为解决云制造系统的同类型多任务调度问题，建立了该问题的数学模型，提出了一种离散粒子群遗传混合算法，以所有任务的总完成时间及成本最优为目标进行求解 . 该算法采用整数编码方法建立粒子的位置矢量与服务分配的映射关系，在采用标准粒子群算法更新粒子位置时，引入了遗传算法的交叉和变异操作思想，使用 4 种方法按条件“逐级叠加”的方式对粒子位置进行更新，以保证种群的多样性 . 算例仿真结果表明，该算法是有效的且具有较高的执行效率 .

In order to implement the scheduling of multiple tasks with the same type in cloud manufacturing systems, a mathematical model is established and is solved by using a discrete particle swarm-genetic hybrid algorithm with two objectives, namely the least total completing time and the least cost of all tasks being considered simultaneously. The hybrid algorithm employs integer coding method to establish the mapping between particle location matrix and service allocation scheme, and introduces the crossover and mutation idea of genetic algorithm to update particle swarm position with four formulas being conditionally used in a progressive and overlaying way, and thus the diversity of groups is ensured effectively. Simulated results indicate that the proposed algorithm is of high effectiveness and execution efficiency.