## 1 Introduction
In addition, in [7] the authors studied the PFSP with makespan and proposed a tie-breaking mechanism for the IG algorithm, while in [8] an IG and a discrete differential evolution algorithm were proposed and compared. In this study, we employ new hard VRF instances which are first introduced in [9], and they also applied an IG algorithm. In addition, the same problem was studied in [10] to minimize the makespan over [PERSON]'s benchmark suite. The IG algorithm was applied to various variants of PFSP such as no-wait flow shops in [11; 12; 13]; blocking flow shops in [14; 15; 16; 17]; no-idle flow shops in [18; 19; 20]; energy-efficient PFSP in [21; 22]; multi-objective PFSP in [23; 24] where both studies presented a restarted iterated Pareto greedy algorithm. In a no-wait variant of PFSP, distributed no-wait flow shop problem [11], tabu-based reconstruction strategy [12], and sequence depended setup times [13] were employed with IG algorithm. In blocking variant of PFSP, IG algorithms were combined with local search algorithms [14], constructive heuristics [15; 16], and also embedded in differential evolution framework [17]. In [25] profile fitting and NEH heuristic algorithms were proposed for the same problem. In a no-idle variant of PFSP, iterated reference greedy algorithm [18], and variable IG algorithm [19] were presented. In addition, IG algorithm was employed for the mixed no-idle PFSP [20]. IG algorithm was also applied to PFSP with different objective functions such as total tardiness criterion [26; 27]; total flowtime criterion [28]. In [1], they carried out an exhaustive review and computational evaluation of heuristics and metaheuristics published until 2017 for the PFSP to minimize the makespan. Therefore, for the further analysis of the literature of PFSP, the indicated manuscript [1] should be examined. In traditional search algorithms, swap and insertion neighborhood structures are generally employed. The swap neighborhood exchanges two jobs in a solution, whereas the insertion one removes a job from a solution and inserts it into another position in the solution. Recently, block move-based local search algorithms are presented for the single machine-scheduling problems in the literature [29; 30; 31; 32]. [PERSON] et al. [31] developed a _Block Move_ neighborhood structure in which \(l\) consecutive jobs (called a block) are inserted into another position in the solution. They represent a block move by a _triplet_\((i,\ k,\ l)\), where \(i\) denotes the position of the first job of the block, \(k\) the target position of the block to be inserted and \(l\) the size of the block. It is obvious that one edge insertion, two edge-insertion and 3-block insertion are the block move neighborhoods with \(l=1\), \(l=2\), and \(l=3\). Similarly, [PERSON] and [PERSON] [32] developed a variable neighborhood descent algorithm with three distinct block move neighborhoods and employed in a memetic algorithm. Then, a memetic algorithm with block insertion heuristic is presented in [29]. Moreover, in [33], a variable block insertion heuristic (VBIH) algorithm was employed to solve the blocking PFSP with makespan criterion. In IG algorithms, some solutions components are removed from the current solution and reinserted into the partial solutions. In other words, a number, \(dS\), of jobs are removed randomly, which is known as the destruction phase. Then, in the construction phase, these \(dS\) jobs are reinserted into the partial solution in the same order they are removed. For each of \(dS\) jobs, it makes a number \(n-dS+1\) of insertions. However, the VBIH algorithm removes a block of jobs \(\pi_{b}\) with size \(b\) from the current solution and it makes a number \(n-b+1\) of block insertions only. That is the difference between IG and VBIH algorithms. The main contributions of the paper can be outlined as follows. VBIH is employed to solve PFSP with makespan criterion using the new hard VRF benchmark sets [9].