The goal of this research is to accelerate improvement heuristics which use a graph to model the system and calculates the makespan, i.e., longest path in the graph, during each iteration. These heuristics iteratively perturb the graph and recalculate the makespan in each iteration until a satisfactory schedule is determined. We propose Improved Structural Perturbation Algorithm (ISPA) to accelerate the calculation of the length of the longest path in the graph in each iteration. This will decrease the overall computation time of these scheduling improvement heuristics. Scheduling perturbations are represented by structural perturbations of the graph (edge additions and deletions). ISPA partitions nodes in the graph into two types of sets and applies two different processes to calculate the effects of the perturbations depending on the set the node was in. The major contribution of this study is that ISPA executes once to update the length of the longest path regardless of the number of added and deleted edges. This results in a more efficient algorithm in terms of time complexity than previous algorithms. To show this performance improvement, an experiment was performed applying ISPA to a Simulated Annealing (SA) heuristic and compare it with applying the commonly used Standard Longest Path Algorithm (SLPA) and two other existing methods to the SA heuristic. The experiment shows that ISPA outperforms existing methods in all cases. Moreover, for these SA problems, ISPA saved 9%-65% of the execution time compared to SLPA for the job-shop scheduling problems. The time savings increase with size (number of nodes) of the problem. ISPA is applicable to other iterative heuristics, such as Tabu-search, Genetic Algorithms, and Shifting Bottleneck.

这项研究的目的是加速改进启发式试验，该启发式试验使用图形对系统进行建模并在每次迭代过程中计算makepan（即图形中的最长路径）。这些启发式方法会迭代扰动图形，并在每次迭代中重新计算有效期，直到确定满意的计划为止。我们提出了改进的结构扰动算法（ISPA）来加速。   在每次迭代中计算图中最长路径的长度。这将减少这些调度改进试探法的总体计算时间。调度扰动由图的结构扰动（边添加和删除）表示。ISPA将图中的节点划分为两种类型的集合，并根据节点所在的集合应用两个不同的过程来计算扰动的影响。这项研究的主要贡献在于，ISPA执行一次以更新最长的长度路径，无论添加和删除边的数量如何。就时间复杂度而言，这导致比以前的算法更有效的算法。为了显示这种性能改善，进行了将ISPA应用于模拟退火（SA）的实验启发式方法，并将其与将常用的标准最长路径算法（SLPA）和其他两种现有方法应用于SA启发式方法进行比较。实验表明，在所有情况下，ISPA均优于现有方法。 此外，对于这些SA问题，与SLPA相比，与车间作业调度问题相比，ISPA节省了9％-65％的执行时间。节省的时间随着问题的大小（节点数）而增加。ISPA适用于其他迭代启发法，例如禁忌搜索，遗传算法和转移瓶颈。