避免了两类种群同步进化带来的数据扰动问题。通用性种群对设计变量种群施加约束，保证二者变量共享的一致性。通过单相异步电动机产品族优化设计实例，验证了优化方法与算法的有效性。

英文摘要：

To deal with the tradeoff between platform commonality and instance products performances in product family design, characteristics of products using scalable platform development strategy were analyzed. Then, based on the two-dimensional chromosome representation scheme of multi-platform design space, a hybrid co-evolutionary optimization method for scale-based product family was proposed. Evolutions of commonality and design variable populations were run in relevant master-slave processes. The Pareto front between commonality and performance was calculated by Non-dominated Sorting Genetic Algorithm Ⅱ （NSGA-Ⅱ） in the master process. And the product family variable configuration under each commonality level was optimized by Particle Swarm Optimization （PSO） algorithm in parallel in the slave process so as to avoid the data disturbance in synchronous evolution. Constraints were exerted on all variable swarms by the commonality population to guarantee the parameters sharing consistency. Finally, the feasibility and effectiveness of proposed approach were demonstrated by a case of optimizing a family of three capacitor-run single-phase induction motors.