## 1 Introduction  
Sustainability in manufacturing industries is mainly measured by their competitiveness in the market place. Competitiveness is referred to timely product delivery with the best quality, minimum manufacturing time and price to customers. Minimum manufacturing time can be obtained by optimal production sequences that can minimize makespan or total flowtime. Note that a manufacturing company can fail to satisfy production plans although the other production entities such as operators, maintenance, inventory, quality control, etc. are in control due to the lack of optimal or near optimal production sequences in the shop floor. For this reason, seeking optimal or near-optimal production sequences and schedules is vital to manufacturing companies in order to minimize the makespan, which also minimizes idle times on the machines and maximize machine utilization. The permutation flow shop scheduling problem (PFSP) has been widely studied in the literature and has extensively been applied in the inustry. There are many different fields in real-life where PFSP can be used [1]. It is yet an exceptionally active topic of investigation, especially because flow shop environments are at the center of real-life scheduling problems in various fields of high social or economic impact. In addition, the flow shop layout is a regular configuration in many manufacturing companies. The basic PFSP consists of a set of \(n\) jobs which are processed by \(m\) machines. These jobs follow the same route and their operations on the machines cannot be interrupted. All the jobs must be processed in the same order on the machines and the aim is to find the best permutation \(\pi=\{\pi_{1},\pi_{2},\ldots,\pi_{n}\}\) of these jobs with respect to the given objective. In this study, our aim is to maximize the throughput of the system by maximizing the utilization rate of the machines which means minimizing makespan. To compute the makespan, \(\pi\) denotes the given arbitrary solution, where job \(\pi_{i}\) is the job at the \(i\)th position of solution \(\pi\). \(C_{i,k}\) is denoted as the completion time of job \(\pi_{i}\) on machine \(k\) at position \(i\). Following this notation, completion times of jobs at each machine are computed as in the following Equations (1)-(5), where \(p_{\pi_{i},k}\) is the processing time of job \(\pi_{i}\) at the \(k\)th machine. The makespan of solution \(\pi\), denoted as \(C_{max}(\pi)\), is the completion time of the last job (i.e., \(n\)) on the last machine (i.e., \(m\)). It is simply denoted as \(C_{nm}\) and calculated as follows:  
\[C_{1,1}=p_{\pi_{1},1} \tag{1}\]  
\[C_{i,1}=C_{i-1,1}+p_{\pi_{i},1}\forall i=2,\ldots,n \tag{2}\]  
\[C_{1,k}=C_{1,k-1}+p_{\pi_{1},k}\forall k=2,\ldots,m \tag{3}\]  
\[C_{i,k}=max\big{\{}C_{i-1,k},\ C_{i,k-1}\big{\}}+p_{\pi_{i},k}\forall i=2, \ldots,n;\forall k=2,\ldots,m \tag{4}\]  
\[C_{max}(\pi)=C_{nm}. \tag{5}\]  
The PFSP with makespan criterion is denoted as \(Fm|Perm|Cmax\) according to the notation of [2] and has been proven to be NP-hard for the makespan criterion [3], so it is challenging to solve it with exact methods. Therefore, metaheuristic algorithms were employed to solve the problem and obtain near-optimal solutions. In recent years, various metaheuristic algorithms have been presented to solve various variants of PFSP with different objectives. One of the state-of-the-art algorithms for PFSPs is the iterated greedy algorithm (IG) presented by [4]. We focused on the recent literature that considers the IG algorithm in their solution approaches. The IG algorithm was employed to PFSP with makespan criterion in [4; 5; 6; 7; 8; 9]. In [5], to improve the solution quality, a local search was applied to the partial solution after the destruction step of the IG algorithm, while in [6] sequence depended setup times were employed for the PFSP with makespan criterion.