## 5 Instance Calculation  
To verify the practical application value of the BWOA based on the investigation of the pipeline processing situation in the ship pipeline-processing workshop of a large shipyard in Guangxi, Table 3 was appropriately scaled and generated to solve the production-scheduling problem of the company's pipeline-processing workshop. The actual description was as follows: multiple sets of pipelines had to go through [5; 6] processing steps (i.e., namely cutting, bending, calibration, welding, cleaning and polishing, and pump-pressure testing). The number of parallel machines for each step was 2; that is, the machine sequence numbers were 1 to 12 in sequence. The total number of pipe fittings was \(N\in[10,200]\). For each workpiece's process, the fuzzy processing time \(\bar{P}_{ijk}=(P_{ijk}^{1},P_{ijk}^{2},P_{ijk}^{3})\) of the corresponding equipment indicates that the machine could not process the corresponding process. The fuzzy processing schedule was determined by the factory technical personnel based on simulation data and the actual operating experience of the workshop operator. Figure 5: Partial mapping cross schematic diagram of the algorithm. Figure 6: Priority protection cross schematic diagram. The set parameters for BWOA were as follows: The population size was set to 100; the maximum iteration count, 3000; the reproduction rate, 0.8; the mutation rate, 0.2; and the cannibalism rate, 0.2. Set parameters for the GA were as follows: The population size was set to 100; the maximum number of iterations, 3000; the reproduction rate, 0.8; and the mutation rate, 0.2. We ran each 20 times, recorded the five better feasible solutions, and then compared them with the solutions provided by experienced dispatchers in the factory. Table 4 shows the results of BWOA and GA, as well as the comparison of the solutions provided by dispatchers. The improved BWOA iteration process is shown in Figure 7.  
Decoding the optimal feasible solution (411, 466, 518) obtained from BWOA in the table, we present the fuzzy Gantt chart of the scheduling scheme in Figure 8.  
The optimal pipeline production scheduling scheme after BWOA calculation can be obtained from Figure 8, and the scheduling results are explained here due to the excellent scheduling scheme, high utilisation of processing machines and dense data. In the pipeline processing workshop of this shipyard, take the processing flow of pipe fittings 1 (blue) as an example: firstly, the fuzzy start time of the first process of pipe fittings 1 is moment 0, that is, the process can be scheduled to be processed on \(M_{1}\) at moment 0, and the fuzzy completion time of the first process on \(M_{1}\) is (88, 99, 106). After the first process is completed, the second process of tubing 1 is processed on \(M_{4}\), which has a fuzzy start time of (112, 129, 148) and a fuzzy finish time of (184, 213, 246), the third process is processed on \(M_{5}\), which has a fuzzy start time of (203, 225, 258) and a fuzzy finish time of (253, 279, 323), and the fourth process is processed on the process is machined on \(M_{8}\) with a fuzzy start time of (248, 285, 319) and a fuzzy finish time of (280, 324, 365), the fifth process is machined on \(M_{9}\) with a fuzzy start time of (280, 324, 365) and a fuzzy finish time of (355, 408, 457), the sixth process is machined on \(M_{12}\) with a fuzzy start time of (355, 408, 457) and fuzzy completion time is (377, 434, 486). It can be seen that this allocation scheme fully utilized the production resources of each machine, reduced the fuzzy completion time from (628, 709, 791) to the optimal value (411, 466, 518), and significantly improved production efficiency. Experiments also showed