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

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 where an objective can be converted into an optimization problem. Optimization problems are classified into single-objective and multi-objective problems (Ali & Khan, 2012, 2013a). Single objective optimization problems are those problems that have only one objective to minimize/maximize. Multi-objective optimization problems can be categorized into two or more goals to minimize/maximize. Evolutionary algorithms can quickly solve optimization problems (Anchor et al., 2002; Mugambi & Hunter, 2003).

Evolutionary algorithms are generic population-based and evolution-based metaheuristic algorithms (Hruschka, Campello & Freitas, 2009; Slowik & Kwasnicka, 2020). Evolutionary algorithms are helpful to minimize/maximize real-world problems (complex problems). These algorithms have gained popularity in the last decade due to several advantages in the optimization field compared to traditional techniques (Slowik & Kwasnicka, 2020; Rajabi & Witt, 2020).

For multi-objective optimization problems (Gómez et al., 2013; Rizk-Allah, Hassanien & Slowik, 2020), the researchers proposed many multi-objective evolutionary algorithms such as Multi-Objective Particle Swarm Optimizer (MOPSO) (Dou et al., 2021), Non-Dominated Sorting Genetic Algorithm II (NSGA-II) (Cai et al., 2019; Yi et al., 2020), Multi-Objective Comprehensive Learning Particle Swarm Optimizer (MOCLPSO) (Zhang, Wang & Ye, 2018), Attributed Multi-Objective Comprehensive Learning Particle Swarm Optimizer (AMOCLPSO) (Ali & Khan, 2013b), and the Multi-Objective Group Counseling Optimizer (MOGCO) (Ali & Khan, 2013a). However, these algorithms have failed to find out the best spread of solutions and convergence near the actual Pareto optimal front. And take more fitness evolution value to find out the best solution.

Moreover, the textile dyeing industry is an essential unit because it converts the raw material of textile fibers into finished products. The dye used in this process depends on the type of material and the specific requirement of the final product. In the dyeing industry, the dyeing process needs more chemicals that’s why the wastewater from the dyeing process is more hazardous than the other processes.

The dyeing process is the most common and essential factor of textile products in successful trading. Instead, with time, the dyeing industry still uses the oldest methods and techniques to dye the fabrics. The modern dyeing process consists of different steps based on fiber nature, dye properties, and pigments used for the materials like (Zhou et al., 2017; Hsu et al., 2009): structure of the chemical, commercial availability, classification, fixing features, economic considerations, etc. In the dyeing process, fresh water is used to clean, dye, and apply the auxiliary chemicals to the fabrics and rinsing. The dyeing process depends on three steps, as shown in Fig. 1.

The dyeing industry consumes a large quantity of freshwater and produces much-polluted water from the different preparations, including dyeing and finishing steps. In addition, the contaminated water has riches from the dyeing process with colors and chemicals (Jiang et al., 2010).

This article proposes an extended version of the MOGCO algorithm called Multi-Objective Group Counseling Optimizer II (MOGCO-II) based optimization model. The main contributions of this study are as follows:

• 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 multi-objective (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.

Related 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 non-dominated 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 time-consuming algorithm and takes more fitness evolution value to find the optimal solution of complex problems.

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 single-object 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 multi-objective optimization methods. These test functions have some particular types of features that are representative of various real-world optimization problems.

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.

Experiments and Results

The comparison of the proposed algorithm is made with five well-known evolutionary algorithms: MOPSO, MOCLPSO, AMOCLPSO, NSGA-II, and MOGCO. In “Research 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, the comparisons of MOGCO-II performed on 10,000 fitness evolution for ZDT1, ZDT2, ZDT3, ZDT6, and 30,000 for ZDT4 with MOPSO, MOCLPSO, NSGA-II, and MOGCO.

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.

Table 3:

Results of generation distance metric for ZDT1.

FE	Algorithms	Best	Worst	Average	Median	Standard deviation
10,000	MOPSO NSGA-II MOGCO MOCLPSO MOGCO-II	4.85 × 10–01 3.48 × 10–02 5.71 × 10–02 4.82 × 10–01 2.73 × 10–02	1.32 × 10+00 1.27 × 10+00 1.01 × 10–01 2.07 × 10+00 4.74 × 10–02	8.57 × 10–01 1.42 × 10–01 7.98 × 10–02 1.30 × 10+00 3.55 × 10–02	8.40 × 10–01 8.84 × 10–02 8.07 × 10–02 1.25 × 10+00 3.57 × 10–02	1.97 × 10–01 1.98 × 10–01 1.06 × 10–02 3.81 × 10–01 3.60 × 10–03

DOI: 10.7717/peerj-cs.932/table-3

Table 4:

Results of diversity metric for ZDT1.

FE	Algorithms	Best	Worst	Average	Median	Standard deviation
10,000	MOPSO NSGA-II MOGCO MOCLPSO MOGCO-II	6.39 × 10–01 3.09 × 10–01 1.20 × 10–01 7.99 × 10–01 4.46 × 10–02	9.03 × 10–01 7.96 × 10–01 2.81 × 10–01 9.85 × 10–01 2.13 × 10–01	8.12 × 10–01 4.54 × 10–01 1.92 × 10–01 9.14 × 10–01 1.09 × 10–01	8.16 × 10–01 4.29 × 10–01 1.85 × 10–01 9.19 × 10–01 1.04 × 10–01	4.68 × 10–02 9.23 × 10–02 4.08 × 10–02 3.84 × 10–02 3.43 × 10–02

DOI: 10.7717/peerj-cs.932/table-4

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.

Test function 2 (ZDT2)

The ZDT2 benchmark function is used for the second experiment. Tables 5 and 6 show the performance metric’s comparison of MOCLPSO, MOPSO, MOGCO, NSGA-II, and the proposed algorithm. The tables show that MOGCO-II performs better than the existing algorithms.

Table 5:

Results of generation distance metric for ZDT2.

FE	Algorithms	Best	Worst	Average	Median	Standard deviation
10,000	MOPSO NSGA-II MOGCO MOCLPSO MOGCO-II	0.00 × 10+00 4.62 × 10–02 6.55 × 10–02 0.00 × 10+00 1.89 × 10–02	6.15 × 10–01 1.49 × 10+00 1.59 × 10–01 2.99 × 10–01 6.96 × 10–02	4.76 × 10–01 2.67 × 10–01 1.14 × 10–01 1.01 × 10–01 4.18 × 10–02	0.00 × 10+00 1.73 × 10–01 1.17 × 10–01 0.00 × 10+00 4.26 × 10–02	1.27 × 10–01 3.11 × 10–01 2.08 × 10–02 4.35 × 10–02 1.15 × 10–02

DOI: 10.7717/peerj-cs.932/table-5

Table 6:

Results of diversity metric for ZDT2.

FE	Algorithms	Best	Worst	Average	Median	Standard deviation
10,000	MOPSO NSGA-II MOGCO MOCLPSO MOGCO-II	7.33 × 10–01 4.62 × 10–01 1.91 × 10–01 9.69 × 10–01 3.72 × 10–02	1.10 × 10+00 1.00 × 10+00 5.39 × 10–01 1.01 × 10+00 2.72 × 10–01	9.77 × 10–01 8.01 × 10–01 3.18 × 10–01 9.98 × 10–01 1.64 × 10–01	1.00 × 10+00 9.40 × 10–01 2.99 × 10–01 1.00 × 10+00 1.55 × 10–01	6.56 × 10–02 2.01 × 10–01 6.87 × 10–02 6.37 × 10–03 5.77 × 10–02

DOI: 10.7717/peerj-cs.932/table-6

Figure 9 presents the results produced by MOCLPSO, MOGCO, MOPSO, NSGA-II, and the proposed algorithm. The results show the best Pareto fronts have by the algorithms after 50 runs at 10,000 fitness evaluations for the test function ZDT2. 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.

Test function 3 (ZDT3)

The ZDT3 benchmark function is used for the third experiment. Tables 7 and 8 show the performance metric’s comparison of MOCLPSO, MOPSO, MOGCO, NSGA-II, and the proposed algorithm. The tables show that MOGCO-II performs better than the existing algorithms.

Table 7:

Results of generation distance metric for ZDT3.

FE	Algorithms	Best	Worst	Average	Median	Standard deviation
10,000	MOPSO NSGA-II MOGCO MOCLPSO MOGCO-II	3.94 × 10–01 3.52 × 10–02 2.84 × 10–02 7.09 × 10–01 1.14 × 10–02	1.88 × 10+00 1.27 × 10+00 8.67 × 10–02 2.35 × 10+00 3.89 × 10–02	1.14 × 10+00 1.89 × 10–01 5.02 × 10–02 1.75 × 10+00 2.23 × 10–02	1.13 × 10+00 1.23 × 10–01 4.95 × 10–02 1.83 × 10+00 2.10 × 10–02	3.27 × 10–01 2.40 × 10–01 1.31 × 10–02 4.30 × 10–01 6.69 × 10–03

DOI: 10.7717/peerj-cs.932/table-7

Table 8:

Results of diversity metric for ZDT3.

FE	Algorithms	Best	Worst	Average	Median	Standard deviation
10,000	MOPSO NSGA-II MOGCO MOCLPSO MOGCO-II	7.85 × 10–01 5.43 × 10–01 8.99 × 10–02 7.81 × 10–01 5.53 × 10–02	9.93 × 10–01 8.39 × 10–01 2.03 × 10–01 1.02 × 10+00 1.54 × 10–01	8.98 × 10–01 6.59 × 10–01 1.46 × 10–01 8.87 × 10–01 1.01 × 10–01	8.94 × 10–01 6.50 × 10–01 1.46 × 10–01 8.92 × 10–01 1.01 × 10–01	4.99 × 10–02 7.12 × 10–02 2.82 × 10–02 5.75 × 10–02 1.99 × 10–02

DOI: 10.7717/peerj-cs.932/table-8

Figure 10 presents the results produced by MOCLPSO, MOGCO, MOPSO, NSGA-II, and the proposed algorithm. The results show the best Pareto fronts have by the algorithms after 50 runs at 10,000 fitness evaluations for the test function ZDT3. 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.

Test function 4 (ZDT4)

The ZDT4 benchmark function is used for the fourth experiment. Tables 9 and 10 show the performance metric’s comparison of MOCLPSO, MOPSO, MOGCO, NSGA-II, MOGCO, and the proposed algorithm. The tables show that MOGCO-II performs better than the existing algorithms.

Table 9:

Results of generation distance metric for ZDT4.

FE	Algorithms	Best	Worst	Average	Median	Standard deviation
30,000	MOPSO NSGA-II MOGCO MOCLPSO MOGCO-II	1.00 × 10–01 3.99 × 10+00 3.84 × 10–02 8.57 × 10–02 1.62 × 10–02	3.24 × 10–01 1.70 × 10+01 2.09 × 10–01 1.88 × 10–01 2.88 × 10–01	1.48 × 10–01 1.12 × 10+01 8.17 × 10–01 1.63 × 10–01 8.77 × 10–02	1.45 × 10–01 1.04 × 10+01 6.92 × 10–02 1.69 × 10–01 5.50 × 10–02	3.13 × 10–02 4.13 × 10+00 3.84 × 10–02 2.39 × 10–02 7.29 × 10–02

DOI: 10.7717/peerj-cs.932/table-9

Table 10:

Results of diversity metric for ZDT4.

FE	Algorithms	Best	Worst	Average	Median	Standard deviation
30,000	MOPSO NSGA-II MOGCO MOCLPSO MOGCO-II	8.59 × 10–01 8.57 × 10–01 1.20 × 10–01 9.79 × 10–01 7.81 × 10–02	9.91 × 10–01 1.07 × 10+00 6.26 × 10–01 1.01 × 10+00 4.91 × 10–01	9.28 × 10–01 9.15 × 10–01 3.18 × 10–01 9.97 × 10–01 2.34 × 10–01	9.27 × 10–01 9.14 × 10–01 3.14 × 10–01 9.98 × 10–01 2.30 × 10–01	2.51 × 10–02 3.28 × 10–02 1.09 × 10–01 5.47 × 10–03 1.01 × 10–01

DOI: 10.7717/peerj-cs.932/table-10

Figure 11 presents the results produced by MOCLPSO, MOGCO, MOPSO, NSGA-II, and the proposed algorithm. The results show the best Pareto fronts have by the algorithms after 50 runs at 30,000 fitness evaluations for the test function ZDT4. 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.

Test function 5 (ZDT6)

The ZDT6 benchmark function is used for the fifth experiment. Tables 11 and 12 show the performance metric’s comparison of MOCLPSO, MOPSO, MOGCO, NSGA-II, MOGCO, and the proposed algorithm. Again, the tables show that MOGCO-II performs better than the existing algorithms. Tables 10 and 11 offer the performance metric comparison for ZDT6 of MOCLPSO, MOPSO, NSGA-II, and propose algorithm after 50 runs at 10,000 fitness evaluations for the ZDT6 test function. Again, the tables show that MOGCO-II performs better than the existing algorithms.

Table 11:

Results of generation distance metric for ZDT6.

FE	Algorithms	Best	Worst	Average	Median	Standard deviation
10,000	MOPSO NSGA-II MOGCO MOCLPSO MOGCO-II	3.99 × 10–01 3.57 × 10–01 2.10 × 10–03 3.56 × 10–02 2.26 × 10–03	5.79 × 10+00 5.87 × 10+00 2.31 × 10–01 5.21 × 10+00 1.06 × 10–01	1.60 × 10+00 1.83 × 10+00 7.39 × 10–02 2.96 × 10+00 2.25 × 10–02	8.46 × 10–01 1.63 × 10+00 6.28 × 10–02 3.68 × 10+00 1.06 × 10–02	1.58 × 10+00 1.04 × 10+00 6.38 × 10–02 1.93 × 10+00 2.43 × 10–02

DOI: 10.7717/peerj-cs.932/table-11

Table 12:

Results of diversity metric for ZDT6.

FE	Algorithms	Best	Worst	Average	Median	Standard deviation
10,000	MOPSO NSGA-II MOGCO MOCLPSO MOGCO-II	8.72 × 10–01 9.32 × 10–01 2.34 × 10–01 7.51 × 10–01 2.17 × 10–01	1.37 × 10+00 1.24 × 10+00 1.83 × 10+00 1.31 × 10+00 2.70 × 10+00	1.16 × 10+00 1.06 × 10+00 8.30 × 10–01 9.75 × 10–01 6.71 × 10–01	1.18 × 10+00 1.04 × 10+00 8.67 × 10–01 9.33 × 10–01 2.91 × 10–01	1.35 × 10–01 7.62 × 10–02 4.44 × 10–01 1.57 × 10–01 5.63 × 10–01

DOI: 10.7717/peerj-cs.932/table-12

Figure 12 presents the results produced by MOCLPSO, MOPSO, NSGA-II, MOGCO, and the proposed MOGCO-II algorithm. The results show the best Pareto fronts of ZDT6 delivered by the algorithms after 50 runs at 10,000 fitness evaluations. This figure shows that MOGCO-II performs better.

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. For washing a vessel, 350 L of freshwater is required. In addition, the vessel must be cleaned twice for black color, and for all other colors, the vessel washes only once. So, if the model can minimize the washing of dyeing vessels, it can reduce freshwater consumption.

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.

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