An evolutionary algorithm for multi-objective optimization of freshwater consumption in textile dyeing industry

Optimization is challenging even after numerous multi-objective evolutionary algorithms have been developed. Most of the multi-objective evolutionary algorithms failed to find out the best solutions spread and took more fitness evolution value to find the best solution. This article proposes an extended version of a multi-objective group counseling optimizer called MOGCO-II. The proposed algorithm is compared with MOGCO, MOPSO, MOCLPSO, and NSGA-II using the well-known benchmark problem such as Zitzler Deb Thieler (ZDT) function. The experiments show that the proposed algorithm generates a better solution than the other algorithms. The proposed algorithm also takes less fitness evolution value to find the optimal Pareto front. Moreover, the textile dyeing industry needs a large amount of fresh water for the dyeing process. After the dyeing process, the textile dyeing industry discharges a massive amount of polluted water, which leads to serious environmental problems. Hence, we proposed a MOGCO-II based optimization scheduling model to reduce freshwater consumption in the textile dyeing industry. The results show that the optimization scheduling model reduces freshwater consumption in the textile dyeing industry by up to 35% compared to manual scheduling.


INTRODUCTION
Optimization is a well-known technique to find the optimal solution to a complex problem (Eita & Fahmy, 2010;Mirjalili & Lewis, 2016). There are numerous problems in real life that can be categorized as complex problems (Pham et al., 2006). It is tough to solve these problems using traditional algorithms. Optimization plays an essential role in solving these complex problems due to resource efficiency. These problems have many scenarios We proposed the new version of the MOGCO algorithm called MOGCO-II to optimize fresh water consumption in the textile dyeing industry. We tested the proposed algorithm using several standard benchmark functions: ZDT1, ZDT2, ZDT3, ZDT4, ZDT6, and performance metrics: generation distance metric and diversity distance metric (Xu et al., 2020). The comparisons of MOGCO-II were performed with several evolutionary multiobjective (EMO) algorithms: MOPSO (Dou et al., 2021), MOCLPSO (Zhang, Wang & Ye, 2018), NSGA-II (Yi et al., 2020), and MOGCO (Ali & Khan, 2013a).
The rest of the paper is organized as follows: "Related Work" explains the related work. "Research Methodology" describes the methodology used for this research work. "Proposed Algorithm MOGCO-II" describes the proposed algorithm. "Experiments and Results" presents the experiments and results. "Optimization of Freshwater Consumption in Textile Dyeing Industry" describes the Optimization model for the dyeing industry, and "Conclusion" concludes this research work. Yi et al. (2020) proposed a new heuristic-based multi-objective optimization algorithm called non-dominated sorting genetic algorithm II (NSGA-II). NSGA-II is used for nondominated problems, but it can not solve the issues dominated. It also uses more time and fitness evolution values to determine the optimal results.  Dou et al. (2021) proposed a new version of particle swarm optimizer (PSO) called multi-objective particle swarm optimizer (MOPSO). However, the PSO (Coello, Pulido & Lechuga, 2004;Kennedy & Eberhart, 1995) only solves the non-dominated complex multi-objective optimization problems. So, MOPSO integrated the concept of Pareto dominance that's why MOPSO successfully solved the dominated complex problems. However, the MOPSO is a time-consuming algorithm, and it takes more fitness evolution value to find out the optimal results for the multi-objective optimization problems. Zhang, Wang & Ye (2018) proposed the new version of comprehensive particle swarm optimizer (CLPSO) called multi-objective complete learning particle swarm optimizer (MOCLPSO) (Huang, Suganthan & Liang, 2006;El-Zonkoly, Saad & Khalil, 2013). The CLPSO is used for non-dominated problems (Liang, Zhigang & Zhihui, 2010). The MOCLPSO solves both dominated and non-dominated problems. The results show that MOCLPSO finds a much better spread of solutions near the actual Pareto front and faster convergence to the true Pareto front than other algorithms. But MOCLPSO is also a timeconsuming algorithm and takes more fitness evolution value to find the optimal solution of complex problems.

RELATED WORK
The researchers introduced a new multi-objective algorithm of PSO called AMOCLPSO (Ali & Khan, 2013b). A particle used its personal best and local or global best positions by linear summation in particle swarm optimization (PSO). However, finding the best local or global locations is time-consuming in complex problems. AMOCLPSO overcome this problem. This technique does not use local or global best positions to modify a particle's velocity; instead, it uses the best view of a randomly selected particle from the whole population to update each dimension's rate.
The researchers introduced a technique called Multi-Object Group Counseling Optimizer (MOGCO) in Ali & Khan (2013a) in which they extended the existing Group Counseling Optimizer (GCO) (Eita, Shoukry & Iba, 2014). GCO is only used for singleobject optimization problems, but MOGCO is used for multi-object optimization problems. MOGCO provides a dominant solution for multi-object optimization problems. MOGCO is the only algorithm that can sleeve the entire Pareto front for all the test functions used for testing the algorithms. Zhou et al. (2017) proposed an optimization model based on a genetic algorithm to optimize fresh water consumption in the textile dyeing industry. It aimed to reduce freshwater consumption in the textile dyeing industry by optimizing the production schedule based on the dyeing color and depth. The optimization model is developed by using Matlab and establishing a database of different orders of different orders of textile companies of China. The proposed model is compared to traditional production scheduling and the results show that the proposed optimization model could reduce freshwater consumption by about 18% to 21%. Jiang et al. (2010) proposed an optimization production scheduling based on genetic algorithms for this research using a Chinese enterprise's data set of dyeing department. This research minimized freshwater consumption by 20% to 21% and reduced production time by 10% to 12%. So, through this research, control of the consumption of fresh water reduces the quantity of polluted water. This leads to the arrest of the water problems of the environment. Hsu et al. (2009) proposed a genetic algorithm-based production scheduling technique for optimizing the yarn industry's production scheduling. This research used the data set of the yarn dyeing department of a chines based enterprise. This reduces freshwater consumption in the dyeing process of yarn, eliminating the quantity of polluted water and water environmental problems.
The comparative analysis of selected literature is shown in Table 1.

RESEARCH METHODOLOGY
The Zitzler Deb Thiele's (ZDT) family of test functions are used for the experimental results, a popular set of functions for benchmarking the performance of different multiobjective optimization methods. These test functions have some particular types of features that are representative of various real-world optimization problems. It is failed to find out best spread of solution and convergence near the true pareto optimal front.
Optimization Multi-Objective Optimization, Non-Dominated Problems, Genetic Algorithm.
It takes more fitness evolution value to find out optimal front. Also failed to find out best spread of solution and convergence near the true pareto optimal front. It is a time-consuming algorithm and it takes more fitness evolution value to find out the optimal results for the multi-objective optimization problems. It is also a time-consuming algorithm and takes more fitness evolution value to find the optimal solution of complex problems. This technique does not use local or global best positions to modify a particle's velocity; instead, it uses the best view of a randomly selected particle from the whole population to update each dimension's rate.  (2000) is perhaps the most widely used benchmark problem for multiobjective optimization algorithms. ZDT3 is disconnected on both the Pareto optimal set and front, the latter of which consists of one composite convex/concave component and several convex components. It should also be noted that ZDT4 has one parameter of the different domains (Ali & Khan, 2013a), whereas all other parameters have the environment (Dou et al., 2021). Nevertheless, the ZDT problems share many of the characteristics, such as how multimodality can cause Pareto many-to-one problems (ZDT6), multifrontal problems (ZDT4), and so-called disconnected problems (ZDT3). Importantly, all ZDT problems employ only one position parameter, meaning it is a function of only one parameter. The ZDT test suite offers two main advantages: (1) well-defined Pareto optimal fronts, (2) test results are commonly available from various other research papers, which facilitates comparisons with new algorithms. The details of the ZDT test suit are given in Table 2. Two performance metrics are also used to evaluate the algorithm's results: Generation Distance Metric and Diversity Distance Metric (Navarro-Muñoz et al., 2020).

Establishment of the database for production scheduling
We established a database with the following data: order, dye, auxiliary, freshwater, wastewater data. In addition, energy consumption data: based on the investigation of any Non Convex, Nonuniformly Space dyeing enterprise. We obtained the order data from the ERP department, dye data, and auxiliary data from the department of production measurements. Data for energy consumption and water consumption data have been elicited from the department of measuring equipment (dyeing vessels) (Zhou et al., 2017).
Order data contain fabric type, color, depth of color, the material's weight, delivery date, and other information. Dye data have dye rate and COD of dye. Auxiliary data provide extra details of chemical composition. Energy data may consume vessels' energy, detail dyeing machine, volume, bath ratio, and temperature. Water consumption data contain the detail of discharge wastewater at every step, COD, size, color, electrical conductivity, temperature, and the suspended solids. The above mentioned data and parameters can be changed based on enterprise investigation.

Assumptions used for production scheduling
Some assumptions help optimize production scheduling in the textile dyeing industry (Zhou et al., 2017).
Simplify the problem for the orders and vessels by creating one-to-one relations among ships and rules. Obtain the following data: the data of order, the data of dye, the data of auxiliary, the data of freshwater, the data of wastewater, and the data of energy consumption from the database. It does not need washing when switching the order between the same and dark colors.
The fabric, which has the same color but different depth, needs a 5 m 3 volume of freshwater.
The fabric, which has a different color and depth, needs a 10 m 3 volume of freshwater.

Scheduling methods in dyeing enterprises
There are the following scheduling methods in dyeing enterprises: (Jiang et al., 2010;Hsu et al., 2009). Important parameters: The delivery time is the most critical parameter for the order. For urgent orders and special orders (orders for unique customers), the enterprises can sacrifice profit to achieve customer relations and reputation. Orders consolidation: The same cloth color, depth of color, cloth type, and production process should be put together in the same dyeing vessel. Sorting orders: Firstly, orders should be sorted based on different colors. After grouping based on colors, sort each group of orders based on color depth from light to dark.

Optimizing production scheduling strategies
There are following Optimizing Production Scheduling Strategies: The dyeing vessels can be used for the production of any order. If the order's size is greater than the capacity of vessel production, then the order should be divided into multiple parts. If the orders are small and have the same color, type of cloth, and depth of color, we should put these orders simultaneously in the same vessel (Zhou et al., 2017). Parameters of the order are: order number, customer name, delivery date, the color of cloth, depth of color and weight of the material, Parameters of the quantity of freshwater and wastewater, electrical conductivity, COD, volume, temperature and suspended slides, these all parameters are obtained from the DBMS. The fabric colors are divided into eight different colors: black, blue, cyan, green, orange, purple, red, and yellow. Every color further can be divided into light, medium, and dark colors based on color depth (Zhou et al., 2017). An order almost covers 10 to 12 h in actual production. But we will assume a fixed digit for every order, which means that the order will be switched after a fixed duration of time. So the order changing completely depends on the time interval used for each order (Zhou et al., 2017). The rinsing water can reuse directly, and the light-polluted wastewater and heavily polluted wastewater must be treated separately (Zhou et al., 2017).

PROPOSED ALGORITHM MOGCO-II
MOGCO successfully solved the multi-objective optimization problems (Ali & Khan, 2013a). But it has failed to find out the best spread of solutions and convergence near the actual Pareto optimal front, taking more fitness evolution value to find out the optimal show. To solve these problems, a Pareto dominance-based Multi-Objective Group Counseling Optimizer II (MOGCO-II) algorithm is presented to handle multi-objective optimization problems. The flow chart of the proposed MOGCO-II algorithm is shown in Fig. 2. MOGCO-II is the latest version of MOGCO. However, MOGCO-II only updated the part of other members consoling. In this portion, the MOGCO used a random selection technique (Zhou, Liu & Chen, 2011), but MOGCO-II has used the tournament selection technique instead of the random selection technique. After this change, MOGCO-II produces the best solution spread and convergence near the actual Pareto optimal front. Figures 3-6 show the Pareto fronts of ZDT1, ZDT2, ZDT3, and ZDT6, respectively, for MOGCO-II on fitness evolution values 4,000, 6,000, 8,000, and 10,000. Figure 7 shows the Pareto fronts of ZDT4 for MOGCO-II on fitness evolution values 15,000, 20,000, 25,000, and 30,000.
The results show that as we increase the fitness evolution value, the optimal value of the algorithm is not trapped. The increment in the fitness revolution values does not affect the optimality of the algorithm. The algorithm consistently achieved higher optimal values. The results also show that for the test function ZDT1, ZDT2, ZDT3, and ZDT6, the proposed algorithm generates the best Pareto front, the best spread of solutions, and convergence near the true Pareto optimal front on fitness evolution value 10,000, and for ZDT4 generates the best Pareto front, the best stretch of solutions, an intersection near the true Pareto optimal front on fitness evolution value 30,000. Methodology", the results show that the MOGCO-II provides the best Pareto front, the best spread of solutions, and convergence near the true Pareto optimal front on fitness evolution value 10,000 for each ZDT1, ZDT2, ZDT3, ZDT6, and 30,000 for ZDT4. Hence,

Test function 1 (ZDT1)
The ZDT1 benchmark function is used for the first experiment. Tables 3 and 4 show the performance metric's comparison of MOGCO, MOCLPSO, MOPSO, NSGA-II, and MOGCO-II. The results show that MOGCO-II performs better than the existing algorithms. Figure 8 presents the results produced by MOCLPSO, MOGCO, MOPSO, NSGA-II, and MOGCO-II. The results show the best Pareto fronts have by the algorithms after 50 runs at 10,000 fitness evaluations for test function ZDT1. In addition, the results show that MOGCO-II provides the best Pareto front, the best spread of solutions, and convergence near the actual Pareto optimal front compared to other algorithms.

OPTIMIZATION OF FRESHWATER CONSUMPTION IN TEXTILE DYEING INDUSTRY
In this work, we proposed MOGCO-II based optimization model to reduce freshwater consumption in the textile dyeing industry. For this purpose, we used the data set of Sitara Industries Faisalabad, Pakistan. We used three machines in the proposed model: Open, Pressure, and Jet. The open vessel is used for cotton fabric. The pressure vessel is used for PolyCotton fabric, and the Jet is used for both cotton and PolyCotton fabrics.
Moreover, the main parameter is the delivery date because every order must be dyed before delivery. The proposed model calculates each dyeing slot's time, checking that any space is accessible after completing the areas for dyeing all the orders. If the slots are free,  the model can adjust the new order between the free slots of pre-orders based on the fabric's quality and color. When a new order is entered, the model reschedules all orders and regenerates the new schedule for dyeing the orders. This process is repeated whenever a new order is entered into the model. The main target of proposed model is to minimize dyeing vessels' washing before dyeing the orders, which reduces freshwater consumption.  The data set is collected from Sitara Textile Industries Sargodha road Faisalabad, Pakistan. The Sitara Industry works on the exhaust method of dyeing (Jiang et al., 2010), and there are two types of cloth (Cotton and PolyCotton). The Open and Jet vessels are used for dyeing cotton and dyeing poly cotton. The Jet and Pressure vessels are used that's why we collected the data of cotton and poly cotton for the vessels: Open, Jet, and Pressure. The parameters of the collected data are the following: order number, order place date, order delivery date, company name, cloth type, cloth quality, cloth color, color depth, dyeing time, freshwater used for washing the vessel, hard water used for dye the cloth and freshwater used for cleaning the dyed fabric.

Results
The results prove that reducing freshwater consumption in the textile dyeing industry has remarkable benefits for the environment and could reduce wastewater treatment costs. The wastewater is treated as light polluted wastewater and high polluted wastewater. Table 13 shows the manual scheduling of the dataset collected from the Sitara Industries Faisalabad, Pakistan. In this manual scheduling, freshwater consumption is 51,100 L, as shown in Table 13. Tables 14 and 15 offer the proposed model's optimization scheduling without and with urgent orders. In the optimization schedule, freshwater consumption is 43,050 and 44,900, reduced to 16% and 15% respectively compared to manual scheduling, as shown in Table 16. Zhou et al. (2017) used a dataset of 6 months, and almost all other researchers also used a dataset of at least 6 months. In these research studies, the variation is up to 21.3%. But the proposed model used data set of just 2 months and provides a 16% improvement. If the model is applied to the 6-month dataset, the progress will be almost 32%.

CONCLUSION
In this research, we proposed an algorithm that can be used for multi-objective optimization problems, particularly for optimizing freshwater consumption in the textile industry. We compared the proposed algorithm with MOPSO, NSGA-II, MOCLPSO, and MOGCO for the test functions ZDT test suite, performance metrics, and computational time. The results show that the proposed algorithm outperforms as compared to the other algorithms. This research also suggested a MOGCO-II optimization model reduce freshwater consumption in the textile dyeing industry. The variation between manual scheduling and optimization schedule is up to 35%. The limitations of the MOGCO-II algorithm are that it is only used for multiobjective optimization problems. The proposed model for optimization scheduling only deals with three vessels: open, pressure, and Jet. Furthermore, the proposed model was only tested on the data set of the exhaust textile dyeing process. Therefore, we can work on a continuous method and can be used more than three vessels in the future.