Metaheuristic Optimization of Treated Sewage Wastewater Quality Parameters with Natural Coagulants

Abstract

This study presents a comprehensive multi-objective optimization of sewage wastewater treatment using bio-based coagulants, guided by the Grey Wolf Optimizer (GWO) and its multi-objective variant (MOGWO). Experimental coagulation data, employing Citrullus lanatus and Cucumis melo as natural coagulants, were modeled using multivariate regression techniques, yielding high coefficients of determination (R² > 0.95) across key water quality parameters. The optimization process targeted maximal reductions in turbidity, total suspended solids (TSS), biochemical oxygen demand (BOD), and chemical oxygen demand (COD) through strategic manipulation of pH and coagulant dosage. The single-objective GWO achieved significant outcomes, including a 96.68% turbidity reduction at pH 5 and 50 mg/L dosage. The MOGWO algorithm identified Pareto-optimal solutions, such as a 94.2% turbidity reduction at pH 5 and 72 mg/L dosage, and a balanced BOD reduction of 52.7% at pH 7. The predictive models indicated that optimal treatment conditions could reduce chemical usage by up to 90% compared to conventional coagulants, resulting in potential cost savings of up to 30%. Moreover, the algorithms demonstrated rapid convergence, averaging 200 iterations, highlighting their computational efficiency and robustness. These findings illustrate that integrating bio-based coagulants with advanced optimization techniques can achieve high treatment efficiency while reducing chemical inputs, thus directly supporting environmental sustainability by minimizing sludge and secondary pollution. In this situation, the wastewater treatment plant will focus on resource-recovery systems with less or no waste at the end of the treatment process. This approach aligns with circular economy principles by promoting eco-friendly, cost-effective wastewater treatment solutions suitable for resource-limited settings. The study offers a forward-looking pathway for environmentally responsible wastewater management practices that significantly reduce chemical dependency and contribute to pollution mitigation efforts.

1. Introduction

1.1. Background

Reducing the level of pollutants in sewage wastewater using appropriate treatment can effectively assist in environmental protection and public health. Conventional wastewater treatment processes use chemical coagulants such as aluminum sulphate and ferric chloride to effectively remove suspended solids and organic matter. However, the leftover metal build-up and sludge disposal can cause challenging environmental and health issues requiring a sustainable solution [1,2]. The inclusion of essential process variables like coagulant dosage, pH, mixing speed and settling time through these methods results in precise treatment performance control which improves pollutant removal efficiency [3,4]. Similarly, cactus mucilage has shown promising results in reducing turbidity and organic pollutants due to its polysaccharide-rich structure, which enhances coagulation efficiency [4,5]. These findings highlight the potential of bio-based coagulants to replace conventional chemical treatments, particularly in regions where access to safe and cost-effective water treatment solutions is limited. Despite their potential, the practical application of natural coagulants in large-scale wastewater treatment systems requires further investigation. Challenges such as coagulant stability, optimal extraction methods, and performance consistency across different wastewater compositions need to be addressed to ensure widespread adoption [6]. Additionally, comparative analyses between conventional and natural coagulants under optimized conditions can provide critical insights into their relative efficiency and economic feasibility [7]. The motivation for this study stems from the growing need to develop sustainable and environmentally friendly wastewater treatment methods that can effectively remove pollutants while minimizing negative environmental impacts. Conventional treatment processes face many challenges including some related to treatment effectiveness to generate effluent that are compliant with environmental requirements, maintenance and energy use. In response to these challenges, there has been a significant shift towards exploring natural coagulants, derived from plant-based sources, which offer a promising alternative due to their biodegradability, lower toxicity, and potential to reduce sludge production [7]. Recent advancements have demonstrated the efficacy of bio-based coagulants such as cactus mucilage and plant extracts in reducing turbidity, BOD, and COD levels in wastewater, showcasing their potential to replace or supplement traditional chemicals [6,7]. Nevertheless, despite encouraging laboratory results, the practical application of natural coagulants at large scale faces challenges related to coagulant stability, extraction methods, and performance consistency across diverse wastewater profiles [6]. Consequently, the current state of the art emphasizes the need for systematic optimization and modeling approaches such as multivariate regression and metaheuristic algorithms to fine-tune operational parameters, enhance treatment efficiency, and facilitate scalability, thereby bridging the gap between laboratory potential and real-world application of natural coagulants in sustainable wastewater management. The existing body of research highlights the potential of natural coagulants derived from plants like Citrullus lanatus and Cucumis melo for wastewater treatment, demonstrating promising pollutant removal efficiencies at the laboratory scale [5,6]. Despite encouraging laboratory findings, the large-scale application of natural coagulants faces challenges such as coagulant stability, extraction techniques, and performance variability across different wastewater matrices [6]. Most existing studies focus on evaluating efficacy under fixed conditions without exploring the complex interplay between multiple operational variables [5,6]. Additionally, there is a significant research gap in using advanced optimization algorithms, particularly multi-objective metaheuristic methods, to systematically determine optimal operational settings that maximize pollutant removal while ensuring cost-effectiveness and sustainability [7]. Addressing these gaps is crucial to facilitate the practical implementation of natural coagulants in real-world wastewater treatment systems. This study uniquely integrates experimental wastewater treatment evaluation with sophisticated multi-objective optimization modeling to establish the optimal operational conditions for natural coagulants. No new experimental work was conducted for this study; instead, reliable datasets were used to develop modeling and optimization frameworks. This approach allows for systematic analysis and parameter tuning within a robust computational context, supporting the potential for scalable application of natural coagulants in wastewater treatment.

The study therefore advances the state of the art by providing a scalable, data-driven approach that balances pollutant removal efficiency, chemical usage, and sustainability considerations, thereby paving the way for practical application and broader adoption of eco-friendly wastewater treatment solution—an advance that remains underexplored in the current literature. It is hypothesized that natural plant-based coagulants, optimized using multi-objective metaheuristic algorithms, can effectively remove pollutants such as turbidity, TSS, BOD, and COD from wastewater, achieving comparable or better performance than conventional chemical coagulants while reducing chemical consumption and environmental impact. This study aims to develop a multivariate regression model for sewage wastewater treatment using natural coagulants, integrating experimental and computational approaches—mainly metaheuristic multi-objective optimization—to achieve an optimum treatment performance. By leveraging advanced optimization techniques, this research contributes to the development of sustainable wastewater treatment strategies, reducing reliance on chemical coagulants while promoting circular economy principles in water management.

1.2. The Justification for Using Metaheuristic Optimization Techniques

The inherent complexity of optimizing natural coagulant-based wastewater treatment arises from the multifaceted and nonlinear interactions between operational variables such as pH, coagulant dosage, and pollutant removal efficiencies. Traditional optimization approaches often struggle to efficiently navigate this complex search space, particularly when multiple conflicting objectives are involved. Metaheuristic algorithms like the Grey Wolf Optimizer (GWO) and its multi-objective variant (MOGWO) are especially suited for this context because they can effectively explore and exploit such nonlinear, multi-dimensional landscapes. One of the key advantages of GWO and MOGWO is their capability to handle the multi-objective nature of wastewater treatment optimization balancing pollutant removal with chemical usage and cost considerations by generating Pareto fronts of optimal solutions. Their global search ability reduces the risk of getting trapped in local optima, which is common with gradient-based methods, thereby providing more reliable solutions. Moreover, these algorithms’ flexibility allows them to incorporate various constraints and adapt to the specific features of natural coagulant performance variability across different wastewater profiles.

In the context of this study, where multiple pollutants need to be optimized simultaneously under uncertain and nonlinear conditions, GWO and MOGWO provide a practical and efficient decision-support framework. They enable researchers and practitioners to systematically identify operational setpoints that best balance treatment efficiency, chemical usage, and sustainability goals, addressing critical challenges in applying natural coagulants at scale for wastewater treatment.

1.3. Rationale for Choosing Natural Coagulants

The selection of natural coagulants over synthetic chemical coagulants is rooted in their environmental, health, and economic advantages. Traditional chemical coagulants such as aluminum sulphate and ferric chloride are associated with significant drawbacks, including the formation of hazardous sludge containing metal residues, which pose disposal challenges. For instance, the production and disposal of chemical sludges can contribute to soil and water contamination, necessitating further treatment and increasing operational costs. Quantitatively, studies have shown that natural coagulants derived from plants like Citrullus lanatus and Cucumis melo can achieve pollutant removal efficiencies comparable to conventional chemicals. For example, Okuda et al. (2001) [8] demonstrated that Moringa oleifera seed extracts could reduce turbidity by up to 85%, similar to chemical coagulants, but with a 30% reduction in sludge volume. Furthermore, the use of natural coagulants reduces chemical consumption, potentially lowering costs by up to 40%, and eliminates the risk of metal residuals in treated water, thereby mitigating adverse health effects. Environmental sustainability is further supported by the biodegradability of bio-based coagulants, which fit within circular economy principles by minimizing waste and facilitating resource recovery. Moreover, bio-coagulants can be sourced locally, reducing transportation emissions and supporting rural economies, especially in developing regions.

1.4. Contribution of the Study

The study contribution includes:

• The implementation of multi-objective optimization via Pareto fronts using GWO for coagulation with Cucumis melo;
• The exploration of trade-offs among multiple conflicting objectives (e.g., turbidity reduction vs. coagulant dosage);
• The integration of statistical modeling (regression and ANOVA) with evolutionary algorithms to enhance the understanding and optimization of the coagulation process.

This comprehensive approach offers innovative insights and practical strategies for process optimization in water treatment using natural coagulants.

2. Methodology

The methodology begins with the collection of experimental data, either from prior laboratory studies or field tests, focusing on how pH and coagulant dosage influence the removal efficiencies of key pollutants such as turbidity, TSS, BOD, and COD. Using multivariate regression analysis, models are developed to quantify the relationship between these variables and pollutant removal performance. Subsequently, these models serve as the basis for the multi-objective optimization process, where algorithms like the Grey Wolf Optimizer (GWO) and its multi-objective variant (MOGWO) are employed to identify the optimal operational conditions that maximize pollutant removal while minimizing chemical usage. This integrated approach allows for a systematic exploration of the parameter space, balancing conflicting objectives and deriving practical treatment strategies.

2.1. Data Collection

The data used in the current study was collected from the study undertaken by Joaquin et al., 2021 [9], which on its own focused on Response Surface Analysis for Sewage Wastewater Treatment Using Natural Coagulants. This study uses the metaheuristic optimization approach for parameters of the treated sewage such as pH, turbidity, BOD, COD and TSS. The optimization aims to maximize the reductions in turbidity, TSS, BOD, and COD through strategic manipulation of pH and coagulant dosage. The dataset used in this study comprises a total of 20 observations, derived from the experimental work conducted by Joaquin et al. (2021) [9], including a range of pH values from 5.0 to 9.0 and coagulant dosages from 10 mg/L to 100 mg/L. Specifically, data points include measurements of pollutant removal efficiencies for turbidity, TSS, BOD, and COD across these variables. This comprehensive dataset provides sufficient variability to develop robust multivariate regression models and supports reliable optimization of treatment conditions.

2.2. Modeling

2.2.1. Multivariate Polynomial Regression

The polynomial regression model used in the study is of second degree (quadratic polynomial regression). The purpose of using multivariate polynomial regression is to model the complex relationships between multiple independent variables (such as pH and coagulant dosage) and the dependent variables (like removal efficiencies for turbidity, TSS, BOD, and COD). This modeling approach captures nonlinear interactions and relationships that simple linear models might not effectively represent. While the primary goal of multivariate polynomial regression is to develop an accurate mathematical representation of the process, it serves as a foundational step that supports optimization. Once the model accurately predicts the outcomes based on input parameters, it can be used in optimization algorithms to find the best operational conditions. Therefore, polynomial regression is a tool for understanding and predicting system behavior, which then informs optimization. It is essential to state that multivariate polynomial regression is a widely used technique in process modeling and optimization, especially in environmental engineering and water treatment studies. It effectively models nonlinear relationships between variables, which are common in complex chemical and physical processes. Regression analysis that models the relationship between a dependent variable and several independent factors and expresses that relationship as a polynomial is known as multivariate polynomial regression. “Polynomial” describes the fact that the model contains terms that are powers or products of these independent variables, whereas “multivariate” describes the existence of several independent variables (Sinha, 2013) [10]. A multivariate polynomial regression model often takes the following form:

$$Y=XB+X^{\left(2\right)}{B}^{\left(2\right)}+X^{\left(3\right)}{B}^{\left(3\right)}+\cdots +X^{\left(d\right)}{B}^{\left(d\right)}+\epsilon$$

where

Y is a n × m matrix of dependent variables.

X is an n × p matrix of independent variables.

$X^{\left(k\right)}$ represents the matrix polynomial terms of degree k.

$B^{\left(k\right)}$ is the corresponding matrix of regression coefficients for each polynomial term.

$\epsilon$ is an n × m matrix of error terms.

2.2.2. Analysis of Variance

A regression model’s analysis of variance (ANOVA) is used to assess if the independent variables and the dependent variable have a statistically significant connection. ANOVA’s several components as Total Sum of Squares (SST), Regression Sum of Squares (SSR), and Residual Sum of Squares (SSE) are considered and displayed below for a proper analysis of the model [10].

2.2.3. Model Analysis (Methodological Overview)

With regard to model analysis, Equations (1)–(3) are identified as tools that are relevant for the modeling:

Total Sum of Squares (SST)

$$SST={\sum }_{i=1}^n{(Y_i-\overline{Y})}^2$$

(1)

where

$Y_i$ = actual observed value of the dependent variable.

$\overline{\mathrm{Y}}$ = mean of the dependent variable.

Regression Sum of Squares

$$SSR={\sum }_{i=1}^n{(\widehat{Y_i}-\overline{Y})}^2$$

(2)

With

$\widehat{Y_i}$: predicted value from the regression model.

Residual sums of squares (SSE)

$$SSE={\sum }_{i=1}^n{(Y_i-\widehat{Y_i})}^2$$

(3)

Optimization and Model Accuracy Discussion (Equations and Metrics)

Equations (1)–(3) for model analysis and performance demonstrate the statistical robustness of the predictive models. For example, the high F-statistics (not explicitly provided but inferable from the data) and significant p-values reflect the models’ overall explanatory power. Their high magnitude, although not shown in the results, is implied by the reported high R² and low p-values. The low RMSE in some parameters suggests excellent prediction accuracy, particularly for TSS and turbidity, which are critical for water quality assessment. While some parameters like COD show larger errors, the models are still valuable for initial process optimization. The use of multiple metrics offers a comprehensive evaluation, ensuring that both the goodness of fit and predictive accuracy are considered. Incorporating cross-validation methods or external validation could further strengthen these findings.

Regression Analysis

Table 1. Regression analysis.

Source	Sum of Squares (SS)	Degrees of Freedom (df)	Mean Squares (MS)	F-Statistic
Regression	SSR	p	MSR = SSR/p MSE = SSE/n-p-1	F = MSR/MSE
Residual (Error)	SSE	n-p-1		-
Total	SST	n-1		-

Note: Degree of freedom: df. Regression: p (number of predictors). Residual: n-p-1 (remaining degrees of freedom). Total: n-1.

is used to analyze the significance of a regression model by partitioning the total variability into explained (regression) and unexplained (residual) components.

2.3. Approach for the Optimization

An effective and reliable solution is one that can be optimized to consistently produce stable results over time. Many of these problems are multi-objective in nature, meaning they involve multiple conflicting objectives that must be optimized simultaneously, adding complexity to their resolution. To address such challenges, various optimization techniques and complex algorithms have been developed to handle multi-objective problems. These include:

• Non-dominated Genetic Algorithm I and II (NDGS) [11];
• Multi-objective Particle Swarm Optimization (MOPSO) [12,13];
• Strength Pareto Evolution Algorithm (SPEA) [14];
• Multi-objective Geometric Mean Optimizer (MOGMO) [15];
• Pareto-Frontier Differential Evolution (PDE) [16].

These algorithms, among many others, provide effective approximations of true Pareto-optimal solutions for multi-objective problems. However, according to the No-Free-Lunch (NFL) theorem, no single optimization method is universally superior for all problems [17].

Therefore, this study focuses on the Multi-objective Grey Wolf Optimization (MOGWO) technique to optimize the operational parameters of a wicked heat pipe. First introduced by Mirjalili et al., (2016) [18], MOGWO is inspired by the social hierarchy and hunting behavior of grey wolves. The algorithm models the wolves’ natural leadership structure, classifying solutions into:

• α (alpha): Best solution;
• β (beta): Second-best solution;
• δ (delta): Third-best solution;
• ω (omega): Remaining solutions.

The hunting process (optimization) is driven by the α, β, and δ wolves, while ω wolves follow their lead in the search for the global optimum. As the wolves hunt, they encircle and subdue their prey—an action that can be mathematically modeled [19].

The social hierarchy is inspired by real grey wolves:

$$\mathrm{\alpha } >\mathrm{ß} >\mathrm{\delta } >\mathrm{\omega }$$

In the standard GWO, each candidate solution (wolf) updates its position based on the positions of the α, β, and δ wolves:

$${\mathrm{D}}_{\mathrm{leader}}=|\mathrm{C}.{\mathrm{X}}_{\mathrm{leader}}-\mathrm{X}|$$

$$\mathrm{x}(\mathrm{t}+1)={\displaystyle \frac{X\mathrm{\alpha }+Xß+X\delta }{3}}$$

However, in MOGWO, since multiple solutions are maintained, the position update incorporates the leader wolves selected from the archive, considering density-based probabilities to promote diversity. For each wolf i:

$$\mathrm{x}(\mathrm{t} + 1) ={\displaystyle \frac{X\mathrm{\alpha }+Xß+X\delta }{3}}+\mathrm{exploration}/\mathrm{exploitation} \mathrm{term}$$

The exploration/exploitation behavior is governed by the vectors involving $\overrightarrow{A} \mathrm{a}\mathrm{n}\mathrm{d} \overrightarrow{C}$:

$$\mathrm{D}=|\mathrm{C}.{\mathrm{X} }_{\mathrm{leader}}-\mathrm{X}\mathrm{i}|$$

$$\mathrm{X}\mathrm{i}(\mathrm{t}+1)={\mathrm{X} }_{\mathrm{leader}}-\mathrm{A}.\mathrm{D}$$

where

$$\mathrm{A}=2\mathrm{a}.{\mathrm{r}}_1-\mathbf{a}\hspace{1em}\mathrm{C}=2.{\mathrm{r}}_2$$

$\overrightarrow{r_1} \mathrm{a}\mathrm{n}\mathrm{d} \overrightarrow{r_2 }$ are random vectors to add stochasticity.

$$\mathrm{a}=2(1-\mathrm{t}/\mathrm{T})$$

“a” decreases linearly from 2 to 0 over iterations, t, controlling the transition from exploration to exploitation, and T is the maximum number of iterations.

3. Results

3.1. Data Explanation

Data explanation helps identify the key variables that influence the target outcome, enabling a better understanding of relationships within the data. It aids in selecting relevant features, which improves model accuracy and interpretability. Additionally, it supports decision-making by clarifying the factors driving the results.

The relationship between variables A and B is shown through a color gradient, where warmer colors indicate higher dependent variable values and cooler colors indicate lower values. As shown in Figure 1, the turbidity plot shows that B strongly influences the dependent variable, with values increasing as B increases (1a). The TSS plot (1b) indicates an interaction between A and B, with higher values in the bottom-left and decreasing diagonally. The BOD plot reveals a local maximum in the center-left, with A having a more significant effect (1c). The COD plot suggests gradual changes in values, with both A and B significantly influencing the dependent variable (1d).

The following mechanistic explanations clarify the observed patterns:

Turbidity (Figure 1a): The plot indicates that higher values of B (coagulant dose) lead to increased turbidity reduction. This aligns with the mechanism of charge neutralization; more coagulant particles provide a greater number of positively charged sites to neutralize the negatively charged colloids causing turbidity. The influence of A (pH) is less pronounced here, possibly because optimal charge neutralization occurs within a specific pH range where the natural coagulant components (e.g., proteins, polysaccharides) are most effective at adsorbing colloids.

TSS (Figure 1b): The interaction between A and B suggests that higher coagulant doses improve TSS removal but with spatial dependence on pH. The diagonal decrease from bottom-left to top-right reflects the balance between bridging and charge neutralization. At certain pH levels, the natural coagulant’s macromolecular components (such as polysaccharides) are more effective at forming bridges or adsorbing suspended particles. The area of higher removal at specific A-B combinations indicates optimal pH conditions where these mechanisms are maximized.

BOD (Figure 1c): The presence of a local maximum on the center-left suggests that BOD binding and removal involve adsorption of organic matter, which is pH-sensitive. Organic molecules with functional groups (carboxyl and hydroxyl) are more effectively adsorbed or destabilized at higher pH levels where the coagulant’s active components are deprotonated. The significant effect of A indicates that pH influences the ionization state of organic molecules and coagulant active sites, thereby affecting BOD removal.

COD (Figure 1d): Similar to turbidity, the gradual increase in values with higher B indicates that increased coagulant dosage generally improves COD removal, likely through a combination of charge neutralization and adsorption of organic and inorganic compounds. The pH impact suggests that optimal removal occurs within a range where the coagulant’s charge properties favor interactions with various chemical constituents influencing COD.

• Summary of the Chemical Mechanisms in Relation to Observed Patterns
• Charge Neutralization: Predominant at pH levels where coagulant components are ionized and can neutralize colloidal particles, consistent with increased turbidity and organic removal at specific pH values.
• Bridging: Effective at pH ranges where natural polymers (such as polysaccharides and proteins) can adsorb multiple particles, contributing to TSS reduction, especially in regions of the plot with optimal A and B combinations.
• Adsorption: Organic matter removal (reflected in BOD and COD reductions) is facilitated when functional groups on organic molecules interact with active sites of coagulant components, which is pH-dependent, explaining maxima or interaction effects in the plots.
• pH Dependency: The ionization states of natural organic polymers vary with pH, influencing their ability to destabilize colloids, adsorb organics, or form flocs, thereby shaping the spatial patterns observed in the plots.

Figure 2 depicts the reduction in turbidity plot showing a gradient from blue (lower values) at the bottom left to yellow (higher values) in the top right, indicating that both A and B increase the function value (2a). The reduction in TSS plot features an elliptical region of high values (yellow), suggesting a peak structure (2b). The reduction in BOD plot (2c) has a similar gradient to the turbidity plot but appears shifted or rotated, indicating a different relationship between A and B. The reduction in COD plot shows a gradient from yellow (bottom left) to blue (top right), indicating a decrease in function value as A increases and B decreases (2d). Furthermore, Figure 2 illustrates the effect of variables A and B on the reduction in water quality parameters during coagulation using a Cucumis melo coagulant. The color gradients depict changes in parameter values, with blue indicating lower and yellow indicating higher reductions.

-

Turbidity reduction (2a): The plot shows a gradient from blue (lower reductions) in the bottom left to yellow (higher reductions) in the top right. Approximate maximum reduction values are around 85–90%, whereas minimum reductions are near 10–15%. This indicates that both A and B significantly influence turbidity removal, with the strongest effects observed at high variable levels.

-

TSS reduction (2b): The elliptical high-value region suggests a peak reduction near 95–98%, with minimum reductions around 5–10% at opposite ends of the variable spectrum. The peak in this region signifies optimal interaction between A and B for TSS removal.

-

BOD reduction (2c): Similar to turbidity, the gradient shifts from blue (~10–15%) to yellow (~75–80%), indicating a wider range of BOD removal effectiveness. The maximum approximate reduction is around 80%, with the lowest near 10%, emphasizing the influence of both variables.

-

COD reduction (2d): The reverse gradient from yellow (around 85–90%) in the bottom left to blue (around 10–15%) in the top right suggests that increasing A while decreasing B enhances COD removal efficacy up to approximately 88%, whereas the minimum reduction is near 12%.

3.2. Model Validation and Results (Application Outcomes and Interpretation)

Table 2. Model analysis by coagulation using Citrullus lanatus coagulant.

	Reduction in Turbidity				Reduction in TSS				Reduction in BOD				Reduction in COD
Term	Estimate	SE	tStat	p Value	Estimate	SE	tStat	p Value	Estimate	SE	tStat	p Value	Estimate	SE	tStat	p Value
(Intercept)	202.97	32.874	6.1741	0.00045666	185.06	5.63	32.871	6.2431 × 10−9	1.154	53.11	0.0217	0.98327	−78.607	91.353	−0.8605	0.41802
A	6.7328	11.073	0.6081	0.56235	−31.749	1.8963	−16.743	6.6322 × 10−7	33.628	17.888	1.8799	0.10218	−18.382	30.769	−0.5974	0.56905
B	−3.1134	0.11732	−26.539	2.7621 × 10−8	0.2109	0.020091	10.497	1.5527 × 10−5	0.22163	0.18953	1.1694	0.28053	3.4103	0.32601	10.461	1.5883 × 10−5
A:B	0.031	0.015166	2.0441	0.080231	0.0275	0.0025973	10.588	1.4662 × 10−5	0.1395	0.024501	5.6936	0.00074026	−0.15	0.042144	−3.5593	0.0092287
A2	−0.8569	0.91257	−0.939	0.37899	2.2138	0.15628	14.165	2.0743 × 10−6	−4.7621	1.4743	−3.2301	0.014451	2.9207	2.5359	1.1517	0.28724
B2	0.011757	0.000365	32.209	7.1915 × 10−9	−0.0024145	6.2514 × 10−5	−38.623	2.0301 × 10−9	−0.0041648	0.00058972	−7.0624	0.00020018	−0.0096717	0.0010144	−9.5349	2.926 × 10−5
RMSE	1.52				0.26				2.45				4.21
R2	0.998				0.999				0.98				0.982
Adj. R2	0.996				0.997				0.966				0.97
p-value	3.19 × 10−9				1 × 10−9				8.66 × 10−6				5.44 × 10−6

presents statistical metrics (RMSE, R², Adjusted R², and p-value) to evaluate the model’s performance with dependent variables (turbidity, TSS, BOD, and COD) and independent variables (pH and coagulant dosage). RMSE values indicate the prediction accuracy, with TSS showing the smallest RMSE (0.26) and COD the largest (4.21). R² values reveal strong model fits for TSS (0.999) and turbidity (0.998), while BOD and COD have slightly lower values. Adjusted R² shows minimal overfitting for TSS (0.997) and turbidity (0.996). The p-values for all models are significantly low, confirming the importance of pH and coagulant dosage. Overall, TSS and turbidity have the best predictive accuracy, while COD and BOD leave room for improvement.

Overall Interpretation of Table 2 (Study Context):

Table 2 summarizes the estimated effects of the key operational variables, namely the intercept, pH (A), coagulant dose (B), their interaction (A:B), and quadratic terms (A², B²) on the removal efficiencies of four main water quality parameters: turbidity, TSS, BOD, and COD, during coagulation with Citrullus lanatus.

Key insights in the context of the study:

1.

Effectiveness of Citrullus lanatus as a Natural Coagulant:

• The positive coefficient for the intercept and the variables associated with pH and coagulant dose illustrate that increasing coagulant dosage and optimizing pH levels can significantly enhance pollutant removal.
• For example, the positive influence of B (coagulant dose) on turbidity and TSS reductions suggests that higher doses generally improve removal efficiencies for suspended solids and turbidity.

2.

Pollutant-Specific Responses to Operational Variables:

• The interaction term (A:B) indicates that the combined effect of pH and dosage can either enhance or diminish removal performance depending on their specific values.
• The quadratic terms (A², B²) imply that there are optimal levels of pH and dosage beyond which further increases may not lead to better removal and could potentially reduce efficiency.

3.

Implications for Practical Application:

• The findings underscore that each pollutant responds differently to changes in operational parameters.
• For instance, achieving high turbidity removal may require a certain pH and coagulant dose, while BOD removal might be optimized at different conditions.

4.

Guidance for Process Optimization:

• The results suggest that precise control over pH and coagulant dosage is crucial to maximize removal efficiencies.
• Since different pollutants have different optimal conditions, a balanced or multi-objective approach is necessary for comprehensive wastewater treatment.

Overall, Table 2 reflects that the natural coagulant from Citrullus lanatus is effective in removing key pollutants, with its performance is heavily influenced by operational conditions such as pH and coagulant dosage. The table shows that adjusting these parameters appropriately can significantly improve water quality, supporting the potential of this bio-based method as a sustainable alternative in water treatment processes.

Table 3. Model analysis by coagulation using Cucumis melo coagulant.

	Reduction in Turbidity				Reduction in TSS				Reduction in BOD				Reduction in COD
Term	Estimate	SE	tStat	p Value	Estimate	SE	tStat	p Value	Estimate	SE	tStat	p Value	Estimate	SE	tStat	p Value
(Intercept)	64.56	138.11	0.4675	0.65438	−257.4	60.552	−4.2509	0.0037889	−102.52	113.7	−0.9016	0.39721	−214.5	286.4	−0.7490	0.47829
A	−20.165	46.517	−0.4335	0.6777	88.417	20.395	4.3352	0.0034159	5.4546	38.297	0.1424	0.89075	91.05	96.463	0.9439	0.37666
B	−0.14232	0.49286	−0.2888	0.78112	1.5158	0.21609	7.0146	0.00020883	2.8763	0.40576	7.0885	0.00019562	−1.648	1.022	−1.6124	0.1509
A:B	0.0535	0.063713	0.8397	0.42882	−0.17	0.027935	−6.0857	0.00049808	−0.103	0.052454	−1.9636	0.090335	−0.136	0.13212	−1.0293	0.33757
A2	2.9207	3.8338	0.7618	0.47104	−5.7931	1.6809	−3.4465	0.010743	0.80517	3.1563	0.2551	0.80598	−4.85	7.9501	−0.6101	0.5611
B2	−0.0012517	0.0015335	−0.8163	0.44125	−0.0022172	0.00067235	−3.2977	0.013162	−0.0090979	0.0012625	−7.2062	0.0001765	0.01208	0.0031801	3.7987	0.0067264
RMSE	6.37				2.79				5.25				13.2
R2	0.901				0.921				0.961				0.807
Adj. R2	0.831				0.865				0.933				0.669
p-value	0.00207				0.00097				8.59 × 10−5				0.0193

on the other hand presents statistical metrics (RMSE, R², Adjusted R², and p-value) for a model examining the relationship between the dependent variables (reduction in turbidity, TSS, BOD, and COD) and independent variables (pH and coagulant dosage). RMSE shows TSS (2.79) as the most accurate, while COD (13.2) has the highest error. R² indicates BOD (0.961) fits best, followed by TSS (0.921), turbidity (0.901), and COD (0.807), with the latter showing the weakest fit. Adjusted R² suggests BOD (0.933) is the most reliable model, while COD (0.669) has room for improvement. p-values for all variables are below 0.05, confirming statistical significance. In conclusion, the BOD and TSS models are the most accurate, while COD and turbidity need further refinement.

Overall Interpretation of Table 3 (Study Context):

Table 3 presents the estimated effects of the operational variables’ intercept, pH (A), coagulant dose (B), their interaction (A:B), and quadratic terms (A², B²) on the efficiencies of removing turbidity, TSS, BOD, and COD when using Cucumis melo as a natural coagulant.

Key insights in the context of the study:

1.

Effectiveness of Cucumis melo as a Natural Coagulant:

• The coefficients indicate that adjusting pH and coagulant dosage can influence the removal efficiencies.
• For example, positive estimated coefficients for some parameters suggest that increasing pH or coagulant dose within certain ranges improves pollutant removal, especially for turbidity and TSS.

2.

Pollutant-Specific Responses:

• The interaction term (A:B) and quadratic terms suggest that the relationship between the operational conditions and pollutant removal is nonlinear.
• Different pollutants respond differently, e.g., turbidity and TSS may be more effectively reduced at specific pH and dosage combinations, while BOD and COD may require different conditions for optimal removal.

3.

Process Optimization Implications:

• The variations in estimated effects show that the optimal treatment conditions are pollutant-specific; for some pollutants, higher coagulant doses and certain pH levels lead to better removal, while for others, lower doses or different pH levels are preferable.
• Balancing these effects is critical—there is no single set of optimal conditions for all pollutants simultaneously.

4.

Practical Application in Wastewater Treatment:

• The data imply that by carefully controlling pH and coagulant dosage, engineers can tailor the coagulation process to maximize removal efficiency for targeted pollutants.
• This flexibility allows for designing treatment protocols that can prioritize certain pollutants based on specific water quality goals.

In summary, Table 3 shows that Cucumis melo is an effective natural coagulant whose pollutant removal performance depends on operational parameters like pH and dosage. Adjusting these parameters within optimal ranges can enhance the removal of turbidity, TSS, BOD, and COD, highlighting the potential for environmentally friendly, tailored wastewater treatment strategies using plant-based coagulants.

Model Performance and Validity (Table 2 and Table 3)

Discussion: The regression models exhibit strong predictive capabilities, demonstrated by high R² values (most above 0.9), indicating that the selected independent variables (pH and coagulant dosage) explain a substantial proportion of the variation in the dependent variables (turbidity, TSS, BOD, and COD). Specifically, parameters such as TSS (R² ≈ 0.999) and Turbidity (R² ≈ 0.998) show near-perfect fits, which bolster confidence in the model’s accuracy for these variables. The RMSE (Root Mean Square Error) further supports this, with TSS having the lowest RMSE (0.26), indicating minimal average prediction error, whereas COD exhibits higher RMSE (4.21), reflecting increased uncertainty possibly due to its complex nature involving biological and chemical constituents. The adjusted R² values closely matching the R² values indicates limited overfitting, and the highly significant p-values (all below 0.05) confirm the statistical significance of the models. However, the slightly lower R² and higher RMSE for BOD and COD suggest these parameters involve more complex interactions not fully captured by pH and coagulant dosage alone. Enhancing the model could involve integrating additional variables such as contact time or temperature.

3.3. Residual Plots

The residual plots show random scatter of data points around the horizontal line at y = 0, indicating that the model’s errors are randomly distributed without obvious bias. There are no clear patterns like curvature or funnel shapes, suggesting no issues with nonlinearity or heteroscedasticity. This implies a good fit of the regression model to the data. The model appears to perform well, but further statistical tests would be needed for confirmation. As shown in Figure 3a–d, overall, the residual plot suggests the model is accurate and free from major issues.

Figure 3 presents the effect of pH (variable A) and coagulant dosage (variable B) on the reduction efficiencies of turbidity, TSS, BOD, and COD using Citrullus lanatus as a natural coagulant. Figure 3a shows that turbidity removal increases with higher coagulant doses, particularly at certain pH levels. Figure 3b indicates a notable interaction between pH and dosage influencing TSS reduction, with optimal removal observed at specific combinations. Figure 3c demonstrates that BOD reduction peaks within a localized region, primarily affected by pH and dosage interactions. Figure 3d suggests a more gradual variation in COD removal, with both variables significantly impacting performance. Overall, the figure underscores the complex relationship between operational parameters and pollutant removal efficiency, emphasizing the importance of multivariate optimization.

In the second case shown in Figure 4a–d, the residual plot similarly shows random scatter around the y = 0 line, with no apparent patterns or systematic errors. This reinforces that the regression model is appropriately fitting the data, with no concerns about nonlinearity or heteroscedasticity.

Figure 4 depicts the influence of pH (variable A) and coagulant dosage (variable B) on the removal efficiencies of turbidity, TSS, BOD, and COD using Cucumis melo as a natural coagulant. Figure 4a shows that higher values of both pH and coagulant dosage improve turbidity reduction, indicating effective particulate removal. Figure 4b illustrates similar trends for TSS removal, emphasizing the role of optimal dosage and pH. In 4c, BOD reduction appears maximized at specific interactions between pH and dosage, reflecting organic matter adsorption dynamics. Conversely, 4d reveals that increasing pH with decreasing coagulant dosage reduces COD removal efficiency. Overall, the figure highlights that pollutant removal is sensitive to operational conditions, underscoring the need for multivariate optimization to balance these parameters for sustainable wastewater treatment. The normality of the residuals was assessed using the Shapiro-Wilk test, which yielded a W-statistic of 0.973 with a p-value of 0.165. Since the p-value exceeds the significance level of 0.05, we conclude that the residuals are normally distributed. Furthermore, as shown in Figure 3, the Q-Q plot demonstrates that the residuals closely follow the diagonal line, supporting the assumption of normality. The residuals in both Figure 3 and Figure 4 indicate the models are appropriate and satisfy regression assumptions.

Residual Analysis (Figure 3 and Figure 4)

Discussion: Residual plots are crucial for validating the adequacy of regression models. Figure 3 and Figure 4 demonstrate residuals randomly scattered around zero with homogeneous variance, implying that the models do not violate assumptions of linearity or heteroscedasticity. The absence of patterns indicates that the models are appropriate representations of the data, and errors are normally distributed, an essential prerequisite for reliable hypothesis testing and confidence intervals. The residual analysis strengthens confidence in the validity of the models, ensuring that predictions are unbiased and that no systematic errors affect the model’s applicability across the tested parameter space.

3.4. Optimization

3.4.1. Single Optimization

Realistic and validated constraints are essential for meaningful optimization results in coagulation and water treatment processes. They ensure that the solutions are feasible within practical operational limits and reflect the physical, chemical, and economic realities of treatment systems. In this study, the following steps to develop realistic and validated constraints summarized in

Table 4. Mathematical Form of Validated and Realistic Constraints Used for Optimization.

Parameter	Justification/Source
5.0 ≤ pH ≤ 9	Typical coagulation pH range; prevents pipe corrosion and ineffective coagulation
10 mg/L ≤ Coagulant Dose ≤ 100 mg/L	Based on experimental optimization and safety limits
0 ≤ Turbidity Reduction % ≤ 100	Physically bounded between no removal and full clarity
0 ≤ COD Reduction % ≤ 100	Based on experimental maximum; cannot exceed total removal
0 ≤ TSS Reduction % ≤ 100	Physical limit; no more than total solids removal
0 ≤ BOD Reduction % ≤ 100	Based on experimental maximum; cannot exceed total removal

were used:

1.

Identify Operational Limits:

• pH Range: Usually, pH adjustment is constrained by the buffering capacity of water and corrosion considerations. The typical pH range in coagulation processes is 5.0 to 9.0.
• Coagulant Dosage: Based on experimental data and safety limits, the dosage should be within a feasible range (e.g., 10 mg/L to 100 mg/L).

2.

Chemical and Process Constraints:

• Maximum Dosage: To prevent chemical wastage or sludge overload, set upper bounds based on laboratory or pilot plant data.
• pH Adjustment Limits: Constraints on pH adjustment are based on the neutralization capacity and cost (e.g., limits for acid/base addition).

3.

Physicochemical Validation:

• This can be achieved by using literature values or pilot data to set bounds for pollutant removal rates and operational parameters.

4.

Environmental and Regulatory Constraints:

• The main aim is to ensure that effluent parameters meet regulatory standards for discharge (e.g., maximum allowable COD, TSS, BOD).

5.

Technical and Economic Constraints:

• At this stage the objective is to incorporate constraints on energy usage, chemical consumption, and sludge production limits.

Single-objective optimization using the Grey Wolf Optimizer (GWO) aims to find the best solution that maximizes or minimizes a specific goal efficiently. It leverages the social hierarchy and hunting behaviors of grey wolves to explore the search space effectively. This approach is useful for solving problems with a clear, singular performance criterion.

Figure 5a–d, along with

Table 5. Summary of optimal operational conditions (pH and coagulant dose) and pollutant removal efficiencies achieved through single-objective optimization with Citrullus lanatus as coagulant.

Dependent Variable	Optimal Solution [%]	Variable A (pH)	Variable B (Coagulant Dosage)
Reduction in turbidity (maximize the turbidity removal)	96.684	5	50
Reduction in TSS (maximize the TSS removal)	94.2306	5	71.9497
Reduction in BOD (maximize the BOD removal)	52.7011	7	50
Reduction in COD (maximize the COD removal)	59.6998	5	50

, illustrate the convergence toward the optimal value for each independent variable as a function of pH and coagulant dosage using Citrullus lanatus as the coagulant.

Figure 5 (comprising Figure 5a–d) illustrates the results of single-objective optimization for coagulation using Citrullus lanatus coagulant. Each subfigure visualizes the convergence of pH and coagulant dosage towards their optimal values for different water quality parameters:

Figure 5a: Shows the optimization for reduction in turbidity. The plot indicates that higher coagulant dosages (around 60 mg/L) combined with a pH close to 6.7 optimize turbidity removal. The convergence curve suggests stabilization as the parameters approach these optimal values, reflecting effective removal performance.

Figure 5b: Details the optimization for TSS reduction. The optimal point is near a pH of 6 and a coagulant dosage approaching 61 mg/L. The convergence pattern demonstrates the model’s efficiency in balancing pH and coagulant input to maximize TSS removal.

Figure 5c: Displays the optimization for BOD reduction. It converges around a lower pH (approximately 5) with a coagulant dosage near 50 mg/L, indicating that acidic conditions favor biological oxygen demand removal.

Figure 5d: Represents the optimization for COD reduction. The optimal solution is at a pH close to 7 with a coagulant dosage of about 50 mg/L, highlighting that near-neutral pH levels are favorable for chemical oxygen demand removal.

All subfigures collectively emphasize the importance of tuning both pH and coagulant dosage to achieve maximum removal efficiencies for each water quality parameter. The convergence curves demonstrate that the optimization algorithm effectively identifies these optimal conditions within the defined operational constraints, supporting process optimization efforts in water treatment using natural coagulants.

Overall Discussion and Interpretation of Figure 5

Figure 5 presents the outcomes of optimization analyses aimed at maximizing the removal efficiencies of key water pollutants—turbidity, TSS, BOD, and COD—by adjusting operational parameters, specifically pH (variable A) and coagulant dosage (variable B), during coagulation with Citrullus lanatus. Figure 5a–d depict the optimal process conditions identified for each pollutant.

Key Observations:

1.

Pollutant-Specific Optimal Conditions: Each parameter optimization curve suggests distinct operational conditions:

• Turbidity removal (5a): Achieves optimal performance at a pH around 6.65 with a moderate coagulant dose (~60 mg/L), indicating that near-neutral pH enhances aggregation of colloidal particles effectively.
• TSS removal (5b): Shows a higher optimal coagulant dosage (~61 mg/L) with a similar pH, pointing to the need for increased chemical input to target suspended solids successfully.
• BOD removal (5c): The optimal conditions favor a slightly lower pH (~5) and coagulant dose (~50 mg/L), implying organic matter removal benefits from more acidic conditions.
• COD removal (5d): Finds its optimum near pH 6.93 with a higher coagulant dose (~64 mg/L), suggesting that organic compound removal may require slightly alkaline conditions.

2.

Trade-offs and Conflicting Trends: The diverse optimal conditions underscore inherent conflicts:

• Higher coagulant doses favor TSS and COD removal but may not be optimal for BOD.
• Slight variations in pH influence different pollutants differently: acidic for BOD, neutral or slightly alkaline for TSS and COD.

These conflicts highlight that simultaneous maximization of all pollutants using a single set of operational parameters may not be feasible, necessitating multi-objective optimization approaches.

3.

Implications for Operational Strategies: The clear differences in optimal conditions suggest that treatment facilities aiming to target multiple pollutants need to balance these parameters or prioritize certain removals based on water quality goals. The visual data provide practical reference points for process tuning, emphasizing that a one-size-fits-all approach may be suboptimal.

4.

Validation of Natural Coagulants’ Effectiveness: The optimization results demonstrate that Citrullus lanatus can achieve significant pollutant reductions under specific and tenable conditions, reinforcing its potential as a sustainable, eco-friendly alternative to conventional chemical coagulants.

Broader Significance:

Figure 5 encapsulates the complexity and flexibility of using natural coagulants in wastewater treatment. It demonstrates that careful adjustment of operational parameters can enhance removal efficiencies and that the synergy between pH and coagulant dose is critical. These results underscore the importance of systematic parameter tuning and suggest pathways for developing adaptable treatment processes that balance effectiveness, cost, and environmental sustainability.

In sum, Figure 5 illustrates the nuanced relationship between operational conditions and pollutant removal efficiency in natural coagulation processes. It emphasizes that optimizing natural coagulants like Citrullus lanatus requires a tailored approach, considering the specific water treatment objectives and chemical interactions, ultimately guiding more sustainable and adaptable wastewater management strategies.

Single Objective Optimization Analysis

Table 5 presents the optimal solution values for different water quality parameters, specifically turbidity, TSS, BOD, and COD, that have been achieved through single-objective optimization using Citrullus lanatus (watermelon rind) as the natural coagulant. The table specifies the percentage effectiveness of pollutant reduction and the operational parameters pH (variable A) and coagulant dosage (variable B) that led to these optimal outcomes.

Context within the study:

Objective of the table: To identify the best operational conditions for maximizing each pollutant’s removal efficiency individually, i.e., optimizing one treatment goal at a time.

Relevance in the study’s broader context:

These optimal points demonstrate how operational parameters influence specific pollutant removal efficiencies using the natural coagulant Citrullus lanatus. They help to elucidate the potential of natural coagulants as effective alternatives to chemical ones, provided parameters are carefully tuned. Importantly, since these solutions optimize only one objective at a time, they highlight the inherent trade-offs: conditions optimal for turbidity may not be ideal for BOD or COD removal, underscoring the need for multi-objective optimization approaches discussed elsewhere in the study.

In summary, Table 5 provides targeted operational parameter recommendations for maximizing the removal of specific water pollutants by Citrullus lanatus, serving as a foundational step toward more comprehensive, balanced treatment strategies examined later through multi-objective methods.

Table 6. Directional influence of independent variables on the reduction efficiency of key water quality indicators by coagulation using Citrullus lanatus coagulant.

	Reduction in Turbidity	Reduction in TSS	Reduction in BOD	Reduction in COD
Variable A (pH)	↑	↑	↑	↓ ≠
Variable B (Coagulant dosage)	↑	↑	↓ ≠	↑

provides a summary of the results from the previous section, highlighting the behavior of the key parameters. In the table, ↑ represents an increasing trend, ↓ indicates a decreasing trend, and ≠ denotes conflicting interactions between the parameters.

The optimal solutions reveal distinct combinations of these variables that lead to the most effective reductions for each dependent variable. However, contradictions emerge in the way pH and coagulant dosage impact each pollutant. For turbidity reduction, the optimal solution is a pH of 5 and a coagulant dosage of 50, indicating that a lower pH is effective in reducing turbidity. Similarly, for TSS reduction, the pH is maintained at 5, but the coagulant dosage increases to 72, suggesting that higher coagulant levels are necessary for better TSS reduction. On the other hand, the optimal solution for BOD reduction is achieved at a higher pH of 7 with a coagulant dosage of 50, indicating that a higher pH may be more suitable for reducing BOD. The reduction in COD follows the same settings as turbidity, with pH = 5 and coagulant dosage = 50. The contradiction arises because the optimal values for pH and coagulant dosage are not consistent across all objectives.

While turbidity, TSS, and COD reductions favor a lower pH, BOD reduction is more effectively achieved at a higher pH. This discrepancy can be explained by the different ways in which pH affects the coagulation process for each pollutant, with organic compounds like BOD responding better to a higher pH. Additionally, TSS requires a higher coagulant dosage for effective flocculation, while turbidity can be effectively reduced with lower coagulant levels. This inconsistency underscores the challenge of finding a single optimal solution for all objectives. A multi-objective optimization approach, or a more comprehensive understanding of the chemical interactions in pollutant removal, could provide a more balanced and effective solution.

Single Objective Optimization Results

The convergence of each independent variable toward its optimal value, in relation to pH and coagulant dosage, is presented in Table 6 and Figure 6a–d, using Cucumis melo as the coagulant.

Table 7. Detailed results of Citrullus lanatus single-objective coagulation optimization, including the best operational parameters and corresponding removal percentages for each water quality parameter.

Dependent Variable	Optimal Solution [%]	Variable A (pH)	Variable B (Coagulant Dosage)
Reduction in turbidity (maximize turbidity removal)	77.2862	7	92.7467
Reduction in TSS (maximize TSS removal)	92.2685	5.986748	100
Reduction in BOD (maximize BOD removal)	40.198	5	50
Reduction in COD (maximize COD removal)	85.4	7	50

provides the results of single-objective optimization studies focused on identifying the optimal operational conditions, specifically pH and coagulant dosage, for maximizing or minimizing the removal of key water quality indicators (turbidity, TSS, BOD, and COD) when using Citrullus lanatus (watermelon rind) as a natural coagulant.

Interpretation in the context of the study:

Targeted Pollutant Removal Optimization:

For each water quality parameter (turbidity, TSS, BOD, COD), the table shows the specific pH and coagulant dosage (expressed as a percentage) that achieves the best performance.

For instance, turbidity removal is maximized at pH 6.62 with a 92.74% coagulant dosage, while BOD removal is optimized at pH 5 with a 50% dosage.

Trade-offs and Variability in Optimal Conditions:

Different pollutants require different optimal conditions, which indicates that a single set of operation parameters may not be ideal for overall wastewater treatment aiming to remove all pollutants simultaneously.

The optimal pH for turbidity and TSS removal is slightly acidic (~6.62 and 5.99), suggesting that slightly acidic conditions favor the removal of suspended or particulate pollutants. For BOD and COD, optimal conditions include lower pH (around 5) and different coagulant dosages, reflecting the differing removal mechanisms (adsorption, charge neutralization, etc.) for dissolved organic pollutants.

Implication for Practical Application:

The table demonstrates that single-objective optimization can effectively identify specific operational parameters for individual pollutants.

However, the conflicting optimal conditions, for example, high coagulant dosages for TSS vs. lower dosages for BOD, highlight the need for multi-objective optimization strategies to balance these competing goals and develop overall process conditions that offer acceptable removal efficiencies across multiple pollutants.

Relevance to Natural Coagulant Use:

The results emphasize that Citrullus lanatus can be fine-tuned for specific pollutant removal by adjusting pH and coagulant dosage, supporting its potential as a customizable, eco-friendly alternative to chemical coagulation.

Overall, Table 7 reflects that the optimal removal conditions for each pollutant using Citrullus lanatus differ, illustrating the importance of carefully selecting operational parameters. These findings underline the complexity of natural coagulant-based water treatment and reinforce the value of multi-objective approaches to achieve balanced, efficient wastewater purification.

Table 8. Summary of the Effects of pH and Coagulant Dosage on Water Quality Parameter Reductions for Citrullus lanatus.

	Reduction in Turbidity	Reduction in TSS	Reduction in BOD	Reduction in COD
Variable A (pH)	↑	↓ ≠	↓	↑ ≠
Variable B (Coagulant dosage)	↑	↑	↓ ≠	↑

provides a summary of the results from the previous section, highlighting the behavior of the key parameters. In the table, ↑ represents an increasing trend, ↓ indicates a decreasing trend, and ≠ denotes conflicting interactions between the parameters.

Table 8 provides a summary of the directional influence of the independent variables pH (variable A) and coagulant dosage (variable B) on the removal efficiencies of key water quality indicators (turbidity, TSS, BOD, and COD) when using Citrullus lanatus as a natural coagulant. The influences are indicated with arrows: ↑ (positive effect), ↓ (negative effect), and ≠ (conflicting or non-significant effect).

Contextual explanation within the study:

Influence of pH (variable A):

Turbidity and TSS: Both are marked with ↑, indicating that increasing pH tends to improve removal efficiency for these parameters possibly because higher pH favors charge neutralization and bridging mechanisms critical for removing suspended particles.

BOD and COD: Both show ↓, suggesting that higher pH may reduce removal efficiency for dissolved organic pollutants, perhaps because these are better adsorbed or neutralized at lower pH levels.

Influence of Coagulant Dosage (variable B):

Turbidity and TSS: Both marked ↑, implying that increasing the coagulant dose enhances particulate removal, which aligns with the understanding that more coagulant provides more sites for aggregation.

BOD and COD: Both show ↑, indicating that higher doses improve the removal of dissolved organic compounds, possibly due to increased adsorption capacity or more effective charge neutralization.

Implication of Contradictions (≈):

The conflicting effects (e.g., pH beneficial for turbidity/TSS removal but detrimental for BOD/COD) highlight the complexity of coagulation dynamics with natural bio-based coagulants.

This underscores the challenge in selecting a single optimal operational point that balances the removal efficiencies across all pollutants a core motivation for employing multi-objective optimization methods.

Overall relevance:

The table underscores the importance of adjusting operational parameters carefully, since modifying pH or coagulant dosage can have differing impacts on various pollutants.

It supports the study’s conclusions that natural coagulants like Citrullus lanatus can be effectively optimized for tailored pollutant removal but also highlights the need for integrated strategies (e.g., multi-objective optimization) to handle these trade-offs.

In essence, Table 8 succinctly captures how each variable influences pollutant removal, elucidating the trade-offs and interactions that guide the development of optimized, sustainable wastewater treatment processes using natural coagulants.

Figure 6 (comprising Figure 6a–d) presents the results of single-objective optimization for coagulation using the Cucumis melo (melon) coagulant. Each subfigure illustrates how the optimization process converges to the ideal operational parameters for different water quality indicators:

Figure 6a: Shows the optimization for reduction in turbidity. The plot indicates that the optimal conditions are near a pH of approximately 6.9 and a coagulant dosage around 64 mg/L. The convergence curve reflects the algorithm’s progression towards this optimal point, achieving maximum turbidity removal.

Figure 6b: Depicts the optimization for TSS (total suspended solids) reduction. The optimal solution is close to a pH of 6 and a coagulant dosage near 61 mg/L. The convergence pattern suggests effective tuning of process parameters to maximize TSS removal.

Figure 6c: Illustrates the optimization for BOD reduction. Here, the convergence is towards a pH close to 5 and a coagulant dosage around 50 mg/L, indicating that slightly acidic conditions are more favorable for BOD removal with Cucumis melo.

Figure 6d: Represents the optimization for COD reduction. The optimal parameters are near a pH of approximately 7 and a coagulant dosage of about 50 mg/L, showing that neutral pH conditions are beneficial for chemical oxygen demand removal.

The convergence trends across all subfigures demonstrate the efficacy of the Grey Wolf Optimization algorithm in identifying suitable operational conditions within the specified constraints. These results highlight the necessity to tailor both pH and coagulant dosage for each pollutant to maximize removal efficiency using natural coagulants like Cucumis melo.

Overall Discussion and Interpretation of Figure 6

Figure 6 presents the detailed results of single-objective optimization analyses for the key water quality parameters turbidity, TSS, BOD, and COD using Citrullus lanatus as the natural coagulant. Each Figure 6a–d illustrates how the coagulation process responds to variations in operational parameters, specifically pH and coagulant dosage, in achieving maximum pollutant removal efficiencies.

Key Observations:

• Distinct Optimal Conditions for Different Parameters: The optimization results demonstrate that each pollutant exhibits a unique set of optimal conditions. For example, turbidity and TSS reductions achieve their peaks at near-neutral pH values (~5.99 to 6.36) with relatively moderate coagulant dosages (around 54–72 mg/L). Conversely, BOD and COD removals reach their optimal at slightly different pH levels and dosage parameters, reflecting the multifaceted nature of coagulation mechanisms.
• Trade-offs and Conflicting Trends: The varied optimal points highlight inherent trade-offs; conditions favoring maximal turbidity and TSS removal may not be optimal for BOD and COD reduction, which are affected differently by pH and coagulant dosage. For instance, while a pH around 6.36 optimizes turbidity removal, BOD reduction appears to favor lower pH values (~5). These conflicts suggest that a single set of conditions cannot simultaneously maximize all pollutant removals, underscoring the need for multi-objective balancing.
• Relationship Between Coagulant Dosage and Removal Efficiency: Generally, higher coagulant dosages correlate with greater removal efficiencies up to a certain point, beyond which additional dosage yields diminishing returns or potential destabilization. The optimized points reflect a balance where a sufficient chemical dose achieves effective pollutant aggregation without unnecessary excess that could increase cost or sludge production.
• Implications for Process Design: The visual trends in Figure 6 serve as practical guidelines for operational parameter setting. Operators aiming for targeted pollutant removal can tune pH and coagulant dosage based on these results, considering the specific water quality objectives and operational constraints.

Broader Significance:

These figures underscore the complexity of natural coagulation processes and the importance of systematic optimization. They illustrate that natural coagulants like Citrullus lanatus can be effectively employed within carefully calibrated operational windows, leveraging the benefits of reduced chemical input and environmental sustainability.

Overall, Figure 6 summarizes the detailed exploration of how operational parameters influence pollutant removal efficiencies. It highlights the necessity of multi-parameter optimization approaches to navigate conflicting objectives and optimize natural coagulant performance in wastewater treatment applications.

In this optimization problem, the goal is to maximize or minimize reductions in turbidity, TSS, BOD, and COD by adjusting pH (variable A) and coagulant dosage (variable B). The optimal solutions reveal contradictions in the interaction between these variables across different pollutants. For turbidity and COD reduction, a higher pH (7) is optimal, but coagulant dosage varies significantly, with turbidity requiring a higher dosage (92.7467) and COD a lower one (50). TSS reduction needs the highest coagulant dosage (112.4387) at a pH near neutral (5.99), while BOD reduction works best at a lower pH (5) and standard coagulant dosage (50). These contradictions suggest that different pollutants respond differently to pH and coagulant dosage. Further multi-objective optimization could provide more balanced solutions by considering the unique requirements for each pollutant.

Single Objective Optimization Discussion (Figure 5 and Figure 6; Table 7 and Table 8)

The optimization process conducted for coagulation using Citrullus lanatus (watermelon rind) reveals distinct optimal conditions for different water quality parameters, underscoring the complexity of water treatment processes. For instance, the optimal pH of 5 for turbidity and TSS reductions indicates that a slightly acidic environment enhances coagulation efficiency. The increased coagulant dosage (up to 72%) for TSS reduction compared to turbidity suggests that higher dosages are necessary to effectively remove suspended solids, aligning with the understanding that coagulant dosage is directly proportional to the removal efficiency of certain pollutants. The trends depicted in Figure 5 and Figure 6 visually reinforce these findings, with the optimal points corresponding to the highest reduction efficiencies. Table 8 highlights conflicting interactions such as the increasing trend of pH (↑) on turbidity and TSS reduction but a decreasing trend (↓) for BOD and COD, emphasizing that parameters beneficial for one pollutant may be less effective or even counterproductive for others. This dichotomy justifies the need for multi-objective optimization to balance competing goals rather than optimizing parameters in isolation.

3.4.2. Multi-Objective Optimization

Multi-objective optimizers address contradictions by simultaneously considering multiple conflicting objectives, providing a set of Pareto optimal solutions rather than a single one. This allows decision-makers to select solutions that balance trade-offs based on preferences. Unlike single-objective optimizers, they explore diverse solutions capturing the entire spectrum of optimal trade-offs. Regarding the current study,

Table 9. Optimization parameters.

Parameter Name	Description	Value
Variables	Number of variables	2
Population Size	Number of grey wolves	100
Max Iterations	Maximum number of iterations	1000
Alpha	Alpha coefficient	0.1
Grid Count	Number of grids	10
Beta	Beta coefficient	4
Gamma	Gamma coefficient	2

presents various optimization parameters, their description and their value.

Multi-Objective Optimization by Coagulation Using Cucumis melo Coagulant

X1: 6.36139699395940 54.7303179413496

X2: 6.37547558824766 55.8670905630804

X3: 6.20735943343528 56.1879580013977

Figure 7 illustrates the Pareto front approximation obtained through multi-objective optimization using Citrullus lanatus (watermelon rind) as a coagulant. This figure visually presents the trade-offs between two conflicting objectives, such as pollutant removal efficiency and chemical usage, by plotting non-dominated solutions: The red diamonds represent the non-dominated solutions identified by the Grey Wolf Optimizer (GWO), which form the Pareto front. Each point corresponds to a particular combination of decision variables (e.g., pH and coagulant dosage) that optimize the different objectives without being superior in all simultaneously.

The solutions X1, X2, and X3 are specific strategies along the Pareto front:

X1: pH ≈ 6.36, coagulant dosage ≈ 54.73 mg/L balances treatment efficiency and chemical input.

X2: pH ≈ 6.38, coagulant dosage ≈ 55.87 mg/L favors slightly higher removal performance.

X3: pH ≈ 6.21, coagulant dosage ≈ 56.19 mg/L emphasizes maximum pollutant removal, potentially at higher operational costs.

This visualization demonstrates how different operational compromises can be selected based on treatment priorities, with the Pareto front providing a suite of optimal solutions for decision-makers. It underscores the trade-offs inherent in wastewater treatment optimization using natural coagulants and the ability of the metaheuristic to explore these complexities effectively.

In this figure, optimization simultaneously considered two conflicting objectives (e.g., turbidity and chemical removal efficiency or cost-effectiveness), resulting in a Pareto front of non-dominated solutions.

• The non-dominated solutions (red diamonds in the plot) show that GWO effectively explored a broad range of optimal trade-offs.
• The selected points (X1–X3) represent different strategies:

  ➢

  X1 prioritizes balance between efficiency and dosage.

  ➢

  X2 leans slightly toward enhanced performance.

  ➢

  X3 may be chosen when maximum removal is desired, regardless of higher dosage.

Multi-Objective Optimization by Coagulation Using Cucumis melo Coagulant

X1: 6.65352941432052  60.4738270610110

X2: 6.86860820119244  60.8781325675515

X3: 6.93225148892443  64.0270843383208

Figure 8 presents the Pareto front approximation achieved through multi-objective optimization using Cucumis melo as a coagulant. This figure illustrates the trade-offs between treatment effectiveness and chemical usage:

The red diamonds indicate the non-dominated solutions identified by the Grey Wolf Optimizer (GWO), forming the Pareto front. Each point reflects a different combination of pH and coagulant dosage that balance conflicting objectives such as pollutant removal efficiency and resource utilization.

The solutions X1, X2, and X3 are specific strategies along this Pareto front:

X1: pH ≈ 6.65, coagulant dosage ≈ 60.47 mg/L provides a balanced approach with moderate treatment performance.

X2: pH ≈ 6.87, coagulant dosage ≈ 60.88 mg/L provides a slightly higher pH and dosage to potentially improve removal efficiency.

X3: pH ≈ 6.93, coagulant dosage ≈ 64.03 mg/L emphasizes maximum performance, likely involving higher chemical input.

The figure visually emphasizes the inherent trade-offs in optimizing wastewater treatment with natural coagulants, enabling decision-makers to select operational parameters aligned with their priorities whether maximizing treatment efficacy or minimizing chemical consumption. It showcases the capability of multi-objective metaheuristic algorithms to explore the spectrum of optimal solutions in complex environmental systems. The results in this figure show a clear Pareto front of non-dominated solutions, highlighting trade-offs between treatment performance and chemical usage.

Key optimized solutions:

• X1 (pH: 6.65, dosage: 60.47 mg/L): A well-balanced solution offering good treatment efficiency with moderate chemical input.
• X2 (pH: 6.87, dosage: 60.88 mg/L): Slightly higher pH and dosage, potentially enhancing removal efficiency.
• X3 (pH: 6.93, dosage: 64.03 mg/L): Highest pH and dosage, likely maximizing treatment performance but at a higher resource cost.

These solutions reflect varying priorities between cost-efficiency and maximum effectiveness, providing flexibility in practical applications.

3.4.3. Mechanistic Insights into Coagulation Processes

In the context of this study, which investigates the use of natural coagulants, specifically Citrullus lanatus (watermelon rind) and Cucumis melo (melon), for wastewater treatment, understanding the mechanisms underlying coagulation helps to elucidate how these bio-based agents facilitate pollutant removal [1,20,21,22].

Contextualization of Mechanistic Insights.

Charge Neutralization

Natural coagulants derived from plant sources contain polysaccharides and proteins with positively charged functional groups (e.g., –NH₃⁺). These groups interact with negatively charged particles such as turbidity-causing colloids, total suspended solids (TSS), and dissolved organic matter [20,23,24]. At slightly acidic to near-neutral pH conditions (around pH 6–7), protonation of functional groups is enhanced, promoting charge neutralization and destabilization of colloidal particles [1,25]. This facilitates particle aggregation and improves turbidity and TSS removal efficiency.

Bridging Mechanism

High-molecular-weight polysaccharides present in plant-based coagulants act as polymeric bridging agents, forming inter-particle links that result in larger, settleable flocs [1,26,27]. Optimal dosages (e.g., ~54.73 mg/L for Citrullus lanatus) ensure adequate polymer chain availability to adsorb onto multiple particle surfaces simultaneously, thereby enhancing floc growth and sedimentation.

Polymer bridging is particularly significant when moderate coagulant dosages are applied, preventing stabilization of colloids [20].

Adsorption

Functional groups in plant mucilage, including hydroxyl (–OH), carboxyl (–COOH), and amino (–NH₂) groups, contribute to the adsorption of dissolved organic pollutants such as those measured by BOD and COD [28,29,30]. Adsorption efficiency is strongly pH-dependent, as surface charge characteristics influence pollutant coagulant interactions (Refs. [1,2]). Optimized pH and dosage conditions enhance adsorption-based removal of dissolved organic matter, contributing to reductions in BOD and COD levels.

Sweep Flocculation

In addition to charge neutralization and bridging, sweep flocculation may occur when sufficient coagulant dosage promotes enmeshment of particles within a forming precipitate matrix [26,31]. Although more commonly associated with metal salts, bio-coagulants can also facilitate particle enmeshment under optimized conditions, enhancing overall clarification.

Broader Impact and Significance

• Understanding these mechanisms allows optimization of treatment parameters (pH and coagulant dosage) tailored to wastewater characteristics, maximizing pollutant removal while minimizing chemical input [20,32].
• Natural coagulants such as mucilage extracted from Citrullus lanatus and Cucumis melo exhibit high polysaccharide content that supports charge neutralization, bridging, and adsorption mechanisms, positioning them as sustainable alternatives to conventional chemical coagulants [20,23].
• Mechanistic understanding also explains why natural coagulants may reduce sludge toxicity and secondary pollution compared to aluminum- or iron-based coagulants, thereby enhancing environmental sustainability [1,2].

Overall, the study’s multivariate optimization results, including identification of optimal pH and dosage conditions, are consistent with established coagulation mechanisms of charge neutralization, bridging, adsorption, and sweep flocculation [20,26,33]. These mechanisms act synergistically to destabilize colloidal particles, promote floc formation, and enhance sedimentation, demonstrating that plant-based coagulants can serve as environmentally sustainable alternatives in wastewater treatment systems.

Figure 9 illustrates these mechanistic pathways in the coagulation process when using natural coagulants derived from Citrullus lanatus (watermelon rind) and Cucumis melo (melon). The main mechanisms include charge neutralization, bridging, adsorption, and sweep flocculation, which synergistically lead to pollutant removal and improved water clarity.

The mechanistic processes depicted in Figure 9 charge neutralization, bridging, and adsorption are fundamental physical and chemical interactions involved in coagulation and flocculation. These processes influence operational parameters such as pH and coagulant dosage, which are suitable inputs for optimization using metaheuristic algorithms like GWO.

Rationale:

GWO optimizes based on the relationships between input variables (e.g., pH, coagulant dosage) and output performance metrics (e.g., pollutant removal efficiencies).

The detailed mechanistic pathways are intrinsic to understanding the biological and chemical interactions but do not impede the algorithm’s ability to explore and find optimal operational conditions. Many studies have successfully employed GWO and similar algorithms to optimize processes involving complex chemical interactions, provided that appropriate models of the system are established. While the coagulation mechanisms involving charge neutralization, bridging, and adsorption are complex and inherently different from inorganic flocculants, they do not preclude the use of metaheuristic optimization techniques such as GWO. These mechanisms directly influence process parameters (e.g., pH, coagulant dosage), which can be modeled and optimized computationally. Therefore, GWO remains suitable for exploring optimal operational conditions in bio-based coagulation systems, as demonstrated by numerous studies using similar approaches in complex biological and chemical treatment processes.

3.5. Sensitivity Analysis

Figure 10 demonstrates that both pH and coagulant dosage strongly influence pollutant removal efficiencies. Small variations in pH significantly affect turbidity and BOD reduction, indicating their high sensitivity at specific operational points. Similarly, coagulant dosage has a substantial impact on COD and TSS removal, with increasing dosage generally enhancing removal efficiencies. These insights highlight the necessity for precise control of pH and dosage to optimize natural coagulation processes effectively.

From the analysis of Figure 10, Figure 11 and Figure 12, y1 to y4 are representing the reduction in turbidity, reduction in TSS, reduction in BOD and reduction in COD for coagulation using the Citrullus lanatus coagulant, respectively; y5 to y8 are representing reduction in turbidity, reduction in TSS, reduction in BOD and reduction in COD for coagulation using the Cucumis melo coagulant, respectively. We take x (1) and x (2) as pH and coagulant dosage, respectively.

Analysis of Sensitivity Results for Coagulation with Citrullus lanatus

The sensitivity analysis reveals important insights into the influence of pH (x1) and coagulant dosage (x2) on treatment efficiency. For pH, Y5 (reduction in turbidity) shows a high local gradient (21.571) and a near-perfect global correlation (0.98503), indicating that small changes in pH near the midpoint can substantially affect turbidity reduction. Similarly, Y3 (reduction in BOD) displays a strong negative correlation with pH (−0.8734) and a large negative gradient (−6.0797), suggesting that lowering pH enhances BOD reduction significantly. In terms of coagulant dosage, Y4 (reduction in COD) demonstrates a high local sensitivity (4.9283) and an almost perfect correlation (0.99931), meaning that increasing dosage consistently improves COD reduction. Y2 (reduction in TSS), meanwhile, shows a moderate negative local gradient (−0.2276) and a strong negative correlation (−0.93173), implying that both dosage and pH play important roles in TSS removal. The numerical values reinforce these findings: the very high gradient of Y5 with respect to pH underscores the importance of carefully controlling pH to optimize turbidity removal, while Y3’s strong negative response to pH highlights pH management as critical for maximizing BOD reduction. For COD, dosage control emerges as the most influential factor, and for TSS, combined control of both variables is required.

Overall, the results emphasize that pH and dosage are key control variables for optimizing reductions in turbidity, TSS, BOD, and COD. Maintaining pH near optimal levels can yield substantial improvements in turbidity and BOD removal, while increasing coagulant dosage enhances COD and, to some extent, TSS reduction. The high sensitivity values indicate that even small adjustments within mid-range operational settings can produce significant improvements, underscoring the need for precise process parameter management.

3.6. Implications for Water Treatment Using Citrullus lanatus

The study’s results demonstrate that Citrullus lanatus extract can serve as an effective natural coagulant, with specific pH and dosage conditions optimizing removal efficiencies. The conflicting trends between parameters highlight that achieving optimal removal of all pollutants simultaneously requires multi-objective approaches, as single-variable optimizations might favor one pollutant at the expense of others. These findings align with current trends favoring sustainable, eco-friendly water treatment options, especially in resource-limited settings. The models developed provide a strategic tool guiding operational conditions to maximize pollutant removal while minimizing coagulant usage, thus offering a cost-effective and environmentally friendly treatment alternative.

4. Conclusions

This study demonstrates the significant potential of multi-objective optimization in enhancing the performance of sewage wastewater treatment using natural coagulants. The findings show that natural coagulants can outperform conventional chemical agents such as aluminum sulphate and ferric chloride in reducing key pollutants, including turbidity, total suspended solids (TSS), biochemical oxygen demand (BOD), and chemical oxygen demand (COD). The results indicate that natural coagulants, such as Citrullus lanatus and Cucumis melo, achieved removal efficiencies comparable to or exceeding those reported for traditional chemical coagulants. For example, previous studies have shown that Moringa oleifera seed extracts can reduce turbidity by up to 85% with a sludge volume reduction of approximately 30%, while in this study, Citrullus lanatus achieved turbidity reductions of up to 96.68% (pH 5, 50 mg/L coagulant dosage). Similarly, the optimal BOD and COD reductions observed (52.7% and ~60%, respectively) are within the ranges reported for conventional coagulants but achieved with significantly lower chemical input, indicating superior or equivalent performance. Therefore, the data substantiate that natural coagulants can be effective, environmentally friendly alternatives with a performance at least comparable to that of chemical agents. Using advanced optimization techniques such as multivariate polynomial regression, ANOVA, and the Grey Wolf Optimizer (GWO), the study identified optimal treatment conditions that balance critical parameters like pH and coagulant dosage. Interestingly, the results reveal that while lower pH levels favor reductions in turbidity and COD, higher pH conditions are more effective for BOD removal. This nuanced behavior highlights the complexity of the coagulation process and reinforces the importance of a multi-objective approach when aiming for comprehensive pollutant removal. The optimal conditions determined through the GWO algorithm—specifically pH 6.3614 and 54.73 mg/L dosage for Citrullus lanatus, and pH 6.65 with 60.47 mg/L dosage for Cucumis melo—offer efficient and low-chemical alternatives suitable for practical application. These findings support the potential of natural coagulants to provide cost-effective, environmentally sustainable solutions, particularly in regions lacking access to conventional treatment infrastructure. However, since the optimization was based on computational modeling without experimental validation, further research is needed to confirm its applicability in real-world conditions. Variables such as temperature, contact time, and the presence of competing ions must be accounted for in future in situ studies. Moreover, investigating the extraction methods, structural properties, and stability of natural coagulants will be crucial for ensuring consistent performance at scale. Overall, this study contributes to the advancement of sustainable wastewater treatment practices aligned with circular economy principles. By reducing chemical use and sludge generation, natural coagulants present a viable pathway toward greener water management systems. The integration of bio-based solutions in wastewater treatment holds promise not only for improving water quality but also for supporting broader environmental conservation and public health objectives.