## 1 Introduction  
Scheduling problems such distribution, transportation, management, construction, engineering and manufacturing, are omnipresent in real-world applications [1]. These scheduling problems are complex and very difficult to solve using conventional techniques. The complexity of these scheduling problems arises due to the presence of a large number of constraints. Due to these reasons, there was ample research conducted in the past few decades that focused on developing different techniques for the optimization of these scheduling problems. Permutation flow-shop scheduling problem (PFSSP), a variation of the classical flow-shop scheduling problem (FSSP), is a problem in operation research in which n ideal jobs, J1, J2,..., Jn, of varying processing times are assigned to m resources (usually machines). The objective is to allocate the available resources to the jobs to maximize (or minimize) performance indicators, such as makespan, tardiness, etc. In classical FSSP, for n jobs on m machines, there are (n! )m different alternatives for sequencing jobs on machines, while in permutation problems, the search space is reduced to n!. Like any scheduling problem, there are constraints and assumptions associated with PFSSP. In this paper, these constraints and assumptions are as follows. 1. On the shop floor, all machines are independent from each other. 2. The operation of all jobs have deterministic processing times. 3. No pre-emption of job operation is permitted. * The set-up times are not considered in these problems. * No machine down-time or maintenance time is considered. * The machine used for each operation of a job is known and fixed. * A job cannot revisit a machine group for more than one operation. * Operation constraints must always be followed. * All jobs must enter the machines in the same order. Since PFSSP are commonly encountered in various industries, researchers developed many methods to optimize the key performance indicators (KPIs) of PFSSP. [PERSON] and [PERSON] (2018) used a hybrid discrete artificial bee colony algorithm for minimizing the makespan in PFSSP. They utilized Greedy Randomized Adaptive Search Procedure (GRASP) to create the initial population and operators such as insert, swap, path relinking to generate new solutions. The authors also improved the local search by further optimizing the best solution. When applied to PFFP, their algorithm had superior performance compared to other algorithms like particle sawm optimization (PSO) algorithm, hybrid GA (HGA), etc. [PERSON] et al. (2018) combined decision tree (DT) and scatter search (SS) algorithms to solve PFSSP. DT was used initially to convert the problem into a tree structure using the entropy function, followed by SS, to do an extensive investigation of the solution space. Simulation results and statistical test comparisons showed the advantage of the authors' proposed algorithm. [PERSON] (2018) proposed two algorithms for solving PFSSP. (1) A constructive greedy heuristic (CG) and (2) stochastic greedy heuristic (SG). The CG was based on a greedy selection, while the SG was a modified version of CG with iterative stochastic start. The authors validated the proposed algorithms by using them to solve benchmark problems, and the results showed that the algorithm was able to come within 6% of the best-known solution. [PERSON] et al. (2018) created a hybrid algorithm by combining greedy heuristic, GA, and variable neighborhood search (VNS) algorithm. The hybrid algorithm was able to take advantage of both GA and VNS, and obtain the best-known makespan for the benchmark problems in a short computational time. [PERSON] et al. (2018) proposed an enhanced GA to solve the distributed assembly permutation flow shop scheduling problems (DAPFSP). The authors used a greedy mating pool to select better candidates. They also updated the crossover strategy and incorporated local search strategies to improve local convergence. [PERSON] et al.