## 5 Computational Results  
To test the performance of the VBIH algorithms proposed, extensive experimental evaluations and comparisons with other powerful methods are provided based on the well-known flowshop benchmark suite of [PERSON] [20]. The benchmark set is composed of 15 groups of the given problems with the size ranging from 20 jobs and 5 machines to 500 jobs and 20 machines, and each group consists of ten instances. However, in [62], these benchmark problems are extended to 200 \(\times\) 5, 500 \(\times\) 5 and 500 \(\times\) 10 sizes with each containing 10 instances. Ultimately, we employ 150 instances as in the DABC_RCT algorithm in [41]. We treat them as blocking flow shop scheduling problems with the total flowtime criterion. In the experimental tests, all algorithms are coded in Visual C++13 and carried out on an Intel(R) Core(TM) i7-2600 CPU with 3.40 GHz PC with 8.00 GB memory. Note that the maximum CPU time is fixed at \(T_{max}=100\times n\times m\) milliseconds for all algorithms compared. We compare to the following best performing algorithms from the literature:  
1. **DABC_RCT in [41]. ** The DABC_RCT algorithm is a very efficient algorithm and has three phases. In the employed bee phase, the TNO procedure is employed with the VLS local search. In the onlooker bee phase, the path-relinking approach is employed to generate the onlooker bees. In the scout bee phase, HPF2 is used to generate the scout bees. We refer to [41] for the details. We have coded the DABC_RCT algorithm in Visual C+13 to have a fair comparison. Note that the DABC_RCT algorithm uses HPF2 heuristic as an initial solution. Since our PFT_NEH(x) heuristic is substantially better than HPF2 heuristic, we employ the PFT_NEH(x) heuristic with \(\mu=0.35\) and \(\delta=15\) as one of the solution in the population. The rest of the population individuals are constructed randomly as suggested in the DABC_RCT algorithm and we denote it as the DABC_RCT algorithm to have a fair comparison. The same parameters are also used which are suggested in the DABC_RCT algorithm [41]. Note that fast fitness calculation is employed to accelerate the insertion and swap neighborhood structures in the VLS local search they employed in the TNO procedure. Figure 11: Interaction plot. IG_RIS algorithm in [47; 54; 55; 56; 57; 58; 59]. To be fair again, we employ PFT_NEH(x) heuristic with \(\mu=0.35\) and \(\delta=15\) as an initial solution in the IG_RIS algorithm. IG_RIS algorithm relies on the destruction and construction procedure, where \(dS\) number of jobs is removed from a solution and they are reinserted to the partial solution sequentially. Then RIS local search is applied to the solution obtained after destruction and construction procedure. Note that fast fitness calculation is employed to accelerate the RIS insertion local search as in this paper. It is also employed in the destruction and construction procedure, too. 3. **VBIH algorithms in this paper. ** Since the PFT_NEH(x) heuristics provide very diversified initial solutions, we run the VBIH algorithm with \(\mu\) values with 0.25, 0.30, 0.35, 0.40, 0.55 and 0.60 with \(\delta=15\). Then we denote them as VBIH1, VBIH2, VBIH3, VBIH4, VBIH5 and VBIH6. In addition, when the maximum block size is equal to 1, the VBIH algorithm becomes an iterated local search. In other words, the current solution is perturbed with several insertion moves and then the VLS local search is applied to the solution after perturbation. Then, the acceptance criterion is imposed to the solution obtained. We denote this variant of the VBIH algorithm as IVLS algorithm. Each instance is run for five (R) independent replications and the relative percentage deviation. RPD is computed as follows: \[ARPD=\sum_{i=1}^{R}\left(\frac{H-BKS}{BKS}\right)*100/R\] (13) where \(H,\ BKS,\ and\ R\) are the total flowtime value generated by the algorithms in each run, the most recent best-known solution value reported in [41], and the number of runs, respectively.