Due to the NP-hard nature, the permutation flowshop scheduling problem (PFSSP) is a fundamental issue for Industry 4.0, especially under higher productivity, efficiency, and self-managing systems. This paper proposes an improved genetic-shuffled frog-leaping algorithm (IGSFLA) to solve the permutation flowshop scheduling problem. In the proposed IGSFLA, the optimal initial frog (individual) in the initialized group is generated according to the heuristic optimal-insert method with fitness constrain. The crossover mechanism is applied to both the subgroup and the global group to avoid the local optimal solutions and accelerate the evolution. To evolve the frogs with the same optimal fitness more outstanding, the disturbance mechanism is applied to obtain the optimal frog of the whole group at the initialization step and the optimal frog of the subgroup at the searching step. The mathematical model of PFSSP is established with the minimum production cycle (makespan) as the objective function, the fitness of frog is given, and the IGSFLA-based PFSSP is proposed. Experimental results have been given and analyzed, showing that IGSFLA not only provides the optimal scheduling performance but also converges effectively.

中文翻译：

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排列流水车间调度的改进遗传改组蛙跳算法

由于具有NP难性，所以排列流水车间调度问题（PFSSP）是工业4.0的基本问题，尤其是在更高的生产率，效率和自我管理系统下。提出了一种改进的遗传改组蛙跳算法（IGSFLA）来解决置换流水车间调度问题。在提出的IGSFLA中，根据启发式最优插入方法（具有适应性约束），生成了初始组中的最佳初始青蛙（个体）。交叉机制同时应用于子组和全局组，以避免局部最优解并加速进化。为了使具有最佳适应性的青蛙进化得更加出色，应用扰动机制在初始化步骤获得整个组的最优青蛙，在搜索步骤获得子组的最优青蛙。以最小生产周期（makespan）为目标函数建立了PFSSP的数学模型，给出了青蛙的适应度，并提出了基于IGSFLA的PFSSP。给出并分析了实验结果，表明IGSFLA不仅提供了最佳的调度性能，而且有效地收敛了。