Performance Comparison of Three Hybridization Categories to Solve Multi-Objective Flow Shop Scheduling Problem

The industries must preserve a rate of constant productivity; however, weaknesses appear at the level of production system which engenders high manufacturing costs. Scheduling is considered the most significant issue in the production system, the solution to that problem need complex methods to solve it. The goal of this paper is to establish three hybridization categories of the evolutionary methods ABC and PSO to solve multi-objective flow shop scheduling problem: Synchronous parallel hybridization using the weighted sum method of the fitness function, sequential hybridization using or not using the weighted sum method of the fitness function, and asynchronous parallel hybridization using the weighted sum method of the fitness function. Then to test these methods in an automotive multi-objective flow shop and to perform an in-depth comparison for verifying how the multi hybridization and the hybridization categories influence the resolution of multiobjective flow shop scheduling problems. The results are consistent with other studies that have shown that the multi hybridization improve the effectiveness of the algorithm. Keywords—Scheduling; multi-objective; flow shop; multi hybridization; artificial bee colony ABC; particle swarm optimization PSO


I. INTRODUCTION
The objectives of companies are diversified and the scheduling became multi-criterion. The scheduling objective are related to the time or the resources or the cost.
The scheduling problem in the production system is a accomplishment of a tasks group by taking in consideration some constraints.
The hybrid metaheuristics are proposed by Talbi [1] and are classified in three classification [2]: • Synchronous parallel hybridization consists of incorporating an approach in an operator of another approach.
• Sequential hybridization is composed by various approaches, the solution of the first approach is an initialization of the next approach.
• Asynchronous parallel hybridization, the hybrid approaches share data throughout the search process.
In the flow shop scheduling problem, every machine can make only a single operation simultaneously and every job can have just a single operation in progress at the same instant. The capacity of storage inter-machines is defined and the preemption of operations is not approved.
However, to the authors' knowledge, very few publications are available in the literature that performed an in-depth comparison for verifying how the multi hybridization and the hybridization categories influence the resolution of multiobjective flow shop scheduling problem.
The objective of this paper is as follows: • To establish three hybridization categories of the evolutionary methods ABC and PSO to solve multiobjective flow shop scheduling problem: Synchronous parallel hybridization using the weighted sum method of the fitness function, sequential hybridization using or not using the weighted sum method of the fitness function, and asynchronous parallel hybridization using the weighted sum method of the fitness function.
*corresponding Author 680 | P a g e www.ijacsa.thesai.org • To make tests of these methods in an automotive multiobjective flow shop.
• To perform an in-depth comparison for verifying how the multi hybridization and the hybridization categories influence the resolution of multi-objective flow shop scheduling problems.
The rest of the paper is organized as follows: the fundamentals of ABC and PSO will be explained in Section 2. In Section 3, the authors described the implementation of the proposed methods. The results and discussion are explained in section 4. In Section 5, the conclusion and perspectives for further research are presented.

A. Fundamentals of Artificial Bee Colony Algorithm
The artificial bee colony ABC algorithm is one of the most newly added swarm-based algorithms. ABC method created by Karaboga, it was copied the intelligent foraging behavior observed in the domestic bees to take the process of foraging [26].
ABC technique was produced for optimization problems in the continuous field. Recently, it was further enlarged for optimization problems in the discrete area [27] [28] [29] [30] [31].
A complete review of the utilization of ABC algorithm can be found in [32].
Four phases make ABC: Initialization bee phase, employed bees phase associate with particular food sources, onlooker bees phase look at the dance of engaged bees within the hive to choose a food source, and scout bees phase search randomly food sources.
In the ABC algorithm, the position of a food source corresponds to a possible feasible solution to the studied problem, and the nectar amount of a food source design the fitness of the solution.
The ABC algorithm merges techniques of local search and global search, trying to balance between the exploration and the exploitation of the search zone.
The main steps of the ABC method are as follows: Initialization Phase (Initialize Population) REPEAT Employed Bees Phase (Put the employed bees on their food sources) Onlooker Bees Phase (Put the onlooker bees on the food sources according to their nectar amounts) Scout Bees Phase (Send the scouts to the search zone for exploring new food sources) Record the best food source attained so far UNTIL requirements are met

B. Fundamentals of Particle Swarm Optimization
Particle Swarm Optimization PSO technique is a popular swarm-intelligence-based algorithm that optimizes a problem using an approach that is motivated by the movements of schooling of fishes or a flock of birds.
It was founded by Eberhart and Kennedy in 1995 [33] and has received significant attention from researchers studying in several research fields and has been successfully employed to many optimization problems since then [34] [35] [36].
The candidate solutions of a studied problem are designed as particles that form a population. The location of each particle is determined with two swarm main characteristics: the particle's position and velocity. The position of a particle represents a specific solution to the studied problem, while velocity is employed to define the direction of the particle in the next iteration.
Two reference values manage the movement of a particle throughout the iterations: The best fitness value obtained by the particle and the best fitness value of the swarm registered so far. The PSO has a memory that deposits the best fitness value of all particles achieved so far, and the corresponding position.
Applying these principles, improvement is accomplished and the PSO is conducted to the optimal solution.
The main steps of PSO are as follows: Randomly generate the initial population and the velocities Repeat Determine the best values of particles in the swarm Change the best particles in the swarm Determine the best particle Update the velocities of particles Update the particle position Until requirements are met

C. The Proposed Methods
The ABC has a high capacity to explore the global optimum who it is not immediately employed, because the ABC stocks it at each iteration, on the other hand, the PSO can immediately employ the global best solution at iteration.
To obtain a better-performing method that exploits and combines advantages of these algorithms, the proposed hybridization between the ABC and PSO is applied.
The proposed hybrid metaheuristics are developed in threehybridization categories: Synchronous parallel hybridization, sequential hybridization and asynchronous parallel hybridization.

1) Synchronous parallel multiple hybridization of ABC with PSO:
The authors developed a new approach of synchronous parallel hybridization of ABC and PSO called HABCPSO. This approach consists to employ in the employed bees phase or/and in the onlooker bees phase or/and in the scout bees phase, the position and the velocity updating process, the Table I shown the configuration of the HABCPSO methods.
Consequently, the procedure of HABCPSO2 and HABCPSO3 can be found in Fig. 1 and Fig. 2  The fitness function F minimized in HABCPSO corresponds to the balanced sum of both objectives functions F1 and F2, with weights ß1 and ß2 defined as follows:

1) Sequential hybridization of ABC with PSO:
The proposed hybrid methods, denoted as [ABC+PSO](F) and ABC(F1)+PSO(F2), are founded on the recombination of two procedures ABC and PSO. The PSO is applied after the ABC.
PSO has used the output of the previous as its inputs, there are acting in a pipeline way.

3) Asynchronous parallel hybridization of ABC with PSO:
The proposed hybrid method denoted as ABC//PSO is founded on the recombination of two procedures ABC and PSO, this share and exchange information throughout the search process. The procedures of ABC//PSO algorithm are illustrated in Fig. 5.
The fitness function F minimized in ABC//PSO corresponds to the balanced sum of both objectives functions F1 and F2, with weights ß1 and ß2 defined by the function 1.

III. RESULTS AND DISCUSSION
Authors are suggested to solve the multi-objective scheduling problem in the automotive company. This company produces automotive parts in different elastomeric materials, including silicone and TPE.
The automotive company workshop is a flow shop contains 17 production lines, each line is composed with seven workstations: • M1: The injection machine.
• M7: The inspection workstation of the finished product.
The real result of scheduling obtained from the production planner is shown in Table II. 683 | P a g e www.ijacsa.thesai.org (IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 12, No. 4, 2021 Several operations of cleaning and tools change or parameter adjustment are managed in the workstations, parallelly with the production operations.
Dates are calculated from an initial time t0, and the time unit is expressed in minute.
The fitness function of total production cost is denoted F1 and the fitness function of the stopping cost and the cost of notuse of the production line are denoted F2.
The fitness function F1 and F2 are given as follows: If the product is maked in the production line 0 ∶ Otherwise W ik = � 1: If the product is maked in the production line 0 ∶ Otherwise Consequently, the fitness function F is given as follows: The value considered for factors β 1 and β 2 is 0.5.
• F ik : Manufacturing operation of the product i in the production line Ch k .
• P i : Finished product after the operation F ik .
• P ik : Manufacturing time of the operation F ik .
• CP ik : Time of the end of the execution of P i in the production line Ch k .
• CP i stk : Storage cost by unit of time of the product P i .
• tp ik : Setup time of the production lineCh k before the operation F ik .
• tp ik arr : Stopping time during the operation F ik in the line Ch k • tp ik nu : Time of no use of the line Ch k before the operation Fik.
• C prod tot : Total production cost.
• C k ui : The production unit cost of the product i in the production line Ch k .
• D ik nett : Operations duration of the cleaning in the production line Ch k .
• D ik chf : Changes format duration in the production line Ch k .
• C arr k : Stopping costs and no use of the production line Ch k per unit time.
• C arr tot : Total stopping cost and no use of line by time unit.
• trop_Ch i : The production time expressed in time unit.
• tarr_Ch i : The stopping time expressed in time unit.
• tnett_Ch i : The cleaning time expressed in time unit.
• Cnou_Ch i : The costs of no use of the production line.
In the employed bees phase; the function of updated memory is as follows [22]: x min , x max are respectively the lower bound and the upper bound of the search scope and y ij is new feasible dimension value of the food sources that is modified from its previous food sources value x ij .
In the onlooker bees phase, the probability value related with the food source (pi) is as follows [22]: fit i is the fitness value of the solution.
The algorithms were programmed in Java and executed in Core ™ i7 CPU with 2.5GHz and 8 Go de RAM.
The ABC stopping criterion defines the maximum number of cycles that a food source can keep without improvement.
The tarr_Ch i and tnett_Ch i values of product i in each production line are given as follows: 10] ∀ i = {1, 2, 3, … , 17} tnett_Ch (P i ) ∈ [5,15] The trop_Ch i value of product i in each production line is given as follows: 684 | P a g e www.ijacsa.thesai.org  The Cpro_Ch i and Cnou_Ch i values of product i in each production line are calculated according to formulas 2 and 3 and fitness function deducted from formulas 4 and 5.

Number of jobs
The global results of the proposed methods are shown in Table II.
The computational results demonstrate that all proposed methods are given the best results compared with the real results in terms of solution quality.
The results show that the synchronous parallel hybridization method HABCPSO3 is given the best results compared with other results obtained by the sequential hybridization methods and the asynchronous parallel hybridization methods.
The results show that the synchronous parallel hybridization method HABCPSO3 is given the best results compared with other results obtained by the synchronous parallel hybridization methods, the synchronous parallel hybridization method HABCPSO5 is given the equal results to the results obtained by the synchronous parallel hybridization methods HABCPSO6 independent of the hybridization type. These are presented in Fig. 6.
The ranking of the synchronous parallel hybridization methods in terms of performance according to the hybridization type is shown in Table III.   Fig. 7 is shown that the sequential hybridization method ABC(F1)+PSO(F2) is given the best results compared with other results obtained by the other sequential hybridization methods.
As shown in Fig. 7: • The sequential hybridization method [ABC+PSO](F) is given the best results compared with the results obtained by the sequential hybridization method [PSO+ABC](F).
• The sequential hybridization method ABC(F1)+PSO(F2) is given the best results compared with the results obtained by the sequential hybridization method PSO(F1)+ABC(F2).  The ranking of the sequential hybridization methods in terms of performance according to the fitness function F or F1 and F2 is shown in Table IV.
The results show that the asynchronous parallel hybridization method ABC//PSO is given the equal results to the results obtained by the sequential hybridization method ABC(F1)+PSO(F2), the asynchronous parallel hybridization method ABC//PSO is given the best results compared with other results obtained by the other sequential hybridization The ranking of the asynchronous parallel hybridization method and the sequential hybridization methods in terms of performance according to the fitness function F or F1 and F2 is shown in Table V.
As shown in Fig. 8: • The synchronous parallel hybridization method HABCPSO2 is given the equal results to the results obtained by the sequential hybridization method ABC(F1)+PSO(F2) and the asynchronous parallel hybridization method ABC//PSO.
• The synchronous parallel hybridization HABCPSO4 is given the equal results to the results obtained by the Sequential hybridization [PSO+ABC](F).
• The synchronous parallel hybridization method HABCPSO2, the sequential hybridization method ABC(F1)+PSO(F2) and the asynchronous parallel hybridization method ABC//PSO are given the best results compared with other results obtained by the synchronous parallel hybridization HABCPSO4 and the sequential hybridization [PSO+ABC](F).    The ranking of the synchronous parallel hybridization methods HABCPSO2 / HABCPSO4 and the asynchronous parallel hybridization method ABC//PSO and the sequential hybridization methods ABC(F1)+PSO(F2) / [PSO+ABC](F) in terms of performance according to the fitness function is shown in Table VI.
The ranking of all proposed methods in terms of performance according to the fitness function F or F1 and F2 is shown in Table VII. Summing up the results according to the ranking of the proposed methods in terms of performance, it can be concluded that: • The proposed methods are given the best results compared with the real results of scheduling.
• The synchronous parallel hybridization of ABC in its three phases using the fitness function F is produced the best result.
• The synchronous parallel hybridization of ABC in its two phases (onlooker bees phase and scout bees phase) using the fitness function F is produced the equal results to the results of the synchronous parallel hybridization of ABC in its two phases (employed bees phase and scout bees phase) using the weighted sum method of the fitness function F.
• The synchronous parallel hybridization of ABC in its two phases using the weighted sum method of the fitness function F (employed bees phase and onlooker bees phase) is given 100% results equal to the results of the sequential hybridization of ABC with PSO using the weighted sum method of the fitness function F and equal to the results of the asynchronous parallel hybridization of ABC with PSO using the weighted sum method of the fitness function F.
• The sequential hybridization of ABC with PSO using the weighted sum method of the fitness function F is given the better results than the sequential hybridization of PSO with ABC using the fitness functions F1 and F2.
• The synchronous parallel hybridization ABC in its onlooker bees phase using the weighted sum method of the fitness function F is produced the equal results to the results of the sequential hybridization of ABC with PSO using two fitness functions F1 and F2.
• The synchronous parallel hybridization of ABC in its employed bees phase using the weighted sum method of the fitness function F is produced the better result than the synchronous parallel hybridization of ABC in its scout bees phase using the weighted sum method of the fitness function F.
The authors' attention was concentrated not only on develops these three hybridization categories of the evolutionary methods ABC and PSO but also on tests of these hybrid methods in an automotive multi-objective flow shop and on their performance evaluation to make a perform comparison. The main limitation of the experimental that it is take into account the fitness function F1/F2 only in the sequential hybridization of ABC and PSO.

IV. CONCLUSION
Powerful methods to solve the multi-objective flow shop scheduling problem are required, due to high level of its complexity.
An adequate hybridization of multiple algorithmic concepts is the key to accomplishing top performance in solving scheduling problems.
Based on the overall experimental results, it can be decided that the proposed methods were capable to solve multiobjective flow shop scheduling problem successfully, efficiently, and robustly in terms of solution quality.
The paper presents a pilot study for verifying how the multi hybridization and the hybridization categories influence the resolution of multi-objective flow shop scheduling problems.
The proposed methods have great potential for other applications such as multi-objective job shop scheduling problem resolution and multi-objective open-shop scheduling problem resolution.
As a future research, we intend to apply the ideas presented in this paper to other scheduling problems such as multiobjective job shop scheduling problem and multi-objective open-shop scheduling problem using other hybrid methods in three hybridization categories.