## 1 Introduction  
There have been extensive studies about permutation flowshop scheduling (PFSP) in the literature with many important applications in manufacturing and service systems [1; 2; 3; 4]. The traditional PFSP is concerned with scheduling \(n\) jobs through \(m\) machines in such a way that the same sequence is applied to each machine. An important assumption is such that work-in-process inventory is allowed since there are infinite buffer capacities amongst consecutive machines. Hence, allowing jobs to be waiting in front of machines for their next operations words. On the other hand, if any storage capacity amongst machines is not available, the traditional PFSP is said to be blocking flowshop scheduling problem (BFSF) [5]. In this case, a job cannot leave the machine unless the next machine is free. Its industrial applications can be found in [5; 6]. A comprehensive review on flowshop scheduling with blocking and no-wait constraint can be found in [PERSON] and [PERSON] [7]. The makespan criterion for the BFSP is commonly used in the literature. This problem is also denoted as \(F_{m}/blocking/C_{max}\) with the notation of [PERSON] et al. [8] in the literature. Although [PERSON]'s algorithm [9] can solve it optimally with two machine case (\(m=2\)), it is proven to be NP-Hard by [PERSON] and [PERSON] [7] when \(m>2\). For this reason, efforts have been devoted on developing heuristic and meta-heuristic approaches for scheduling a large number of jobs, which is commonly needed for real-life problems. Since the problem is NP-Hard, constructive heuristics and meta-heuristic algorithms have been attracted attention to solve the BFSP with the makespan criterion. Regarding the constructive heuristics, [PERSON] et al. [10] presented a profile fitting (PF) heuristic to solve BFSP with the performance measure of minimization of cycle time. The PF heuristic greedily establishes a sequence with the next job having minimum idle and blocking times on machines. [PERSON] [11] presented a similar heuristic for flowshop scheduling problems with finite and unlimited buffers in order to maximize the buffer usages and to minimize the machine blocking times. However, it was not able to obtain better results than the NEH heuristic, which is initially proposed in [12] to solve the traditional PFSP. Depending on the makespan properties defined by [PERSON] and [PERSON] [13], [PERSON] [6] presented a note on constructive heuristics and proposed three constructive heuristics, called MM, MM combined with NEH (MME), and PF combined with NEH (PFE), respectively for the BFSP with the makespan criterion. It was shown that the MME and PFE heuristics generated better results than the NEH heuristics up to 500 jobs and 20 machines. [PERSON] et al. [14] proposed an improvement heuristic to minimize cycle time and [PERSON] and [PERSON] [15] considered the minimization of total tardiness in a flowshop with blocking and presented some constructive heuristics with promising results. Furthermore, [PERSON] and [PERSON] [16] developed some effective heuristics based on PF approach. These PF-based heuristics are inspired from LR heuristic proposed by [PERSON] and [PERSON] [17] for the PFSP with the total flowtime criterion. In their work, the PF heuristic is combined with the partial NEH implementation and they called the heuristics as PF_NEH(x), WPF_NEH(x) and PW_NEH(x), where \(x\) is the number of sequences generated by considering the first \(x\) number of jobs in the initial order of jobs. In order not to ruin good characteristics of the PF heuristic, the NEH heuristic is applied to only the last \(\delta\) jobs. Their PW_NEH(x) heuristic with \(x=5\) was substantially better than NEH, MME, PFE, WPFE and PWE heuristics from the literature. Regarding the meta-heuristic algorithms for BFSP with the makespan criterion, the literature can be found in [18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29; 30; 31; 32; 33].