An energy-efficient flow shop scheduling using hybrid Harris hawks optimization

Received Jul 22, 2020 Revised Oct 12, 2020 Accepted Mar 17, 2021 The energy crisis has become an environmental problem, and this has received much attention from researchers. The manufacturing sector is the most significant contributor to energy consumption in the world. One of the significant efforts made in the manufacturing industry to reduce energy consumption is through proper scheduling. Energy-efficient scheduling (EES) is a problem in scheduling to reduce energy consumption. One of the EES problems is in a flow shop scheduling problem (FSSP). This article intends to develop a new approach to solving an EES in the FSSP problem. Hybrid Harris hawks optimization (hybrid HHO) algorithm is offered to resolve the EES issue on FSSP by considering the sequence-dependent setup. Swap and flip procedures are suggested to improve HHO performance. Furthermore, several procedures were used as a comparison to assess hybrid HHO performance. Ten tests were exercised to exhibit the hybrid HHO accomplishment. Based on numerical experimental results, hybrid HHO can solve EES problems. Furthermore, HHO was proven more competitive than other algorithms.


PROPOSED ALGORITHM
We proposed hybrid HHO, which combined HHO with strategies swap and flip in the stage local search. The exploration and the exploitation phase are two main strategies for the HHO algorithm in search of prey. Hard besiege, soft besiege, hard besiege with progressive rapid lived, and soft besiege with progressive rapid lived are four main behaviors of the HHO algorithm. These behaviors are in the exploitation phase. This algorithm was used to solve continuous problems. Therefore, we developed the HHO algorithm to minimize energy consumption in FSSP with the sequence-dependent setup time. FSSP was considered as an NP-hard combinatorial problem that can be solved by discrete search space. We propose four stages in the Hybrid HHO algorithm. These stage includes; 1) The random population of rabbits and large rank value (LRV), 2) Exploration phase, 3). Exploitation phase, and 4) Local search phase with flip and swap. Pseudocode hybrid HHO (proposed procedure) is shown in Algorithm 1. A description of the stages of the Hybrid HHO algorithm is explained in the following section.
Algorithm 1 Pseudocode of Hybrid HHO algorithm Inputs: Maximum iterations t and the population size N Outputs: fitness value and the rabbit location random population initialization Xi(i = 1,2,...,N) for iteration 1 to t fitness value calculation of hawks = * Set Xrabbit as the rabbit location (best location) for (each hawk (Xi)) do Reform the first energy E0 and jump strength J (E0=2rand()-1, J=2(1-rand()) Update the E using (3)) if (|E|≥ 1) then (Exploration phase) The location vector update using (1) if (|E| < 1) then (Exploitation phase) if (r ≥0.5 and |E|≥ 0.5 )then (The vector location update of soft besiege using (4)) else if (r ≥0.5 and |E| < 0.5 ) then (The location vector update of hard besiege using (6)) else if (r <0.5 and |E|≥ 0.5 ) then (The location vector update of soft besiege with progressive rapid dives using (20) else if (r <0.5 and |E| < 0.5 ) then (The location vector update of hard besiege with progressive rapid dives using (10) assure no repetitive number in the same s rabbit position +1 Apply LRV on each rabbit position +1 for = 0:

The random population of rabbit and large rank value
The position of the initial rabbit population was generated randomly. This research proposed that population positions had to ensure that no numbers were repeated. Figure 1 shows the illustration of the initialization of the rabbits' random population. In Figure 1 there were the same numbers in the population. It resulted in a population that could not be converted into a discrete search space. In converting continuous numbers to discrete search space, this research proposed converting rabbit positions (continuous value) to job permutations by applying LRV. LRV is seen as a successful way to convert continuous values to job sequence of permutation [25]. In LRV, continuous values were ranked from the largest to the smallest values. Figure 2 describes the Illustration of the LRV application.  ( ) was formulated with (2).
(2) ( ) was the location of each eagle in the iteration t. Furthermore, N was the total number of eagles. The HHO algorithm was transferred from exploration to exploitation. That behavior was based on prey energy (rabbit). The energy of prey (rabbit) was drastically reduced during escape behavior. In (3) showed the prey energy formula (rabbit).
E indicated the energy coming out of the prey. T formulated the maximum number of iterations. 2 0 displayed the initial state of energy of the rabbit.

Exploitation phase
In this section, the exploitation phase strategies of HHO are explained. Harris hawk performed four strategies: hard besiege, soft besiege, hard besiege with progressive rapid dives, and soft besiege with progressive rapid dives. In the soft besiege strategy, when the rabbits still had enough energy, they tried to escape from Harris hawk. These eagles then surrounded it gently, and they made the rabbit more tired. Furthermore, they did a surprise pounce. This behavior was formulated in (4) and (5).
∆X (t) showed the difference between the rabbit position vector and the current location in iteration t. r5 described random numbers in the range (0.1). During the runaway procedure, the rabbit random jump strength was formulated as J=2(1-r5). The value of J changed randomly at each iteration. The second strategy was hard besieged. Rabbits were already exhausted, and they had low runaway energy. Harris hawk did not surround rabbits, and they did pounce shocks. A new position on the hard besiege strategy was formulated in (6).
The third strategy was soft besiege with progressive rapid dives. Rabbits were assumed to have enough energy to escape successfully because Harris hawk built a soft siege before the shock pounced. To make a soft siege, the eagle could evaluate the next step based on (7). The current position was updated using (6). In this strategy, Harris hawks did irregular, sudden, and fast dives to get close to its prey. Harris hawks dive pattern was formulated in (8).
LF indicated the levy fight function. S showed a random vector of size 1xD. D described the dimensions of the problem. The LF function was calculated using (9).
and were random values in the range (0.1), β was the default constant of 1.5. Therefore, the strategy of Soft besieges with progressive rapid dives was shown in (10). Y and Z were obtained using (7) and (8). The fourth strategy was hard to besiege with progressive rapid dives. This behavior was carried out if the rabbit did not have enough energy to escape. Harris hawk does hard besiege. Furthermore, they surprise shocking rabbits. In (10) shows the rule in hard besiege conditions. Y and Z were obtained using the new rules in (7) and (8). Xm(t) was obtained by using (2).

Local search
The swap and flip are two are local search procedures proposed to improve the HHO performance. The swap illustration can is seen in Figure 3. In the swap operation, two positions were chosen randomly, and they were then swapped. Furthermore, the flip procedure was done by reversing the randomly selected job sequence. The flip operation was illustrated in Figure 4. In hybrid HHO, each iteration t, swap, and flip operations were repeated by the number of jobs. In this problem, the objective function in this study is minimizing total energy consumption (TEC). The EES FSSP issue was developed by Li, et al. [26]. The EES FSSP model to reduce energy consumption is as follows: Objective function =min (11) Subject to : 1, = ( 1, −1 , 1 ) + 1, , = 2 . .
= ∑ =1 ( . + . + . ) (20) Formula (11) describes the objective function, which minimizing energy consumption in the FSSP model. The finish time of sequence one on machine 1 formulates in constraint (12). Constraint (13) explains the settlement time of job sequence one the machine 2 to m. The settlement time of sequence i from machine 1 describes in constraint (14). The finish time of job sequence i in machine j is shown in constraint (15). Constraint (16) describes a total processing time machine. The total of setup time is stipulated constraint (17). Constraint (18) explains the completion time of machine j from permutation. Whereas constraint (19) indicates the total idle time of j machine permutation. Finally, constraint (20) describes the permutation TEC (objective function).

Data and experimental setup
Experimental data from previous studies were used. Some processing time data were based on research conducted by Carlier [27], Heller [28], and Reeves [29]. The setup time for the first order job was generated from uniform random numbers (5,10). The setup time for moving jobs sequence i to i+1 was generated from uniform random numbers (5,10). Uniform random data of consumption of process energy, setup, and idle time series were as follows: uniform (10,20), uniform (5,10), and uniform (1,5). Table 1 portrayed a list of problems from numerical experiments. Reeves [29] This research conducted several experiments to determine the hybrid HHO parameters' effect on energy consumption and computing time. Two parameters were used in this experiment include population and iteration. Iteration included three levels, namely iteration 5, 25, and 50. Furthermore, the population consisted of three levels, namely the population 10, 25, and 50. Each data repeatedly experimented for nine times. We used 10 case data jobs and machines as shown in Table 1. Therefore, the experiments were carried out as many as 90 times. Each experiment recorded energy consumption and computational time. 1160 Furthermore, we also tested the effect of parameters on the structure of energy consumption. The structure of energy consumption comprised process energy consumption, setup energy consumption, and idle energy consumption. In this experiment, we implemented case 3, case 8, case 9, and case 10. Furthermore, the best parameters of the results of the experiment were compared with some previous algorithms, including GA [12], NEH [13], CDS [14], ACO [15], and hybrid metaheuristic [10]. The experiment was done by Matlab R16 software on a Windows 10 Intel® Core ™ i5-8250U RAM 4 GB processor. The performance of the Hybrid HHO algorithm was measured by the Efficiency Index (EI). EI formula was presented in (21).

The comparison of various parameters toward energy consumption
The results of the hybrid HHO parameter experiment on energy consumption were shown in Table 2. It reflected that the higher the number of iterations resulted in smaller energy consumption. Furthermore, the lower the number of iterations would lead to greater energy consumption. In population parameters, the higher the population resulted in lower energy consumption. Furthermore, the lower population produced higher energy consumption. Overall these findings were consistent with the findings reported by Tang, et al. [30]. It is now generally accepted that population and proper iteration reduce FSSP energy consumption. For the case of small jobs, the best parameter uses population numbers and small iterations. Conversely, for large jobs, the population and iteration used are high. Table 2 also displayed the result of the comparison of multiple parameters toward computation time. In iteration parameters, significant iterations increase computational time. Conversely, a small iteration decreases computational time. Furthermore, in the iteration parameter, a large population increases computational time. Conversely, a small population decreases computing time. The number of jobs affects the computational time. Experimental results showed that large jobs increase computational time.

The comparison of various parameters toward structure energy consumption
Experimental results of the effect of parameters on structure energy consumption were presented in Table 3. It showed that FSSP energy consumption with the sequence-dependent setup was influenced by setup and idle time. Overall, these findings are consistent with the study results by Utama, et al. [10]. Furthermore, the higher iteration and population would decrease the energy consumption setup and idle. Conversely, the smaller iteration and population would increase the energy consumption setup and idle.  Table 4 indicated the other EIP algorithms against the proposed algorithm. The proposed algorithms were compared with including GA [12], NEH [13], CDS [14], ACO [15], and hybrid metaheuristic [10]. The results suggested that the proposed algorithm was more competitive than other algorithms. This result was proven by the EIP value <100%. The values of EIP including GA [12], NEH [13], CDS [14], ACO [15] and Hybrid Metaheuristic [10] were as follows 98.79%, 97.81%, 97.73%, 98.79%, and 99.00%. Therefore, it was clear that the Hybrid HHO algorithm significantly improves the FSSP energy efficiency solution's quality. Hybrid HHO is an efficient algorithm for solving EES in FSSP with the sequence-dependent setup.

CONCLUSION
This study discussed the energy-efficient scheduling (EES) in FSSP with the sequence-dependent setup to minimize energy consumption. This study succeeds in proposing the hybrid Harris hawk optimization (hybrid HHO) algorithm to solve the EES in the FSSP with the sequence-dependent setup problem. The higher the number of iteration and populations can reduce energy consumption. However, these produced significant computation time. Setup and idle time are time structures that influence to reduce energy consumption. Furthermore, the proposed procedure was tested with several algorithms. The test outcome demonstrated that the hybrid HHO algorithm was more effective than other procedures. Further research should be aimed at developing procedures and dynamic job arrival. Future studies also need to develop the hybrid HHO procedure with other metaheuristic procedures to produce more best results.