Document Type : Research Paper
The escalating scarcity of freshwater resources in arid and semi-arid regions has rendered the utilization of non-conventional water sources, such as treated municipal wastewater, an unavoidable imperative in the agricultural sector. Treated Municipal wastewater, owing to its richness in essential macronutrients (particularly nitrogen, phosphorus, and organic matter) possesses considerable potential to enhance the yield of agronomic crops, including forage maize. Nevertheless, the concurrent presence of heavy metals such as nickel (Ni), zinc (Zn), cadmium (Cd), and lead (Pb) in treated wastewater composition poses significant risks to both human and animal food chain safety, as well as long-term soil quality. Consequently, the fundamental challenge in treated wastewater irrigation management lies in determining the optimal blending ratio with fresh water (well water) such that the nutritional benefits of the effluent are harnessed while maintaining tissue concentrations of toxic elements within permissible thresholds. Owing to the inherent conflict between maximizing crop yield and minimizing heavy metal uptake, this problem resides firmly within the domain of multi-objective optimization. Classical irrigation management approaches are ill-equipped to resolve these competing objectives simultaneously, necessitating advanced computational and multi-criteria decision-making frameworks. The objective of this study was to develop an integrated regression-optimization framework based on the NSGA-II multi-objective genetic algorithm to determine the optimal blending ratio of well water and treated municipal wastewater for forage maize irrigation and to conduct a comprehensive analysis of the trade-offs between quantitative yield and product biosafety.
The field data utilized in this study were derived from a three-year investigation (2020–2022) conducted at a farm located in Amij-Kola village, Babolsar County, Mazandaran Province, Iran. The experiment was executed in PVC lysimeters measuring 60 cm in diameter and 100 cm in height, arranged in a randomized complete block design with three replications. Irrigation treatments comprised five blending levels of well water and treated municipal wastewater: (I1) 100% well water, (I2) 25% wastewater + 75% well water, (I3) 50% wastewater + 50% well water, (I4) 75% wastewater + 25% well water, and (I5) 100% wastewater. For the purposes of this study, only data from non-magnetized water treatments were employed. The independent variables consisted of six irrigation water quality parameters: electrical conductivity (EC), sodium concentration (Na⁺), sodium adsorption ratio (SAR), calcium concentration (Ca²⁺), magnesium concentration (Mg²⁺), and total nitrogen (N). The dependent variables comprised five objectives: forage maize grain yield (ton/ha) as the maximization objective, and the tissue concentrations of four heavy metals (Ni, Zn, Cd, and Pb (µg/g)) as the minimization objectives. In the initial phase, to model the relationships between water quality and plant responses, three regression structures (linear, full quadratic, and full interactions) were fitted to the averaged dataset using Ridge regression (λ=0.1). The adjusted coefficient of determination (Adjusted R²) served as the criterion for selecting the optimal model. In the second phase, employing the selected model as the fitness function, the NSGA-II multi-objective genetic algorithm was executed with a population size of 500 and 1000 generations to derive the Pareto front. The search space was strictly bounded between the values of pure well water and pure wastewater to ensure the physical feasibility of the generated solutions. Simulated Binary Crossover (SBX) with a rate of 0.7 and polynomial mutation with a rate of 0.2 were utilized to produce offspring. Following Pareto front extraction, the balanced solution was identified using the ideal point method, incorporating user-defined weights (yield: 40%, each heavy metal: 15%). A combined sensitivity analysis was also performed to prioritize the water quality parameters. Finally, the optimal blending ratio was computed using the linear mixing equation for five linear parameters and subsequently validated.
Evaluation of the regression models revealed that the full interactions model, with an average adjusted R² of 0.9968 across all five objectives, demonstrated markedly superior performance compared to the linear (0.9898) and full quadratic (0.9940) models. This model achieved near-perfect predictive accuracy, particularly for cadmium and lead concentrations (R²adj ≈ 1.000). The NSGA-II algorithm successfully converged, yielding a final Pareto front comprising 500 non-dominated solutions. The convergence history indicated that the fitness function stabilized completely after approximately 600 generations. The final Pareto front substantiated a profound structural conflict between the yield objective and the heavy metal objectives; specifically, movement towards yields exceeding 24.5 ton/ha was inevitably accompanied by an exponential increase in lead and cadmium concentrations. Combined sensitivity analysis identified sodium concentration (Na⁺) as the most influential parameter governing the yield-toxicity trade-off, exhibiting a sensitivity coefficient of -0.232. The sodium adsorption ratio (SAR) ranked second in importance with a coefficient of +0.207, underscoring the dualistic and nonlinear behavior of sodium in forage maize physiology. The balanced solution selected from the Pareto front recommended an optimal blending ratio of 23% wastewater to 77% well water. This solution achieved a grain yield of 24.54 ton/ha, thereby not only maintaining the yield at the record level of the 100% wastewater treatment (24.46 ton/ha) but also improving it by 0.33%. From a biosafety perspective, this solution reduced lead concentration from 46.85 to 14.19 µg/g (a 70% reduction) and cadmium concentration from 8.39 to 0.96 µg/g (an 89% reduction) compared to the 100% wastewater treatment. Multi-objective response surface analysis further corroborated the nonlinear behavior of sodium; specifically, increasing sodium at lower salinity levels was associated with improved yield, whereas at higher levels, the slope of cadmium and nickel uptake escalated sharply.
This study successfully developed an integrated regression-optimization framework based on the NSGA-II algorithm for the qualitative management of forage maize irrigation with treated municipal wastewater. The findings unequivocally demonstrated that the full interactions regression model, by accounting for complex ion interactions, serves as a precise tool for simulating plant responses. The proposed balanced optimal solution (specifically, blending 23% wastewater with 77% well water) represents an intelligent compromise between food security and product safety, achieving near-maximum yield (24.54 ton/ha) while mitigating heavy metal hazards by 70% to 89% relative to irrigation with 100% wastewater. Both sensitivity analysis and response surface methodology convergently emphasized the pivotal role of sodium concentration and the meticulous management of the sodium adsorption ratio (SAR). The study revealed that the slight increase in heavy metal concentrations observed in the optimal solution relative to pure well water (I1) is an unavoidable cost of harnessing the substantial nutritional potential of wastewater to achieve economically viable yields; nonetheless, the absolute values of these metals remain within internationally accepted permissible limits. The framework presented herein can serve as an effective decision-support tool for farmers, extension specialists, and water resource managers in regions confronting freshwater scarcity yet possessing access to treated wastewater. Future research should focus on modeling the long-term dynamics of heavy metal accumulation in soil profiles and integrating such models with plant growth simulations.
The financial support for this study was provided by Sari Agricultural Sciences and Natural Resources University, Faculty of Agricultural Engineering. This support included a thesis research grant for the first author and separate research grants for the second and third authors, who are faculty members of the same university.
The contributions of the authors to this manuscript, which is derived from a thesis, are as follows:
First author (Narges Shakeri): Data collection, performing calculations, statistical analysis of data, analysis and interpretation of information and results, and drafting the manuscript.
Second author (Dr. Mohammad Mirnaseri, first thesis supervisor): Research design, supervision of the research process, verification and control of results, revision, review, and finalization of the manuscript, numerical coding in MATLAB software, numerical optimization, and assistance to the first author.
Third author (Dr. Mojtaba Khoshrvash, second thesis supervisor): Contribution to research design, research supervision, review and revision of the manuscript, examination of primary data, and guidance of the first author.
Fourth author (Dr. Reza Hasanzadeh Dalir, thesis advisor): Contribution to research design, research supervision, review and revision of the manuscript, and data analysis.
All authors have read and agreed to the published version of the manuscript.
The data of the present study are available upon request from the authors (by emailing the corresponding author).
The authors would like to thank anonymous referees for their constructive comments.
The authors avoided data fabrication, falsification, and plagiarism, and any form of misconduct.
The authors declare no conflict of interest.
