Permutation flow shop scheduling problem with makespan criterion is known to be NP-hard if the number of machines is greater than two. The most known polynomial complexity algorithm for solving PFSP is the constructive NEH heuristic. In this paper we propose the N-NEH+ algorithm which extends the classical NEH heuristic and which is, to our best knowledge, the first deterministic constructive algorithm that can produce a family of solutions having equal quality. The main idea of the N-NEH+ algorithm is to use a list (called N-list) of N jobs to be candidates for partial sequencing. The results of the extensive numerical experiments confirm that the N-list technique performs well in improving the NEH heuristic. Moreover, the proposed approach can be easily adapted for a multi-core processing environment, which is very difficult with other constructive algorithms. Another advantage of the proposed technique is that it can be used to improve many other algorithms for solving permutation flow shop problems.

如果机器数量大于2，则具有makepan准则的置换流水车间调度问题被认为是NP难的。用于求解PFSP的最著名的多项式复杂度算法是构造性NEH启发式算法。在本文中，我们提出了一种N -NEH +算法，该算法扩展了经典的NEH启发式算法，并且据我们所知，它是第一个可以产生具有相同质量的解的确定性构造算法。N -NEH +算法的主要思想是使用N个作业的列表（称为N -list）作为部分排序的候选对象。大量数值实验的结果证实了N列表技术在改善NEH启发式方法方面表现良好。而且，所提出的方法可以容易地适用于多核处理环境，这对于其他构造算法来说是非常困难的。所提出的技术的另一个优点是，它可以用于改进许多其他算法来解决置换流水车间问题。