Energy-Efficient Flow Shop Scheduling Using Hybrid Grasshopper Algorithm Optimization

Manufacturing companies have a significant impact on environmental damage, and manufacturing companies' energy consumption is a widespread issue because the energy used is derived from fossil fuels. This research aims to minimize energy consumption using develop Hybrid Grasshopper Algorithm Optimization (HGAO). The focus of the issue in this article is the Permutation Flow Shop Scheduling Problem (PFSSP). A case study was conducted in offset printing firms. The results showed that the HGAO algorithm is capable of reducing energy consumption in offset printing firms. The higher the population of search agents and iterations produces less energy consumption. The HGAO algorithm is also compared with the genetic algorithm (GA). The results show that HGAO is more efficient in reducing energy consumption than GA.


I. INTRODUCTION 1
Recently, manufacturing companies have had a significant impact on environmental damage (Dai et al., 2013;Maulana et al., 2019;, and electrical energy is the primary source of energy in the manufacturing sector (Fang et al., 2011). Energy consumption is becoming an essential issue in manufacturing companies by making it environmentally sustainable (Jiang et al., 2018). Electrical energy is primarily derived from fossil fuels. The higher energy requires that a company needs, the greater its fossil fuel needs, and it harms the environment. Scheduling plays an essential role in reducing energy consumption (Grobler et al., 2010). One of the scheduling problems is the Permutation Flow Shop Scheduling Problem (PFSSP) (Utama, 2018a;Utama et al., 2020). Many experts claim that the PFSSP case can not be resolved in polynomial time (Utama, Ardiansyah, & Garside, 2019;Utama, Garside, & Wicaksono, 2019). Therefore, PFSSP is included in the NP-Hard problem (Garey et al., 1976). One of the techniques for reducing consumption in the manufacturing sector is the use of energy-efficient machinery (Elias et al., 2019;Utama, 2019a). However, it requires very high costs and is not owned by the small and medium-sized manufacturing industries (Tian et al., 2018). Therefore, scheduling is one strategy for reducing energy consumption (Utama, Widodo, Wicaksono, & Ardiansyah, 2019). The scheduling problem has attracted much attention to researchers. Researchers have previously referred to this issue as Energy Efficient Scheduling (Gong et al., 2020;Öztop et al., 2020).
Based on previous research, there is no research using the Hybrid Grasshopper Algorithm Optimization (HGAO) approach to minimize energy consumption. Therefore, one of the ways to overcome this problem of energy consumption is to use HGAO. HGAO is an algorithm inspired by the behavior of grasshoppers in nature (Saremi et al., 2017). The researchers have developed a grasshopper algorithm by incorporating local search procedures. This research aims to minimize energy consumption in the PFSSP problem using a Hybrid Grasshopper Algorithm Optimization (HGAO).

II. RESEARCH METHOD
In this section, we explain the PFSSP problem's assumptions, the definition of the problem, the Hybrid Grasshopper Algorithm Optimization procedure, and the method of collect and experiment data.

Assumptions of the Problem
In this PFSSP problem, some assumes used such as: (1) n jobs (n= 1,2,3... I operated in the same order on a sequence of m machines (m= 1,2,3.. j).

Definition of Problem
The problem of energy efficiency in the PFSSP model is modified from S. Li, Liu, and Zhou (2018). The best scheduling is defined as having a minimum TEC. The PFSSP model for minimizing energy consumption is as follows: Objective function = min (1) Subject to : = max ( , ) , ∀ = 1 . . , = 1. .
Equation (1) shows the objective function of the PFSSP problem, namely minimization of the TEC (objective function); Equation constraint (2) explains the completion time of the first job sequence on machine 1; Equation constraint (3) formulates the completion time of machines 2 to m for the first-order job; Equation constraint (4) describes the completion time of the sequence i (sequence 2 to n) jobs processed on machine 1; Equation constraint (5) shows the completion time of sequence i jobs (sequence 2 to n) on machine j (machines 2 to m); Equation constraint (6) explains the total machine busy time on each machine j; Equation constraint (7) shows the completion time of machine j from the permutation sequence; Equation constraint (8) shows the total idle time of the machine j permutation sequence, and Equation constraint (9) formulates PFSSP for energy consumption.

Algorithm Hybrid Grasshopper Algorithm Optimization
This research proposes a Hybrid Grasshopper Algorithm Optimization (HGAO) to minimize energy consumption in the PFSSP problem. HGAO is a combination of Grasshopper Algorithm Optimization and local search processes. The researchers propose transforming grasshopper positions into job permutation sequences by applying Large Rank Value (LRV). LRV is an effective way of transforming continuous values into job permutations (X. Li & Yin, 2013). Continuous values are sorted from the largest to the smallest values in the LRV. Figure 1 displays the illustration of LRV. In addition, the researchers use a local search swap and flip rules to improve the performance of Grasshopper Algorithm Optimization. The description of the swap is illustrated in Figure 2. During swap operations, two locations are chosen randomly and exchanged. Whereas, a flip is achieved by flipping the randomly selected job sequence. The swap operation is shown in Figure 3. The procedure can see the HGAO pseudocode in algorithm 1.
The Grasshopper algorithm is an optimization algorithm that can be used for decision-making. This algorithm is mathematically designed to model and simulate the behavior of grasshopper in search of food. After one of the grasshopper members finds a food source, the other grasshopper herd goes to the food source. This algorithm has been proposed by Saremi et al. (2017). The grasshopper interaction model is modeled in equation (10). Where Xi is the position of the i grasshopper. Si denotes the social interaction of the i grasshopper. Gi is the gravity pressure of the i grasshopper, and Ai is the influence of the i grasshopper wind.

= + +
The value of S is expressed in equation 11. is the distance between grasshopper i to j, is the distance between grasshopper i to j, and N is the number of grasshoppers. The two elements are formulated in equations 12 and 13.
=∑ ( ) Social pressure on grasshoppers can be formulated in equations (14). f is the force of attraction, and l is the duration of the scale of attraction. Then evaluate Gi and Ai formulated in equations (15) and (16). g reflects gravity, .g., implies vector unity concerning the center of the earth, u is current, is vector unity concerning the direction of the wind.
The mathematical model of equation (17) statement above cannot be applied directly to solve optimization problems because grasshoppers quickly return to their comfort zones and do not communicate with other grasshoppers. The above formulation is then transformed into an equation (18).
is the upper limit of the dimension d, is the lower limit of the dimensions, is the lower limit of the dimension d, is the reduction coefficient.  is the maximum value (using 1 and 0.00001), the minimum value (using 1 and 0.00001), is the most recent iteration, and is the maximum number of iterations.

Method of collect and experiment data
The researchers perform case studies in offset printing firms. Six machines must process thirteen jobs. The details on the processing time of each machine and job can be shown in Table  1. The energy consumption of each machine is seen in Table 2. This research used a combination of parameters to assess the influence of the parameters on the objective function. The parameters used for the experiment were the population number and the number of iterations. The population uses three stages, namely 10, 50,

Characteristics of Respondents
The HGOA experiment findings on the combination of population and iteration show that population and iteration parameters have an impact on the quality of the solution (Table 3). The higher the iteration is used, the lower the energy consumption generated. Meanwhile, it could have an impact on the computing time that's getting longer. It also has been confirmed by several scholars, as in the study by Sugioko (2013) and Utama (D. M. Utama, T. Baroto, et al., 2019). They argue that a large number of iterations make the calculation time longer.  explain that the larger the population, the better the solution's quality. If the iteration is getting bigger, the quality of the solution also is better. The total energy consumption based on HGOA is 819.04 KW.

IV. CONCLUSION
This research aims to reduce energy consumption in a flow shop scheduling problem   (HGAO). The results showed that the HGAO algorithm is capable of reducing the energy consumption of offset printing firms. The HGAO algorithm is also associated with the genetic algorithm (GA). The results show that HGAO is more effective in minimizing energy consumption. The results obtained are that the higher the iteration used, the lower the energy consumption generated. Meanwhile, it could have an impact on the computing time that's getting longer. To carry out further studies, it is essential to further improve the question of energy consumption by considering disposal time and setup.