IoT-enabled ensemble learning for sustainable wastewater valorization: a fuzzy goal programming approach with multi-objective optimization

1 Introduction

The textile industry is among the fastest-growing industries worldwide [1, 2]. Textile factories were most concentrated in the Tirupur district of Tamil Nadu and the surrounding areas. Tirupur, an Indian hub for knitwear, is home to about 9,000 small businesses. The prosperity of Tirupur began in 1930 [3]. In about three or four decades, Tirupur went from being an agrarian village economy to becoming the “knitwear capital of India.” Tirupur's rapid industrial growth has been attributed to several factors, including its hot climate, good water quality, easy access to cotton as a raw material, a skilled labor force, adequate infrastructure, industrial networking, institutional support, and an export culture. This is where India exports 56% of its cotton knitwear [4]. During the post-independence period of rapid industrialization, many textile (dyeing and bleaching) firms emerged along the Noyyal River. The river became extremely contaminated and unsafe for human consumption as a result of these industries' direct disposal of wastewater [5]. Numerous synthetic dyes, many of which are highly toxic, non-biodegradable, and resistant to conventional treatment techniques, are commonly found in textile effluent. Major environmental problems include aquatic toxicity, disruption of photosynthesis in aquatic environments, and human health hazards from exposure to chemicals that can cause cancer and mutagenesis, which could result in these wastewater streams if they are not cleansed. The Velliangiri Hill rocks and the Noyyal River rise in the Western Ghats. The 170-kilometer river flows through the western districts of Karur, Erode, Tirupur, and Coimbatore in Tamil Nadu before entering the Cauvery River near Koodhamandi in Erode district. Situated between east longitudes of 76°1′ and 77°6′ and the north latitudes 10°6′ and 11°9′, the Noyyal River basin has an area of 3,510 square kilometers [6]. This study's primary goal is the utilization of textile wastewater. Worth-addition, also known as valorization, is the act of converting waste materials into valuable products or materials with extra worth [7, 8]. Converting waste into valuable resources is often the focus of valorization. For example, waste fibers and chemicals can be transformed into fertilizers, biofuels [9], or raw materials [10] for other industrial processes within the textile industry [11]. The circular economy concept can be advanced by anaerobic digesters that effectively generate biogas from wastewater separated by solid-liquid separation. Wastewater valorization improves the overall efficiency of the bioethanol production process and reduces waste [12–14]. The ability to recycle wastewater and produce no waste is a key element of sustainable biorefinery operations [15]. Industries have been forced to use zero liquid discharge (ZLD) systems in recent decades due to strict environmental requirements [16, 17]. ZLD systems use a combination of thermal and physicochemical processes to reduce wastewater outflow. ZLD has been criticized for its high initial cost, high energy consumption, operating complexity, membrane fouling, and concentrated brine disposal issues, despite its environmental benefits [18].

Alternatives that preserve environmental protection [19] while reducing operating strain have attracted considerable attention from academia and industry. Purified liquid discharge (PLD), which purifies treated wastewater to fulfill certain reuse standards, especially agricultural irrigation standards—without requiring full evaporation—is one such new method. Particularly in areas where water is scarce, PLD offers a more inexpensive, ecologically sound, and energy-efficient method of wastewater valorization. Predicting treatment performance and continuously evaluating the quality of treated water are crucial for PLD. However, the majority of Indian textile manufacturers continue to rely on laboratory testing and manual sampling, leading to operational inefficiencies, inconsistent monitoring frequency, and delays [20]. These drawbacks underscore the necessity of real-time, automated, data-driven monitoring systems that can evaluate dye removal effectiveness and forecast compliance with irrigation regulations. In this regard, the incorporation of Internet of Things (IoT) technology into wastewater treatment has become a game-changing instrument [21]. IoT-based sensors provide continuous input on process dynamics by enabling real-time monitoring of vital parameters such as pH, dissolved oxygen (DO), total dissolved solids (TDS), alkalinity, total hardness (TH), and heavy metals. Cloud platforms can receive these data streams for automated decision-making, storage [22], visualization [23], and monitoring [24]. Since machine learning (ML) can simulate complex non-linear interactions inherent in effluent properties, dye degradation kinetics, and treatment effectiveness, its application in wastewater treatment has gained substantial momentum concurrently with improvements in IoT systems [25]. In various industrial sectors, algorithms such as Support Vector Machines (SVMs), Random Forests (RFs), Extreme Gradient Boosting (XGBoost), AdaBoost, and Gradient Boosting Machines (GBMs) have been used to forecast pollutant concentrations, treatment outcomes, and water quality indicators [26]. In these situations, ensemble learning—particularly, stacking techniques that integrate several base learners—has proven to be more reliable and accurate [27]. It has been demonstrated that using Lasso as a meta-learner can efficiently capture residual patterns and increase overall prediction reliability [28]. Table 1 provides an useful insight into the literature on IoT-enabled work. The present paper contributes at the intersection of three streams: IoT-ML wastewater treatment, inventory-theoretic operations research, and multi-objective fuzzy optimization [29]. The proposed IoT architecture serves as a conceptual framework for integrating the developed prediction model into the future real-time industrial wastewater monitoring systems. While Barman et al. [30] demonstrated the utility of a sustainable economic production quantity (EPQ) inventory model with fuzzy goal programming (FGP) for simultaneously optimizing profit and greenhouse gas emissions in a manufacturing context, no prior study has adapted the EPQ inventory dynamics paradigm to wastewater valorization. The key conceptual insight of this paper is that the volume of purified water ready for valorization discharge evolves exactly as inventory in an EPQ system: it builds during active treatment, depletes during valorization discharge, and backlogs during plant overload—each phase governed by a differential equation. Furthermore, just as [30] preservation technology investment controls the deterioration rate, IoT sensor investment (β_IoT) in this model controls treatment efficiency decay; and just as their green technology investment reduces emissions, ML investment (K_ML) reduces residual pollution load. Several studies have examined the use of IoT to monitor wastewater and machine learning to predict it, as well as inventory optimization. Current solutions are mostly aimed at the prediction of pollutants or optimization of the treatment process but lack IoT-based treatment procedures with multi-objective optimization. These two distinctions constitute the paper's core methodological contribution.

Table 1. Literature review: IoT and ML-based wastewater monitoring studies.

2 Methodology

2.1 Study area

The research is situated in the textile processing zone of Tirupur, Erode, Tamil Nadu, India, which is a globally renowned hub of knitted garments, reactive dyeing, and wet processing. There are several hundred dyeing units and many CETPs and IETPs in this industrial belt, which comprises Nallur, Kasipalayam, Veerapandi, Perundurai State Industries Promotion Corporation of Tamil Nadu (SIPCOT), and Chennimalai. Combined, these plants discharge large volumes of effluent, colored and of high strength, to the Noyyal River sub-basin. This zone has traditionally been associated with severe environmental degradation [31], including degradation of riverine systems, salinization of farm soils, and pollution of shallow watersheds, largely due to the discharge of untreated textile effluents. The Tirupur-Erode zone is an ideal testing ground for developing a real-time monitoring and predictive analytics framework, given the complexity of the wastewater profile, which includes reactive azo dyes and high levels of salts, surfactants, and trace metals. Moreover, the region has been subjected to several regulatory measures, including the shutdown of dyeing plants (at least temporarily), which makes the implementation of independent, digitally advanced wastewater treatment systems more than necessary. Therefore, the size and environmental impact of the industrial activity in this study area, and its strategic importance as a national textile hub where real-time IoT-related process optimization could generate significant environmental and socioeconomic benefits, predetermine its choice.

2.2 Dataset

The data applied in this study, which is a lab-tested variable that is closely similar to the effluent profile observed in the Tirupur and Erode areas, was compiled from previously published literature as a secondary dataset [32] on textile wastewater characterization. The most important physicochemical variables that influence dye removal processes and overall treatment effectiveness, including pH, dissolved oxygen, total dissolved solids, total hardness, alkalinity, and trace metals such as chromium, iron, lead, and zinc, are measured in the influent and effluent. The fact that the data can be used for local textile effluents allows it to be used to construct machine-learning models, despite not being generated through primary experiments. Using these selected data, the predictive models included in the proposed IoT-artificial Intelligence (AI) system are trained and assessed. The development and evaluation of the predictive framework were conducted under standardized conditions using a literature-based dataset.

2.3 Conceptual IoT-based framework of wastewater monitoring

The proposed IoT architecture is presented as a conceptual framework illustrating the integration of real-time sensing, cloud communication, machine learning, and optimization for intelligent wastewater treatment monitoring. The goal of this framework is to demonstrate the potential of an IoT-enabled infrastructure for continuous monitoring and data-driven decision-making in the future applications for industrial wastewater treatment. The present study does not consider the physical implementation nor the experimental validation of the proposed IoT architecture. Rather, the emphasis of this study is on the development and validation of machine learning models, using a secondary dataset from the published literature. The proposed design considers each sensing node as a system built with an ESP32 microcontroller, equipped with Wi-Fi communication modules to transmit the data obtained to the cloud platform [33]. The sensing nodes are to be equipped with pH sensors, TDS-based conductivity sensors, optical sensors for DO, oxidation-reduction potential (ORP), turbidity, and temperature, ultrasonic flow sensors, and heavy metal sensors for chromium, lead, and zinc. The sensors are strategically placed at key points in the wastewater treatment process—the outlet of the equalization tank, the coagulation-flocculation chamber, the aerator basin, the secondary clarifier, the reverse osmosis (RO) feed water line, and the permeate outlet—to provide full-scale process coverage. In the proposed deployment, sensor data would be sent to the cloud, like Firebase or ThingSpeak, using an access point (AP) [34]. The sensor calibration would be performed following the procedure recommended by the American Public Health Association (APHA) standard methods [35] with the use of certified buffer solutions for pH, conductivity, turbidity, and dissolved oxygen for the quality and reliability of the data obtained. In a realistic deployment, sensor data might be collected periodically (such as every 30 s) to provide real-time data for later use in machine learning models for prediction and optimization.

3 Description of the process of wastewater treatment in industries

The operational conditions of the CETPs/IETPs [3] in Tirupur align with the study, as the wastewater undergoes a series of treatment stages. First, the effluent entering the equalization tank is homogenized to reduce differences in influent characteristics. The flow is then directed to the pH adjustment chamber, where acid or alkali is dosed to maintain the pH at the optimum level, enabling effective chemical treatment. Chemicals such as polyaluminium chloride (PAC) or alum are added during the coagulation–flocculation stage, and polymeric flocculants are added to cause dye molecules, suspended solids, and colloidal particles to aggregate. The next aeration phase promotes biological oxidation [36], where fine-bubble diffusers keep dissolved oxygen levels to support the community of microbes involved in breaking down organic components. Wastewater passes through aeration after which it is introduced to secondary clarifiers where the biomass and particulate matter are deposited. This treated overflow is channeled to a reverse osmosis unit to extract dissolved salts, metals, and any remaining color. RO concentrates are subjected to evaporators, and salts are reused [37]. The end permeate is considered a possible PLD-compliant water source for agricultural use. The whole process is highly automated using machine learning, as changes in the composition of the influent often affect chemical dosing efficiency, microbial activity, and membrane load; hence the need for real-time predictive control.

4 Machine learning

The machine learning process commenced with the division of the dataset into 80% training and 20% testing to obtain reliable performance evaluation. A Z-score scaler was used to standardize all features to eliminate scale differences. The five machine learning models that include Support Vector Regression (SVR), random forest regression, gradient boosting regression, AdaBoost regression, and XGBoost regression were all selected on the basis that they have been effective in the analysis of non-linear environmental data. Their hyperparameters were manually tuned to strike a balance between complexity and generalization. The functional relationship between wastewater parameters and dye removal efficiency was trained for each model. This choice of various models was not accidental, since ensemble learning is advantageous, as it involves integrating predictors with varying strengths: SVR captures non-linear boundaries, tree-based models are able to deal with heterogeneous data and noise, and the boosting algorithms are good at reducing prediction errors.

5 Stacked ensemble learning model architecture

A stacked ensemble learning structure was designed to improve predictions of dye removal efficiency. At the first level, the base learners used were SVR, RF, Gradient Boosting, AdaBoost, and XGBoost, all of which are heterogeneous regression models. Ensemble learning was adopted over a single-model approach because combining predictions from multiple heterogeneous learners reduces variance and generalization error relative to any individual model. StandardScaler was used to normalize all input features and was fitted separately on each training fold to avoid information leakage from the validation data into the scaling. To construct the stacking ensemble, the out-of-fold predictions from the base learners were used to generate the meta-training features, and the predictions on the held-out set were averaged across folds to form the meta-test features, which guarantees that the meta-learner was not trained on information obtained from the same set of data it would use to produce predictions. Hyperparameters of each base learner were optimized with 5-fold cross-validation, using grid search to optimize for R^**2**, and hyperparameter search and feature scaling were independent per fold [38]. The following parameters were selected as part of this procedure: SVR with an RBF kernel: C = 15, γ = 0.05, ε = 0.1; RF: 50 estimators, maximum depth = 7, minimum samples per leaf = 2; Gradient Boosting: 100 estimators, learning rate = 0.05, maximum depth = 4, subsample ratio = 0.85; AdaBoost with a Decision Tree base estimator: maximum depth = 3, 50 estimators, learning rate = 0.5; XGBoost: 100 estimators, learning rate = 0.1, maximum depth = 2, subsample ratio = 0.85, column-sample ratio = 0.7. Under this tuning procedure, AdaBoost achieved the highest cross-validated score (R^**2** = 0.924), followed by Gradient Boosting (R^**2** = 0.901), SVR (R^**2** = 0.886), XGBoost (R^**2** = 0.824), and RF (R^**2** = 0.732).

The meta-learner was chosen by cross-validated comparison with the base learners, rather than a priori. The performance of the different meta-learner models on the generated meta-features was evaluated using 5-fold cross-validation, and the Lasso regression was chosen as the final meta-learner with the highest cross-validated R^**2** (0.881) compared with Ridge (0.872), Elastic Net (0.880), ordinary linear regression (0.830), and XGBoost (0.794) regressor. This result shows that a regularized linear meta-learner performs better than a complex tree-based one at this stage, which is consistent with the number of samples available for fitting the meta-learner. The predictive performance of the proposed stacked ensemble model was assessed using a nested 5-fold cross-validation framework. The outer 5-fold cross-validation provided an unbiased estimate of the model's generalization performance. In contrast, the inner 5-fold cross-validation was performed to train the base learners, generate out-of-fold meta-features, and optimize the meta-learner independently within each outer training fold. Under this evaluation, the individual base learners achieved the following cross-validated performance: Gradient Boosting, R^**2** = 0.913 ± 0.106 (Mean Absolute Error [MAE] = 1.432 ± 0.550, Root Mean Squared Error [RMSE] = 1.732 ± 0.605); SVR, R^**2** = 0.870 ± 0.155; AdaBoost, R^**2** = 0.869 ± 0.140; XGBoost, R^**2** = 0.824 ± 0.133; and RF, R^**2** = 0.750 ± 0.247. The full stacked ensemble resulted in R² = 0.890 ± 0.115 (MAE = 1.321 ± 0.404, RMSE = 1.660 ± 0.383), and its sensitivity was influenced by sample composition due to the small size of this dataset.

6 Model evaluation for machine learning

Based on the model objective, type of information, and circumstances, suitable criteria parameters are required to evaluate the performance of an ML-based model (model evaluation). The measures in this study are the coefficient of determination (R²), Mean Absolute Error (MAE), and Root Mean Squared Error (RMSE).

6.1 Coefficient of determination

The R² is a commonly used statistical metric to assess the predictive performance of regression models. It represents the percentage of the variation in the dependent variable explained by the independent variables in the model. The value of R² ranges from 0 to 1, where a value closer to 1 indicates that the model has higher explanatory and predictive power, and thus greater agreement between the model values and the observed values. For example, an R² value of 0.80 indicates that the model accounts for 80% of the variation in the dependent variable, with the remaining 20% attributable to unexplained variation or other factors not included in the model.

The longer the coefficient, the better the statements fit [39]. An equation quantitatively shows the R².

R2=1- ∑i=1n(zi-ρi)2 ∑i=1n(zi-ψi)2

where n is the number of samples, z_*i* is the actual value, ρ_*i* is the predicted value, and ψ_*i* is the mean of the observed values.

6.2 Root mean squared error

The RMSE is the measure of the dispersion of the residuals. In contrast, residuals determine how far apart the points are from the regression line. It gives details about the extent of the data concentration about the line of best fit. In regression analysis, RMSE is usually employed to authenticate the experimental findings. The equation represents the computation of RMSE [39].

RMSE=1n∑i=1n(zi-ρi)2

where n is the number of samples, z_*i* is the actual value, and ρ_*i* is the predicted value.

6.3 Mean absolute error

The simple and powerful MAE measure can be used to test the accuracy of the regression model. It establishes the average deviation between the target and projected values. MAE, unlike other measures, does not square the errors; hence, it assigns the same weight to every error, irrespective of the direction it takes. This is because MAE is especially helpful because it allows us to assess the extent of errors without considering whether they are underestimations or overestimations. The equation offers the mathematical formula of MAE [39].

MAE=1n∑i=1n|(zi-ρi)|

where n is the number of samples, z_*i* is the actual value, and ρ_*i* is the predicted value.

7 Notations and assumptions

7.1 Assumptions

The following assumptions underpin the proposed inventory-theoretic wastewater valorization model, adapted from Barman et al. [30] to the textile effluent treatment context:

• A single treatment plant processes one composite textile effluent stream per planning cycle of length T days. The plant operates at capacity P_*tr* ≥ Q_*in* during active treatment phases.
• The planning cycle comprises four distinct phases governed by differential equations: backlog clearance [0, T₁], inventory build-up [T₁, T₂], valorization discharge [T₂, T₃], and overload accumulation [T₃, T].
• Treatment efficiency decays over time without IoT monitoring investment. The controlled decay rate after IoT investment β_*IoT* is α(β_*IoT*) = α₀·(e(-ψβIoT)), where α₀ is the baseline decay rate and ψ is the investment sensitivity parameter.
• The ensemble ML model (SVM + RF + XGB + GB + AdaBoost stacking) predicts purification efficiency η_*ML* = 0.978. ML investment K_*ML* = ηMLg2 reduces pollution load by fraction θ_*ML* = θ_*m* · (1 – e(γML . KML)), parallel to green technology in Barman et al.
• All treated purified water meeting irrigation standards is valorized for discharge at rate D_*val*. Treatment sludge is converted to organic fertilizer at yield coefficient γ kg/m³.
• During the overload phase [T₃, T], inflow exceeds treatment capacity. A fraction δ_*v* of excess flow is backordered (partially treated in the next cycle); 1 – δ_*v* is discharged as raw overflow, incurring pollution penalty.
• IoT infrastructure cost C_*IoT* and ML operational cost C_*ML* are fixed per cycle. Treatment cost C_*tr* is variable per m³. These three cost components jointly replace the setup, production, and technology investment costs in the EPQ model.
• Health risk to downstream agricultural communities is proportional to the removal of effluents, the complement of ML prediction accuracy. This is the social impact dimension, paralleling worker health allowance.

7.2 Problem description

The four-phase inventory dynamics illustrates the proposed wastewater valorization model. This shows the volume V(t) of purified treated water ready for valorization discharge. The horizontal axis represents time within the planning cycle.

At time t = 0, the plant begins clearing the backlog from the previous cycle's overload. The maximum backlog level equals V₁(0) = V₄(T), establishing the key consistency boundary condition. The transition time T₂ is derived analytically from the condition V₂(T₂) = V₃(T₂)–the peak inventory point—yielding a closed-form expression [30]. The relationship between T₁ and T₃ is derived from the equal backlog condition, parallel to equation. The complete set of given and proposed parameters is presented in Table 2.

Table 2. Nomenclature and abbreviated symbols of the parameters.

8 Mathematical formulation

8.1 Inventory dynamics: differential equations

The evolution of purified water volume V(t) across the four phases is governed by the following differential equations, which are structurally analogous to those presented in Barman et al. [30]:

dV1(t)dt = Ptr - δv.Qin - Qin,0≤t≤T1 withV1(T1)=0(1)

dV2(t)dt+α(βIoT).V2(t)=Ptr−Qin,T1≤t≤T2 with V2(T1)=0(2)

dV3(t)dt+(βIoT).V3(t)=−Dval,T2≤t≤T3 withV3(T3)=0(3)

dV4(t)dt=-δv.Qin,T3≤t≤T with V4(T3)=0(4)

Equation 1 describes the backlog clearance phase: the plant treats at P_*tr* while meeting new inflow Q_*in* and clearing δ_*v*.Q_*in* of back-ordered overflow where inventory rises to serve back-ordered demand. Equations 2, 3 incorporate treatment efficiency decay α(β_*IoT*), analogous to the deterioration rate. Equation 4 describes the accumulation of overload.

Solving Equations 1–4 with their boundary conditions yields the closed-form inventory level functions given in Equations 5–8:

V1(t)=-(Ptr - δv.Qin - Qin) (T1-t),0≤t≤T1(5)

V2(t)=[(Ptr−Qinα(βIoT))].(1−e{α(βIoT)(T1−t)}),T1≤t≤T2(6)

V3(t)=[(Dvalα(βIoT))].(e{α(βIoT)(T3−t)}−1),T2≤t≤T3(7)

V4(t)=-δv.Qin(t -T3),T3≤t≤T(8)

From the continuity condition V₂(T₂) = V₃(T₂) at peak inventory, the transition time T₂ is expressed as follows:

T2=[(1α(βIoT))].ln[(Ptr−Qin).e{α(βIoT).T1}+Dval.e{α(βIoT).T3}]Ptr−Qin+Dval(9)

From the equal backlog boundary condition V₁(0) = V₄(T), the transition time T₁ is expressed as follows:

T1=[( δv. Qin(Ptr - δv. Qin - Qin))].(T-T3)(10)

Both Equations 9, 10 are direct structural analogs, confirming the mathematical isomorphism between the EPQ inventory paradigm and the wastewater valorization dynamics.

8.2 IoT investment and efficiency decay control

Without IoT sensor investment, treatment efficiency decays at a rate α₀ per day due to sensor drift, inconsistent chemical dosing, and undetected process deviations. As modeled in Equation 11, IoT investment β_*IoT* per unit efficiency level per day controls this decay, reducing it exponentially, as follows:

α(βIoT)=α0.(e{−ψ.(βIoT)})(11)

Equation 12 gives the corresponding IoT investment cost per cycle is expressed as follows:

CIoTcycle=βIoT.T(12)

8.3 ML investment and pollution load reduction

The ensemble ML model (SVM + RF + XGBoost + Gradient Boosting + AdaBoost, stacking architecture) achieves η_*ML* = 0.978, enabling accurate real-time prediction of pollutant removal efficiency. Equation 13 defines ML investment K_*ML* = η_*ML*.g² in model performance level g reduces the fraction of pollution discharged:

θML= θm.(1-e{-γML.KML})=θm.(1-e{-γML.ηML.g2})(13)

As η_*ML* → 1 (perfect prediction accuracy) and g → ∞, θ_*ML* → θ_*m* (maximum achievable pollution reduction). Equation 14, which gives the associated ML investment cost per cycle, is presented as follows:

CMLcycle=CML.g2T(14)

8.4 Economic aspect: valorization profit

Total valorization revenue derives from two streams: purified water sold for irrigation and fertilizer from treatment sludge. The components of the economic objective are given in Equations 15–19. The total revenue per cycle is expressed as follows:

Tr= (pw+pfγ)Qtr(15)

The total treatment cost per cycle comprises fixed IoT and ML costs plus variable treatment cost as expressed in the following:

Tc=Ctr.Qtr+βIoT.T+CML.g2.T(16)

The formulation of the purified water inventory follows the holding cost integral proposed by Barman et al. [30], and is expressed as follows:

Viy=∫T1T2V2(t)dt+∫T2T3V3(t)dt =[(Ptr−Qinα(βIoT)).(T2−T1+e{α(T2−T1)}α−1α)] +[(Dvalα(βIoT)).(T2−T3+e{α(T3−T2)}α−1α)](17)

Lost treatment opportunity (unmet valorization, analogous to lost sale cost) is presented as follows:

Ltc=Ic.(1 δv).Qin.(T-T3)(18)

Back-ordered overflow cost (partial overflow treatment in next cycle) is presented as follows:

Boc=bc[((Ptr−Qin−δv.Qin).T122) +δv.Qin.(T22+T322−T3.T)](19)

Combining these terms yields the economic objective function in Equation 20. The total valorization profit per unit time is expressed as follows:

Z1=Tpf=(1T).[Tr-Tc-Ltc-Boc-h.Viy](20)

8.5 Environmental aspect: net pollution load

Total pollution load entering the system per cycle is Q_*in*T. The ML investment reduces pollutant discharge by fraction θ_*ML*. Equation 21 gives the total reduced pollution emissions is expressed as follows:

Tpl=[(Qin-Qtr)T].(1-θML)(21)

Under TNPCB cap-and-trade equivalent: if pollution discharge exceeds standard cap ρ_*p*, the excess is penalized at rate λ; under-discharge earns a subsidy. Equation 22 shows the net pollution cost per cycle, and Equation 23 defines the environmental objective function.

Npc=[Tpl-ρp].λ(22)

The second objective is expressed as follows:

ℤ2=Tpl(minimize net pollution load per cycle)(23)

8.6 Social aspect: health risk to agricultural communities

The health threat in communities where partially purified water is used for irrigation is directly related to the remaining pollutant levels in the treated water that are high enough to pose a health risk. Following the social impact formulation of Barman et al. [30], who modeled the worker health allowance for SO₂ inhalation, the total health risk per cycle is expressed as follows:

ℤ3=Hc .∑jmax(0,cj - cj_lmtcj_lmt).(T3T)(24)

where C_*j* denotes the residual concentration of pollutant (j) in the treated effluent, and c_{*j*_*lmt*} its corresponding regulatory discharge limit. From Equation 24 the max(0, ·) operator ensures that pollutants do not contribute any risk when they are within their regulatory limits and prevents a pollutant from being within its compliance limits while another pollutant exceeds its limits. If the concentration of all pollutants satisfies C_*j* ≤ c_{*j*_*lmt*}, then the health risk objective is assigned a value of zero (ℤ₃ = 0), indicating that the treated wastewater complies with the prescribed regulatory standards and poses no associated health risk upon discharge. As levels of pollutants begin to pass their respective limits steadily, ℤ₃ increases proportionally, directly reflecting the severity of regulatory non-compliance rather than a probability derived from predictive model accuracy. The fraction T3T scales risk by the valorization-active period of the cycle.

8.7 Complete multi-objective sustainable valorization model

Combining the economic, environmental, and social aspects, the complete multi-objective model is presented in Equations 25–27 as follows:

Maximizeℤ1=Tpf(25)

Minimizeℤ2=Tpl(26)

Minimizeℤ3=Hc.∑jmax(0, cj - cj_lmtcj_lmt)·(T3T)(27)

Subject to:

T2=[(1α(βIoT))].ln[(Ptr−Qin).e{α(βIoT).T1}+Dval.e{α(βIoT).T3}]Ptr−Qin+Dval(28)

T1=[( δv. Qin(Ptr - δv. Qin - Qin))].(T-T3)(29)

T>0, 0≤g≤1, βIoT>0, 0<T3<T,

Qtr≤Qin.(T-T3)(30)

The decision variables of the proposed optimization model are Q_*tr*, T₃, g, and β_*IoT*. Furthermore, the machine learning cost parameter satisfies the constraint C_*ML* > 0, since the cost rate is inherently non-negative. This is exactly adapted from EPQ manufacturing [30] to wastewater valorization, while introducing a three-objective architecture that elevates health risk to an independently optimized goal—a structural departure from the two-objective profit/emissions formulation of the source model.

9 Weighted max-min fuzzy goal programming

9.1 Fuzzy membership functions

Fuzzy logic, introduced by Zadeh, models imprecise and uncertain information by allowing intermediate degrees of membership between 0 (non-membership) and 1 (total membership), in contrast to classical binary logic [40]. The most common approach used in multi-objective decision-making problems is the Goal Programming (GP) approach. In GP, we assign a target level to be attained and a pre-determined priority for DM to achieve the target for each objective function. The role of the GP is to minimize unwanted deviations between goal achievement and aspiration levels. As the objective functions ℤ₁, ℤ₂, and ℤ₃ are conflicting, maximizing the profit objective (ℤ₁) generally favors higher values of the treatment quantity Q_*tr*; minimizing pollution and health risk impose quality bounds—no single solution simultaneously satisfies all three. Following Zimmermann, linear membership functions are defined:

ξ1(x)=ℤ1(x) - ℤ1-ℤ1+ - ℤ1- , for ℤ1-≤ℤ1(x)≤ℤ1+(31)

ξ2(x)=ℤ2+ - ℤ2(x)ℤ2+ - ℤ2- , for ℤ2-≤ℤ2(x)≤ℤ2+(32)

ξ3(x)=ℤ3+ - ℤ3(x)ℤ3+ - ℤ3- , for ℤ3-≤ℤ3(x)≤ℤ3+(33)

Here ℤ1+ is the maximum profit achieved by optimizing ℤ₁ alone; ℤ1- is the worst profit from the ℤ2- optimal solution; and analogously for ℤ₂. The health-risk membership formulation maps residual pollutant concentrations relative to regulatory discharge thresholds directly onto the goal satisfaction level, establishing a closed-form relationship between measured water-quality outcomes and policy satisfaction. The IoT-ML system's performance level influences this outcome only indirectly, through its effect on the achievable fraction of pollution reduction.

9.2 Crisp max–min problem

Tirkolaee and Aydin [41] used fuzzy weighted GP optimization of a multi-objective linear programming problem. The weighted max–min FGP model is advantageous because it eliminates the need for the decision-maker to specify aspiration or target values prior to the optimization process. Fuzzy GP is weighted using the max–min approach, shifting the sharp single-objective functional of the proposed multi-objective EPQ model. The weighted max–min FGP crisp formulation is expressed as follows:

Maximize α(34)

subject to the following:

w1(α) ≤ ξ1(x)(35)

w2(α) ≤ ξ2(x)(36)

w3(α) ≤ ξ3(x)(37)

Constraints Equations 28–30

0≤α≤1(38)

where w₁ = w₂ = w₃ = 1 (equal priority weights) and α = min {ξ₁, ξ₂, ξ₃}. The optimal α^* and Qtr* constitute the compromise solution.

9.3 Solution algorithm

This section proposes an algorithm to find the optimal solution for the decision variable Qtr* using the FGP approach. The steps are as follows:

• Step 1. Start.
• Step 2. Declare and assign the values of all known parameters of the model.
• Step 3. Calculate the individual best values ℤ1+, ℤ2-, and ℤ3- of the objective functions ℤ₁, ℤ₂, and ℤ₃ by optimizing each objective separately subject to constraints Equations 28–30.
• Step 4. Determine each objective from the solutions obtained by optimizing the other two objectives individually, and take the worst (min for a maximize-goal, max for a minimize-goal) resulting value.
• Step 5. Calculate the membership functions ξ₁(x), ξ₂(x), and ξ₃(x) using Equations 31–33.
• Step 6. Formulate the crisp max-min problem by substituting ξ₁ and ξ₂ into the constraints Equations 34–38: maximize α subject to ξ₁ ≥ α, ξ₂ ≥ α, ξ₃ ≥ α, and all model constraints.
• Step 7. Solve for the optimal aspiration level α^* and the corresponding optimal treatment volume Qtr. If ξ₃ ≥ α, the binding constraints are ξ₁ and ξ₂; otherwise α^* = ξ₃.
• Step 8. Compute ℤ1, ℤ2, and ℤ3* by substituting Qtr* into each objective function and verify α^* = min{ξ₁, ξ₂, ξ₃}.
• Step 9. Stop.

10 Numerical experiments

To demonstrate the applicability of the proposed mathematical framework, four hypothetical numerical Examples are constructed using assumed parameter values [42]. The adopted values are selected to represent feasible operating conditions for IoT-assisted textile wastewater treatment and are used solely for illustrating the performance of the proposed optimization model. Example 1 incorporates the experimentally validated stacked ensemble learning accuracy (R² = 0.978), whereas Examples 2–4 investigate alternative hypothetical operating conditions. These numerical Examples enable a comprehensive evaluation of the robustness and effectiveness of the proposed optimization framework.

10.1 Example 1

10.1.1 Smart farm wastewater treatment with IoT monitoring and ML purification investment

Here, a numerical experiment is taken into account for a smart-farm wastewater treatment model that simultaneously optimizes three objectives—maximizing profit (ℤ₁), minimizing pollution load (ℤ₂), and minimizing health risk (ℤ₃)—using a FGP approach with IoT monitoring and ML-based purification investment, where the optimal treatment rate Qtr* and ML performance level g^* are determined jointly via an FGP max-min scan to achieve the highest overall satisfaction level α^*. The required parametric values are as follows: η_*ML* = 0.978, Q_*in* = 500 m³/day, T = 20 days, T₃ = 8 days, p_*f* = ₹12/kg, γ = 0.45 kg/m³, C_*tr* = ₹4/m³, p_*w* = ₹1.5/m³, H_*c* = ₹3/kg, H_*c* = ₹3/kg, P_*tr* = 550 m³/day, D_*val* = 480 m³/day, β_*IoT* = ₹7.5/day, C_*ML* = ₹12.2449/day, k_*conv* = ₹1.8125/m³, and Q_max = 500 m³/day.

10.2 Example 2

10.2.1 Fuzzy goal programming model for high-volume industrial wastewater treatment with IoT monitoring and ML purification investment

Here, a numerical experiment is taken into account for a scaled-up industrial wastewater treatment model representing an earlier IoT-ML deployment stage, simultaneously optimizing three objectives—maximizing profit (ℤ₁), minimizing pollution load (ℤ₂), and minimizing health risk (ℤ₃)—using a FGP approach with IoT monitoring and ML-based purification investment, where the optimal treatment rate Qtr* and ML performance level g^* are determined jointly via an FGP max-min scan to achieve the highest overall satisfaction level α^*. The required parametric values are as follows: η_*ML* = 0.991, Q_*in* = 800 m³/day, T = 25 days, T₃ = 10 days, p_*f* = ₹15/kg, γ = 0.48 kg/m³, C_*tr* = ₹5/m³, p_*w* = ₹2.0/m³, H_*c* = ₹4/kg, P_*tr* = 880 m³/day, D_*val* = 768 m³/day, β_*IoT* = ₹8.0/day, C_*ML* = ₹13.0612/day, k_*conv* = ₹8.0/day, C_*ML* = ₹13.0612/day, k_*conv* = ₹2.625/m³, and Q_max = 800 m³/day.

10.3 Example 3

10.3.1 Fuzzy goal programming model with IoT monitoring and ML purification investment

Here, a numerical experiment is taken into account for a wastewater treatment model representing a newly-deployed ML system with limited training data, simultaneously optimizing three objectives—maximizing profit (ℤ₁), minimizing pollution load (ℤ₂), and minimizing health risk (ℤ₃)—using a FGP approach with IoT monitoring and ML-based purification investment, where the optimal treatment rate Qtr* and ML performance level g^* are determined jointly via an FGP max–min scan to achieve the highest overall satisfaction level α^*. The required parametric values are as follows: η_*ML* = 0.842, Q_*in* = 300 m³/day, T = 18 days, T₃ = 6 days, p_*f* = ₹9/kg, γ = 0.40 kg/m³, C_*tr* = ₹3.5/m³, p_*w* ₹3.5/m³, p_*w* = ₹1.2/m³, H_*c*= ₹2.5/kg, P_*tr* = 330 m³/day, D_*val* = 288 m³/day, β_*IoT* = ₹5.5556/day, C_*ML* = ₹10.2041/day, k_*conv* = ₹0.8125/m³, and Q_max = 300 m³/day.

10.4 Example 4

10.4.1 Fuzzy goal programming model for revised dual valorization with fertilizer recovery, irrigation water reuse, and crop yield benefit

Here, a numerical experiment is taken into account for a dual-valorization wastewater treatment model (fertilizer and irrigation water recovery) representing a mid-stage ML deployment requiring further training, simultaneously optimizing three objectives—maximizing profit (ℤ₁), minimizing pollution load (ℤ₂), and minimizing health risk (ℤ₃)—using a FGP approach with IoT monitoring and ML-based purification investment, where the optimal treatment rate Qtr* and ML performance level g^* are determined jointly via an FGP max-min scan to achieve the highest overall satisfaction level α^*. The required parametric values are as follows: η_*ML* = 0.765, Q_*in* = 600 m³/day, T = 30 days, T₃ = 12 days, p_*f* = ₹13/kg, γ = 0.46 kg/m³, C_*tr* = ₹4.5/m³, p_*w* = ₹3.0/m³, H_*c* = ₹3.5/kg, P_*tr* = 660 m³/day, D_*val* = 576 m³/day, β_*IoT* = ₹6.0/day, C_*ML* = ₹9.5238/day, k_*conv* = ₹2.8/m³, and Q_max = ₹9.5238/day, k_*conv* = ₹2.8/m³, and Q_max = 600 m³/day.

11 Results and discussion

This section discusses the results of numerical experiments conducted on the proposed model of sustainable wastewater treatment using an ensemble learning-based approach with IoT. Table 3 presents the optimal solutions derived for four representative operational scenarios corresponding to various textile-cluster conditions, obtained using the weighted max–min FGP formulation. All four reported optima were checked using an exhaustive grid search and found to converge to within 0.002 of the true optimum. The results showed that the proposed multi-objective model can achieve a true and meaningful balance between the three sustainability goals of economics, environment, and society, as the objective of economic sustainability introduces a convex capacity-strain cost term, which allows the objective of economic sustainability to account for the realistic diminishing returns when the treatment intensity approaches the plant's rated capacity. Across all numerical Examples, the optimal treatment volume remained between 90% and 100% of the plant's rated capacity. Moreover, as operational complexity increased, the optimization framework selected treatment volumes that increasingly approached the wastewater treatment plant's rated capacity. This concavity is explicitly shown in Figures 1a, b, which present the three-dimensional response surface of the economic objective ℤ₁ over the (Q_*tr*, g) decision space and the corresponding concavity profile with respect to Q_*tr*, respectively, the treatment-volume decision is indeed a trade-off in the economic sense and not a boundary solution. The overall satisfaction level using Table 3 is the highest among all cases considered (α^* = 73.34%) because the high ML prediction accuracy (η_*ML* = 0.991) and large treatment scale (Q_*in* = 800 m³/day) enable the optimizer to select a high level of ML performance (g^* = 0.7757) without the cost penalty outweighing the profit objective. The economic goal has the highest profit (₹1,461.22/day); the environmental goal results in the largest reduction in the net pollution load (127.47 tons/day); the social goal has the lowest health-risk index (ℤ3* = 0.8636), and the health-risk membership value (ξ₃ = 0.8913) is greater than binding economic and environmental memberships—indicating a slack at this compromise solution. This result is based on the membership-function dataset shown in Table 4. The optimization results demonstrate that the relatively low baseline machine learning prediction accuracy (η_*ML* = 0.765) leads to the proposed framework to achieve the second-highest machine learning satisfaction level (α^* = 73.28%) in Example 4, even at a reduced wastewater inflow rate of Q_*in* = 600 m³/day. This shows that η_*ML* is a limiting condition on performance, not a fixed value that, once set, cannot be changed by the operator, but rather is a variable that is subject to the operator's control.

Table 3. Optimal values across four numerical examples.

Table 4. Dataset for membership functions—Example 2.

The third case is Example 1 (the baseline case), where all three goals are simultaneously binding at the optimum (ξ₁= ξ₂= ξ₃= 0.7090), and the resulting solution is a compromise, in which none of the goals dominates. This is demonstrated in Figures 2a–c, where the membership function for total profit, net pollution load, and health risk all meet at the same level of satisfaction. The economic objective yields a moderate profit (₹623.98/day) at Qtr* = 465.11 m/day, with g^* = 0.6020. Interestingly, the overall satisfaction level of Example 3 is the lowest (α^* = 66.15%) even though the treatment scale is the smallest (Q_*in* = 300 m/day) and the accuracy of the ML is the lowest (η_*ML* = 0.842). Furthermore, the corrected model yields a positive economic objective (ℤ1* = ₹161.51/day) even though Q_*tr* and g were not optimized jointly, but throughput and accuracy were treated as fixed. The health-risk lower bound for the case of all three goals being binding is again strictly positive (ℤ3- = 0.3289), meaning that even in the case of all three goals being perfectly achieved, some pollutant exceedances remain in the lower bound. Table 5 shows the membership-function dataset.

Table 5. Dataset for membership functions—Example 3.

Apparently, both the scale of the inflow and the level of the corresponding ML performance are important factors that strongly affect the performance of the model—but the majority of all the active investment in g has a significant impact: Example 4 achieves near-best satisfaction, even though it is the model with the lowest η_*ML*, demonstrating that an investment in g can make up for a lower baseline accuracy. The response surface and concavity profile for Example 4 (Figures 3a, b) demonstrate the same concave behavior with respect to Q_*tr* as observed in Example 1. This consistency indicates that the underlying economic trade-off structure is preserved across the numerical examples and is not merely an artifact of an individual case. Overall, Example 2 achieves the highest overall satisfaction level among the four numerical examples (α^* = 73.34%), whereas Example 3 exhibits the lowest performance (α^* = 66.15%). A systematic compliance assessment further indicates that none of the four Examples fully satisfies all pollutant discharge limits under the optimized solution. Specifically, pollutant concentrations exceed the prescribed regulatory limits in three of the four Examples, demonstrating that the fuzzy goal programming framework provides a balanced compromise between economic profitability and health risk rather than enforcing strict regulatory compliance. These findings highlight the need to incorporate compliance-based constraints into the optimization model, representing a promising direction for the future research. Collectively, the findings confirm that the proposed FGP model integrated with IoT is a novel, mathematically sound, and scalable solution for sustainable valorization of textile water streams as compared to the static EPQ model with a predefined set of goals, where the model performance is a dynamic decision variable that can be adapted in real time. Example 2 achieved the highest overall satisfaction level among the four numerical examples. In addition, the consistent balance attained among the conflicting objective functions across all examples confirms the effectiveness and robustness of the weighted max–min FGP approach for solving multi-objective textile wastewater treatment optimization problems. The framework grounds health risk in measured pollutant compliance rather than prediction accuracy, and treats ML performance as a real-time, controllable decision variable, yielding consistently profitable, verified solutions. Limitations include incomplete regulatory compliance at the optimum, illustrative parameters pending field calibration, and IoT feasibility validated only through simulation.

12 Sensitivity analysis

A sensitivity analysis was performed to assess the robustness of the proposed model and to meet one of the methodological requirements for multi-objective optimization studies, since the fixed parameter values do not provide information on the stability of the compromise solution under real-world variability [43]. Based on the base scenario from Example 10.1, six key parameters (η_*ML*, Q_*in*, C_*tr*, p_*f*, p_*w*, and H_*c*) were perturbed by both ±10 and ±20%. The resulting global optimization (Q_*tr*, g) was re-solved at each point to obtain genuine re-optimized results, not just approximations. Figures 4a–c present the resulting sensitivity of the economic (ℤ₁), environmental (ℤ₂), and health-risk (ℤ₃) objectives to each parameter. The results demonstrate that the prediction accuracy of the ML model has the biggest impact on the overall satisfaction (α^*), the price of fertilizer (p_*f*) has the second biggest impact, the treatment cost (C_*tr*) has a moderate impact, the inflow rate (Q_*in*) has a moderate impact. In contrast, the health cost coefficient (H_*c*) has only a direct impact on its objective (ℤ₃). It has no net impact on the overall satisfaction (α^*) shown in Figure 4d, as confirmed by an analysis. This analysis helps establish the robustness and practical reliability of the FGP framework for real-world deployment, especially under uncertain or fluctuating operating conditions, as the proposed model's compromise solution is predictable and proportional to realistic changes in parameters, without erratic or unstable behavior.

12.1 Special cases

In order to investigate the behavior of the proposed model further, some special cases are discussed as follows:

• (1) If the ML performance level is not optimized together with the other model performance levels, but rather kept at a minimum level, the model can be rewritten as a regular optimization model with fixed treatment efficiency. Pollutant removal decreases, and results indicate that health risk increases significantly when there is no performance investment through ML.
• (2) If the economic goal is optimized without considering the environmental and social goals, the system chooses the lower level of ML performance and higher profit in the short term; however, residual concentrations of pollutants are still above the set limits. This further verifies that the solution is not applicable in real irrigation reuse.
• (3) Although the social goal (health risk) has been ignored, the model can still achieve reasonable economic and environmental results. Still, the discharge situation will not be safe, as shown by the compliance test in all four numerical examples. This underscores the need to apply social sustainability in wastewater treatment models.
• (4) If the inflow rate gets close to that of the system capacity without a corresponding increase in the level of ML performance, the model results in higher treatment cost, the same ML performance (which means the same pollutant removal), and no improvement in environmental or social impacts. This confirms that smart control systems are vital in designing an optimal system, as well as capacity limitation.

13 Conclusion

Sustainable wastewater treatment research has largely treated IoT-based monitoring, machine-learning prediction, and economic optimization as separate concerns; when social health impacts are considered at all, they are typically absorbed into the economic objective as a cost term rather than optimized in their own right. This study closes that gap through a novel IoT-enabled, ensemble learning-based multi-objective optimization framework for textile wastewater valorization, in which economic profit, environmental pollution load, and social health risk are formulated as three independently optimized objectives and resolved jointly via weighted max–min fuzzy goal programming. Its central structural contribution is to treat machine learning performance as an actively optimized decision variable rather than a fixed model property, enabling the framework to respond to real-time operating conditions in ways that static, parameter-fixed models cannot. The complete mathematical formulation—the four-phase inventory dynamics, the IoT-ML investment structure, and all three sustainability objectives—was independently re-derived and verified through symbolic computer algebra. The social objective was reformulated specifically to depend on measured residual pollutant concentrations relative to regulatory discharge thresholds, rather than on model prediction accuracy alone. Four representative scenarios, spanning realistic ranges of inflow scale (300–800 m/day) and ML maturity (η_*ML* = 0.765–0.991) were solved by jointly optimizing treated volume and ML performance level, with each reported optimum independently cross-validated against an exhaustive grid search to confirm genuine, verifiable solutions rather than solver artifacts.

The numerical results yield four findings of direct practical consequence. All four scenarios achieve profitable operating points—from ₹161.51/day in the smallest-scale scenario to ₹1,461.22/day in the highest-performing one—with overall satisfaction consistently between 66.15% and 73.34%, a stable outcome across markedly different operating conditions. ML performance level, not baseline prediction accuracy, emerges as the primary lever available to operators: the scenario with the lowest baseline accuracy (η_*ML* = 0.765) nonetheless achieves the second-highest satisfaction (73.28%) by adopting the highest optimal ML performance level of any scenario (g^* = 0.852). The two best-performing scenarios are not those with perfectly balanced objectives, but those in which the social objective is satisfied with social membership—while the economic and environmental goals remain binding, indicating that top-tier performance arises when health-risk requirements are comfortably exceeded rather than tightly constrained. Finally, no scenario achieves full regulatory compliance at its optimal level, as the fuzzy compromise balances health risk against profitability rather than treating compliance as a hard constraint—a limitation we note explicitly, since it points to a clear direction for the future model refinement. This study is significant on three counts. It offers, to our knowledge, the first framework in which health risk is grounded in measured pollutant compliance and optimized jointly alongside profit and pollution, rather than approximated through a prediction-accuracy proxy or absorbed into the economic objective—conferring genuine mathematical standing on the social dimension rather than token treatment. It demonstrates, with independently verified numerical evidence, that a plant's real-time-adjustable ML investment matters more to sustainable outcomes than its model's fixed underlying accuracy, a finding with direct bearing on how operators should allocate resources. And by disclosing the regulatory-compliance gap rather than presenting only favorable results, the study establishes a scientifically credible foundation for compliance-constrained extensions of this approach. Taken together, these results confirm that single-objective or accuracy-fixed optimization risks outcomes that are environmentally appealing yet economically or socially fragile, and that jointly optimizing economic, environmental, and social goals is a necessity, not an option, for industrial wastewater treatment policy. By treating ML performance as a real-time, operator-controllable variable, the proposed framework departs from classical EPQ-based sustainability models built on fixed parameters, offering a mathematically rigorous, computationally verified, and practically actionable tool for sustainable textile wastewater valorization. The future studies will incorporate neutrosophic fuzzy modeling for decision-making under deeper uncertainty, deep learning architectures trained on larger field-validated datasets, pilot-scale industrial validation, explicit regulatory-compliance constraints to close the gap identified above, and life cycle assessment to extend the sustainability evaluation beyond the objectives modeled here.

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Footnotes

Edited by: Amrit Das, SRM Institute of Science and Technology (Deemed to be University) Research Kattankulathur, India

Reviewed by: Tapan Senapati, Southwest University, China

Subramanian Selvakumar, Bahir Dar Institute of Technology, Bahir Dar University, Ethiopia

J. Vakula Rani, CMR Institute of Technology, India