Revalorization of Vinasse as a Farmland Improver Through Multi-Objective Genetic Algorithms: A Circular Economy Approach

Abstract

Vinasse is a waste generated from the sugarcane ethanol production process. It is an effluent that, when discharged into the environment, causes serious damage. This study evaluated the potential of vinasse as a regenerator of agricultural soil through Multi-Objective Genetic Algorithms (MOGAs). This study focused on optimizing the amount of vinasse that should be applied, depending on its composition and the needs of the agricultural land. The methodology included five phases where the properties of the cultivated land with and without vinasse were evaluated; with the experimental data, MOGAs were constructed to evaluate soil: (a) fertility, (b) quality, and (c) health. The vinasse was characterized; meanwhile, to understand how the soil behaves depending on the incorporation of vinasse, a factorial experiment was designed in soils where sugarcane is grown in Mexico. The models were built and optimized using MATLAB^® and evaluated using Pareto Front. This study showed that vinasse improved soil fertility, quality, and health, with an optimal ratio of mixture formed by 40% vinasse and 60% irrigation water. This ratio allows the development of appropriate soil conditions for the growth of the crop—this is achieved after the application of the vinasse during the preparation of the land for cultivation, which is reached at approximately 20 cm depth—(a) fertility with K of 150 to 230 mg/kg, P of 25 to 35 mg/kg, and N of 17 to 19 mg/kg; (b) quality with MC of 90 to 95%, OM of 3.5 to 4%, and pH of 6.5 to 7.5 UpH; and (c) health with equity of 78% to 80%, abundance of 75% to 80%, and diversity of 80% to 95%. A comparative analysis between an experimental field with and without vinasse showed a 24% increase (ton/ha) in sugarcane yield. The value of vinasse is highlighted, not only as a waste to be treated, but as a regenerative input aligned with the Circular Economy.

1. Introduction

The world’s land area is 13,000 million hectares (ha), not including Antarctica. In 2022, land for agriculture was approximately 4781 million ha—more than a third of the total land area―; while, within these agricultural lands, 1573 million ha were cultivated—corresponding to 12% of the total land area—[1]. In recent years, exponential population growth has intensified agricultural production. However, due to this intensification, the availability of nutrients in the soil has decreased [2], caused by the overexploitation of agricultural resources. It is a reality that the Earth has been affected by anthropogenic activities [3]. The phenomenon of population growth has led to an overexploitation of agricultural land resulting from poor agricultural practices, e.g., inadequate cropping systems—these being methods that are used without knowledge of the type of crop, agricultural practices, and environmental conditions―, excessive use of chemical fertilizers and pesticides, lack of fallowing, and monoculture; however, other indirect phenomena negatively affect cropland—e.g., pollution, deforestation—which generates desertification, which in turn impacts the availability of food, alters the water cycle and reduces biodiversity, promotes climate change, and leads to urbanization. These phenomena have caused a loss in the fertility and health of arable land [4,5,6,7,8,9,10,11], which affects crop yields and consequently has compromised food availability. The quality of farmland is directly related to soil fertility and health.

The level of soil fertility is related to agricultural yield. Soil fertility is understood as the ability of the soil to supply the nutrients necessary for plant growth. Soil fertility is generally associated with the availability of nutrients so that the crop through the roots achieves proper development; i.e., the soil properties are considered comprehensively [12], together with an adequate supply of water and pest and disease control, among others.

The macronutrients of the soil are nitrogen (N), phosphorus (P), and potassium (K) [13]. NPK improves crop yield and quality [14,15]. K is one of the main macronutrients that promotes overall plant growth, increases crop yield and quality, and increases resistance to stress [16]. Soil Organic Matter (SOM) is related to the physical properties of the soil and provides macronutrients when it decomposes under specific circumstances. When these are absorbed by plants, they are converted into carbohydrates during the process of photosynthesis. A subsequent conversion in plants can produce proteins, as well as other plant compounds. The pH (hydrogen potential) is related to absorption of nutrients, affects microbial activity and soil structure, and generally, it impacts soil health. Soil fertility is restricted by SOM, N, P and K deficiency [17,18]. The P content influences the absolute fertility of the soil [19]. Therefore, fertile land has physical, chemical, and biological conditions for optimal crop development.

Soil health is defined as the continuous capacity of the soil to function as a living ecosystem [20], on which other living beings—plants, animals and human beings [21]—are sustained; and which, in addition, connects agricultural and soil science with policy, stakeholders and the supply chain [22]. Soil health is measured by various physical, chemical, or biological indicators, including N mineralization, microbial biomass, pathogens, microbial activity, fauna, organic carbon, pH, and electrical conductivity.

Soil quality is the condition that establishes that the soil has the necessary properties for the proper development of the crop and the ecosystem. Soil quality is measured by various indicators, with microbial activity being one of the most important. This activity promotes the decomposition of organic matter, the availability of nutrients and the production of biological compounds.

Also, there has recently been an interest in biological indicators, as the scientific community relates soil health to biological activity [23]. In agriculture, soil plays a primary role [24] since food production requires healthy soil [25]. In [26], it is mentioned that soil health depends on soil biota.

Improving the fertility and health of agricultural land contributes to increasing agricultural yields, coupled with the implementation of good agricultural practices, water availability, and pest and disease control. That is why various strategies have been developed from different frameworks with the intention of regenerating the physical, chemical, and biological properties of cropland; some of these include reusing waste from other value chains as a model of Circular Economy (CE).

In [27] 221 definitions of CE were examined where this model is interpreted and implemented in various ways. In this study, CE is defined as a regenerative economic system that follows the principle of re-circularity, wherein the CE approach seeks alternatives for the “End of Useful Life”, considering options of Reduction, Reuse, Recycling and/or Recovery in the value chain. Its objective is to maintain value and sustainable development for the benefit of current and future generations. So, under the CE framework, the reuse of waste components from value chains can be revalued as improvers of the same or another value chain of interest.

Sugarcane ethanol vinasse is a liquid organic waste derived from the production of ethyl alcohol. Vinasse, as a liquid effluent, is generated from distillation columns [28], at a temperature of between 90–100 °C [29], as part of the process of the alcoholic fermentation of cane juice, molasses, or a mixture of molasses and juice [30]. Vinasse is dark brown and has a strong smell; of its total composition, 93% is water [29], and the remaining 7%, is made up of 75% biodegradable organic compounds and 25% minerals [31]. According to [32], vinasse contains some residual sugars, alcohol, and non-volatile compounds.

Vinasse has high values of Chemical Oxygen Demand (COD) and Biological Oxygen Demand (BOD) associated with the suspension of organic solids—Organic Matter (OM)—and minerals—inorganic matter―; it has a low pH [29,32]; and it is highly corrosive [30] due to a high concentration of sulfate residue between 232 and 2900 mg/L left over from the ethanol fermentation step [29]. As it contains high concentrations of mineral salts—potassium and sulfate salts—it contains high values of electrical conductivity [33,34] and a high content of OM [34].

These values endow vinasse waste with high polluting potential because its composition causes soil salinization, generates greenhouse gases, and contaminates groundwater. Despite the adverse values of the components of vinasse, it is rich in OM; consequently, it is rich in valuable nutrients that can be used to increase agricultural yields. The nutrients contained in vinasse are (a) primary macronutrients: N, P, K [35]; (b) secondary macronutrients: sulfur (S), calcium (Ca), and magnesium (Mg); and (c) micronutrients [30].

It is estimated that 12–18 L of vinasse are produced for every liter of ethanol [36]. The distinctive characteristics of vinasse are a function of the composition of the biomass. Ethanol vinasse is highly polluting and can cause serious damage to the ecosystem if it is discharged into the environment indiscriminately, this is not a common practice but it is generated by accidents or accidental spills due to lack of maintenance of the treatment systems of said effluent. It has been reported that historically, vinasse has been used mainly as a soil amendment in the form of fertigation in sugarcane crops [37], as it is a source of nutrients and labile organic matter in cultivated areas [38].

From the above, it is possible to establish that vinasse can improve the yield of sugarcane crops; however, this is not entirely clear, and little attention has been given to the implications of vinasse as an improver of fertility and soil quality for crops. Thus, to fill this gap, the present article addressed the implications of vinasse as an improver of soil fertility, health, and quality for crops; for this, Multi-Objective Genetic Algorithms (MOGAs) were built, and thus, we evaluated how vinasse improves the physical, chemical, and biological properties of cropland.

MOGA is an effective approach to solving optimization problems with multiple objectives [39] as a Genetic Algorithm is a metaheuristic search technique [40]. The real problems are not mono-criteria but multicriteria, where it is desired to improve more than one objective function at the same time as another or others, without affecting them. The goal of multi-objective optimization problems is to find the possible trade-offs of the conflicting target functions; it is difficult to choose one, so a general solution is to determine the set of optimal Pareto solutions [41].

In this article, it was determined how treated vinasse can improve the fertility, quality, and health of the soil from an analysis of the interrelationships among the variables by mapping the space of feasible solutions with MOGAs. This study aimed to answer three questions: (i) What are the beneficial components of vinasse and their adequate values to fortify the soil in fertility, quality and health?; (ii) What are the variables and how can they be related to the fertility, quality and health of the soil?; and (iii) If vinasse has the ability to strengthen the soil of agricultural cultivation of sugarcane, to what extent can sugarcane production improve, without affecting the environment?

This document is organized as follows. Section 1, the Introduction, presents the context of the study. Section 2, Material and Methods, describes the methodological approach used for the analysis, including the description of the study site, the characterization of the vinasse, and the construction of the MOGAs. Section 3, the Results, presents the findings of the impacts of vinasse on farmland properties from the analysis of the Pareto Front of the developed MOGAs. Section 4, the Discussion, contrasts the results obtained in this study with those carried out by the scientific community. Section 5, Conclusions, shows the main contributions of the research.

2. Materials and Methods

The methodological approach used for the study is presented in Figure 1.

The methodology designed to evaluate the effect of vinasse as an improver of fertility, health and quality of soil for cultivation, is presented in five phases, namely:

• Phase I: Identification of Variables. In this phase, the variables that influence sugarcane growth are considered; for this, the information reported in the literature and validated by experts in sugarcane cultivation is considered. The group of experts was made up of three specialists in agronomy, a head of production in the ethanol industry and an expert in soil science. The expert judgment technique was used with these experts, and a structured interview was used to collect tacit knowledge.
• Phase II: Characterization. This includes the determination of the values of the main components of the vinasse obtained from the production of ethyl alcohol: heavy metals, physical and chemical characteristics, true color, toxicity, metals, organic matter, and sulfates. For each determination of vinasse, its beneficial impact on soil fertility, health, and quality was determined. This determination was made based on an analysis of the value of the element and its influence on the properties of the soil; this analysis was then validated by the group of experts.
• Phase III: Design of Experiments (DOEs). This phase involves determining the factors and levels that will be used to map the behavior of the soil’s physical, chemical, and biological variables depending on the incorporation of the vinasse. The definition of variables was validated by the group of experts, its percentage of concentration, and the timing of application. Soil cores were extracted to measure the variables of interest.
• Phase IV: Solving. Based on what was developed in the previous phase, the mathematical models that best represent the behavior of the variables of interest and that influence soil fertility, health, and quality were determined; then, based on MOGAs, the space for feasible solutions was determined.
• Phase V: Evaluation. As a result of the tri-criteria MOGAs, the influence of the variables of interest on fertility, quality and health was determined through an analysis of the Pareto Front; this analysis allows for finding the optimal set of solutions within the space of feasible solutions that cannot be improved toward any goal, without compromising the quality in another.
• Phase VI: Dosage. The last phase considered the determination of the factors and their variables, which have a significant effect as improvers on soil fertility, quality, and health and can contribute to improving sugarcane yield.

The ethanol vinasse was obtained directly from the production process’s vinasse outlet duct without being denatured by an ethanol mill, located in the central region of Veracruz, Mexico, that produces bioethanol and electricity. The soil under study included the cultivated land of three sugarcane varieties (Saccharum spp.): Mex 69-290, ATEMEX 96-40, and ITV 92-1424.

The open-air experimental field to evaluate the performance of the cropland based on the absence or presence of irrigation with vinasse was established in a private property located in Ixtaczoquitlan, Veracruz, Mexico (see Figure 2), where the planting and harvesting of sugarcane are carried out. The geographical location of the area to which the experimental field belongs is between parallels 18° 45′ and 18° 57′ north latitude; the meridians 96° 58′ and 97° 06′ west longitude; altitude between 700 and 1700 m. The relief of the study region is: on the surface, it corresponds to Neovolcanic Axis (77.73%), Sierra Madre del Sur (13.47%) and Coastal Plain of the Southern Gulf (8.80%), with a predominating semi-warm humid climate with abundant rainfall frequently in summer (99.23%), semi-warm humid with rainfall frequently throughout the year (0.53%) and warm humid with abundant rainfall frequently in summer (0.24%), with a temperature range of 18–24 °C and a precipitation range of 1900–2600 mm. The geology of the area belongs on the geological time scale to the Quaternary period (40.65%), Cretaceous (44.80%), and an urban area (14.55%); and the soil presents a composition of sedimentary rock of limestone (28.47%), slate (16.34%), and conglomerate (1.59%); alluvial soil (39.05%); and urban soil (14.55%). The dominant soils are luvisol (34.57%), vertisol (23.01%), leptosol (21.83%), andosol (4.39%), acrisol (0.19%), the urban area (14.55%), and unavailable (1.46%) [42].

The study was carried out in four phases, namely:

(a)

Collection of vinasse samples: the vinasse was collected during the 2022–2023 harvest in April 2023.

(b)

Experimental runs in sugarcane soil (DOEs): the treatment of the soil and its subsequent analysis, by means of soil cores, was carried out in July 2023.

(c)

Application of the optimal dose of the vinasse–irrigation water mixture: the dose was applied to the crop soil in February 2024.

(d)

Yield evaluation: the comparative analysis planted in March 2024 and cut the sugarcane in April 2025, with and without vinasse.

MATLAB^® R2023b (23.2.0.2365128) 64-bit (Win 64), in trial version [43], was used as the programming and numerical calculation platform for developing MOGA models to evaluate soil fertility, health, and quality. The NSGA-II (Non-dominated Sorting Genetic Algorithm II) was used as a MOGA due to its high efficiency in identifying solutions with multiple competitive objectives—for each MOGA (fertility, health, and quality), three objective functions were defined—along with their ability to find optimal Pareto solutions. The genetic operators used in the algorithms are presented in

Table 1. Parameters of genetic operators.

Settings	Operator	Rate/Function	Description
Algorithm	Pareto set fraction	0.80	So that the population on the Pareto front is larger than shown in the default settings.
	Crossover fraction	0.70	To conserve diversity and avoid an early convergence toward a local optimum.
	Mutation function	Adapt Feasible	The operator randomly generates adaptive addresses concerning the last generation.
	Creation	Linear Feasible	When there are linear constraints and no integer restrictions, this feature creates an initial population that satisfies the limits and limitations. It is capable of bringing many individuals within the boundaries of constraints while at the same time creating a dispersed population.
	Distance measure	Distance crowding	Used to compare the distance between an individual and others in the same range.
Population	Population size	100	To have a denser, more connected Pareto front, specify a larger population than the default.
Run-Time Limits	Max generations	1000	The algorithm stops when the maximum number of generations is reached. A high value of generations improves the final solution.

.

3. Results

This section describes the results obtained in each phase.

3.1. Phase I: Identification of Variables

It is currently recognized that multiple variables influence sugarcane growth (see Figure 3); that is why identifying the significant variables that influence the soil for sugarcane cultivation becomes necessary.

3.2. Phase II: Characterization

In this stage, the components of the vinasse were determined. The vinasse analyzed as a by-product of ethyl alcohol production was obtained in situ from the discharge duct, which connects the distillation column with the vinasse pit (see Figure 4).

The vinasse that was analyzed is produced from the distillation column at a temperature ranging between 50–60 °C, while the pit is discharged at a temperature of between 25–30 °C, because before being sent to the pit, its temperature is reduced by turbines. According to information from the company, of the total vinasse that is produced, approximately 50% of the water content evaporates due to the high temperature at which it is generated.

The vinasse was characterized. Due to the scarcity of resources to expand sampling, it was decided to characterize it from nine samples, with the necessary controls and management to preserve the properties of the effluent from the well to the analysis laboratory. To this end, three samples were recovered per harvest—2022, 2023 and 2024—by instant sampling in a plastic container before storing it outdoors. The vinasse was recovered from the pipeline connecting the ethanol plant to the storage well in February. Immediately after each sample was obtained in situ, it was transferred to the laboratory in a thermal vessel to preserve the properties of the effluent. For each determination, and based on the nine samples, sample statistics were obtained that allow us to know the average value of the observations—sample mean, $\overline{x}\mathrm{―}$, and how much variation exists between these observations—sample standard deviation, $s$―.

For each determination, a “Reference” was used, which is related to the standard that establishes the standardized method for the calculation of each determination in natural, drinking, wastewater, and treated wastewater. It is identified for each determination by a (*) that the value has a beneficial impact on the soil in terms of fertility, health, or quality. The values of the determinations are established in three digits as the precision of the measurements.

Table 2. Heavy metals.

Determination	Result		Units	Reference 1	Fertility	Health	Quality
	$\overline{\mathit{x}}$	$\mathit{s}$
Arsenic, by Hydride Generator	0.071	0.015	mg/L	NMX-AA-051-SCFI-2016
Cadmium	0.068	0.065	mg/L	NMX-AA-051-SCFI-2016
Copper	0.252	0.101	mg/L	NMX-AA-051-SCFI-2016		* 3
Total Chrome	<0.300 2	0.100	mg/L	NMX-AA-051-SCFI-2016
Mercury, by Hydride Generator	<0.002	0.001	mg/L	NMX-AA-051-SCFI-2016
Nickel	<1.000	0.500	mg/L	NMX-AA-051-SCFI-2016	*		*
Lead	0.636	0.014	mg/L	NMX-AA-051-SCFI-2016
Zinc	1.185	0.313	mg/L	NMX-AA-051-SCFI-2016	*	*	*

¹ Mexican Standard that establishes the standardized method for calculating the determination. ² A result reported as “<” indicates the practical limit of quantification of the method. ³ Indicates that it has a beneficial impact.

shows the presence of heavy metals in the vinasse sample from the absorption analysis.

Table 3. Physical and chemical characteristics.

Determination	Result		Units	Reference 1	Fertility	Health	Quality
	$\overline{\mathit{x}}$	$\mathit{s}$
Cyanides	<0.025 2	0.012	mg/L	NMX-AA-058-SCFI-2001
Electrical Conductivity	9220.000	1500.000	mS/cm	NMX-AA-093-SCFI-2018	* 4		*
Chemical Oxygen Demand	44,829.545	500.212	mg/L	NMX-AA-030/2-SCFI-2011
Total Phosphates	155.800	29.090	mg/L	NMX-AA-029-SCFI-2001	*	*	*
Total Phosphorus	222.140	31.977	mg/L	NMX-AA-029-SCFI-2001	*	*	*
Fats and Oils	31.600	2.002	mg/L	NMX-AA-005-SCFI-2013
Nitrate Nitrogen	7.140	1.483	mg/L	NMX-AA-079-SCFI-2001	*	*	*
Nitrite Nitrogen	<0.010	0.004	mg/L	NMX-AA-099-SCFI-2021		*
Total Nitrogen	614.560	13.696	mg/L	NMX-AA-079-SCFI-2001	*	*	*
				NMX-AA-099-SCFI-2021
				NMX-AA-026-SCFI-2010
pH, pH measurement at 25 °C	3.800	1.378	UpH 3	NMX-AA-008-SCFI-2016	*	*	*
Total Dissolved Solids	4600.000	890.000	mg/L	NMX-AA-034-SCFI-2015
Total Suspended Solids	4500.000	760.000	mg/L	NMX-AA-034-SCFI-2015
Kjeldahl Total Nitrogen	607.420	89.675	mg/L	NMX-AA-026-SCFI-2010

¹ Mexican Standard that establishes the standardized method for calculating the determination. ² A result reported as “<” indicates the practical limit of quantification of the method. ³ pH Units. ⁴ Indicates that it has a beneficial impact.

presents the physical and chemical characteristics that determine the quality of wastewater; the determination was made by physicochemical analysis.

These are recommended in low concentrations, because in high concentrations they are harmful. Those not included are considered toxic, e.g., lead, cadmium, and arsenic, which affect germination, root development, and biomass production; greases and oils clog the pores of the soil and affect permeability.

The true color of the water—the color of water without turbidity—was determined by a spectrometer at three wavelengths: $\mathsf{\lambda }\left(1\right)=436 \mathrm{n}\mathrm{m}$—aromatic compounds and humic substances―, $\mathsf{\lambda }\left(2\right)=525 \mathrm{n}\mathrm{m}$ and $\mathsf{\lambda }\left(3\right)=620 \mathrm{n}\mathrm{m}$—colored organic matter—(see

Table 4. True color.

Determination	Wavelength (nm)	Result		Units	Reference 1	Fertility	Health	Quality
		$\overline{\mathit{x}}$	$\mathit{s}$
True Color 2	436.000	467.000	13.000	m−1	NMX-AA-017-SCFI-2021	* 3		*
	525.000	306.000	28.000	m−1
	620.000	234.500	11.000	m−1

¹ Mexican Standard that establishes the standardized method for calculating the determination. ² pH value of the filtered sample: 4.0 pH units. ³ Indicates that it has a beneficial impact.

). True color, a quality parameter that indicates the presence of OM and dissolved substances, was determined from a water sample that was previously filtered using a $0.45 \mu \mathrm{m}$ membrane filter.

The results of this analysis indicate a low pH, i.e., it is an acidic substance for irrigation, which causes a decrease in the availability of essential nutrients and a reduction in beneficial microbial activity. The $\mathsf{\lambda }\left(1\right)=467 \mathrm{n}\mathrm{m}$ indicates a high organic load, which is useful if properly degraded; otherwise, the microbial quality of the soil decreases; and the $\mathsf{\lambda }\left(2\right)=306 \mathrm{n}\mathrm{m}$ and $\mathsf{\lambda }\left(3\right)=234.500 \mathrm{n}\mathrm{m}$ reinforce the presence of humic substances and colored OM; if it is not properly degraded, it affects the porosity of the soil.

Table 5. Toxicity.

Determination	Result		Units	Reference 1	Fertility	Health	Quality
	$\overline{\mathit{x}}$	$\mathit{s}$
Acute toxicity with Vibrio fischeri	7.089 3	1.003	UT 2	NMX-AA-112-SCFI-2017

¹ Mexican Standard that establishes the standardized method for calculating the determination. ² UT = Unit of toxicity. It is the degree of toxicity of a mixture or complex sample of which the concentration of the substances it contains is not known. It is calculated: $\mathrm{U}\mathrm{T}=100/\mathrm{C}\mathrm{E}50$, where 100 is the initial concentration of the referred sample in percentage. ³ Toxicity Units (UTs) and Mean Effective Concentrations ($\mathrm{C}\mathrm{E}50$) are reported at 15 min of exposure to Vibrio fischeri bacteria. $\mathrm{C}\mathrm{E}50=1587$. Dissolved Oxygen = 2.50 mg/L. Electrical Conductivity = 9200 microS/cm.

presents the toxicity of vinasse as wastewater using the acute toxicity assessment method with the marine bioluminescent bacterium Vibrio fischeri (NRRL B-11177). Toxicity is an adverse effect manifested by the test organisms in the short term after exposure to a sample. The test is based on measuring the luminescence emitted by the bacterium Vibrio fischeri using a luminometer.

Table 6. Metals.

Determination	Result		Units	Reference 1	Fertility	Health	Quality
	$\overline{\mathit{x}}$	$\mathit{s}$
Calcium	72.178	2.174	mg/L	NMX-AA-051-SCFI-2016	* 2	*
Magnesium	286.360	11.358	mg/L	NMX-AA-051-SCFI-2016	*	*	*
Potassium	2887.200	43.237	mg/L	NMX-AA-051-SCFI-2016	*	*	*

¹ Mexican Standard that establishes the standardized method for calculating the determination. ² Indicates that it has a beneficial impact.

presents the measurements of dissolved, total, suspended, and extractable metals in vinasse, which were made using atomic absorption spectrophotometry.

Table 7. Organic matter and sulfates.

Determination	Result		Units	Reference 1	Fertility	Health	Quality
	$\overline{\mathit{x}}$	$\mathit{s}$
Organic matter	10,980.000	678.959	mg/L	SM 20th 5310 A	* 2	*	*
Sulfates (such as SO4=)	2845.450	107.491	mg/L	Standard Methods 4500-E Ion Sulfate, 23rd Ed. (Turbidimetric)	*	*	*

¹ SM 20th 5310 A, standard method for the determination of total organic carbon in a water or wastewater sample; Standard Methods 4500-E Ion Sulfate, 23rd Ed. (Turbidimetric), a method of chemical analysis for determining the concentration of sulfate ions in water samples. ² Indicates that it has a beneficial impact.

summarizes the values of OM and sulfates in the sampled vinasse. The presence of OM can improve soil fertility, provide carbon and energy to microorganisms, and improve the water-holding capacity and availability of nutrients such as N and P. OM, due to its composition, helps to form aggregates, so the structure and aeration of the soil is improved, a situation that contributes to the development of roots and water infiltration at the same time that the cation exchange capacity is increased and erosion is reduced. Without treatment, it can lead to microbial imbalance and carbon overload. Similarly, the presence of sulfates can affect the soil biota and interfere with the uptake of other nutrients such as Ca.

From this analysis, it is determined that vinasse has valuable components for the soil to support crops, but some of these are present in large concentrations, which in turn is harmful to the soil, e.g., K, in high concentrations in the soil generates interference in the absorption of other nutrients, a situation that affects the growth and development of the crop. In addition, the plant becomes more susceptible to diseases. Therefore, in this study, the dilution of vinasse by irrigation water is presented as a strategy that allows for regulation of the components of the vinasse.

Calcium, magnesium, and potassium are metals that were measured, but there is no regulation that establishes the permissible limits. For Ca, the maximum desired value is 100 mg/L—Ca helps with soil fertility, nutrient availability and improves root growth―, for Mg, it is 150 mg/L—Mg helps maintain the soil structure―, and for K, it is 250 mg/L—K improves the soil structure and strengthens crop growth and yield―. These metals help with soil fertility, health, and quality. In this study, the value of Ca contained in the vinasse complies with the permissible limits, while the Mg and K do not comply with the maximum values of the permissible limits of contaminants in wastewater discharges.

Based on the values obtained from the characterization of the vinasse, and considering NOM-001-SEMARNAT-2021, which establishes the permissible limits of pollutants in the discharge of wastewater into receiving bodies and soils owned by the nation, Table 8 and Table 9 show the verification of the components of the vinasse. It is noted if the value of the component complies with the permissible limits established by current Mexican regulations, and if so, as a revaluation strategy, its dissolution in irrigation water is proposed to reduce the value of the components that exceed the permissible limits.

The values of the components of the vinasse show that the effluent is highly polluting if it is disposed of into the environment without treatment; however, it is a reality that it is an effluent with components of interest for the agricultural sector due to the high concentrations of, e.g., N, P, K and OM. At the same time, it contains metals of interest to plants, e.g., copper, nickel, and zinc. So, its revaluation as an improver of farmland is interesting.

3.3. Phase III: DOEs

In order to understand the behavior of the soil as a function of the incorporation of vinasse, i.e., a mapping, a Design of Experiments (DOEs) was established, the model being a complete factorial design. Of the factors under study, factor A: Place is considered as the Block Factor, because “Field 1” and “Field 2”, as microlocations, belong to the same macrolocation. The other factors are considered fixed. One replicate included 72 runs, which were randomized to distribute the estimation error. The study considered one replication due to the available resources. Table 10 summarizes the factors to be analyzed.

Table 8. Permissible limits.

Parameter	Unit	Rivers, Streams, Canals, Drains	Meets?	Soil (Infiltration and Other Irrigation)	Meets?
Temperature	°C	35	Yes	35	Yes
Fats and Oils	mg/L	21	Not	21	Not
Total Suspended Solids	mg/L	84	Not	140	Not
Chemical Oxygen Demand	mg/L	210	Not	210	Not
Total Organic Carbon 1	mg/L	53	Not	53	Not
Total Nitrogen	mg/L	35	Not	NA 2	---
Total Phosphorus	mg/L	21	Not	NA	---
pH	UpH	6–9	Not	6–9	Not
True Color	Wavelength	Maximum spectral absorption coefficient (m−1)
$\mathsf{\lambda }\left(1\right)=436$	nm	7.0	Not	7.0	Not
$\mathsf{\lambda }\left(2\right)=525$	nm	5.0	Not	5.0	Not
$\mathsf{\lambda }\left(3\right)=620$	nm	3.0	Not	3.0	Not

¹ Under the assumption that organic matter contains 58% organic carbon. ² Not applicable.

Table 8. Permissible limits.

Parameter	Unit	Rivers, Streams, Canals, Drains	Meets?	Soil (Infiltration and Other Irrigation)	Meets?
Temperature	°C	35	Yes	35	Yes
Fats and Oils	mg/L	21	Not	21	Not
Total Suspended Solids	mg/L	84	Not	140	Not
Chemical Oxygen Demand	mg/L	210	Not	210	Not
Total Organic Carbon 1	mg/L	53	Not	53	Not
Total Nitrogen	mg/L	35	Not	NA 2	---
Total Phosphorus	mg/L	21	Not	NA	---
pH	UpH	6–9	Not	6–9	Not
True Color	Wavelength	Maximum spectral absorption coefficient (m−1)
$\mathsf{\lambda }\left(1\right)=436$	nm	7.0	Not	7.0	Not
$\mathsf{\lambda }\left(2\right)=525$	nm	5.0	Not	5.0	Not
$\mathsf{\lambda }\left(3\right)=620$	nm	3.0	Not	3.0	Not

¹ Under the assumption that organic matter contains 58% organic carbon. ² Not applicable.

Table 9. Permissible limits for metals and cyanides.

Parameter	Unit	Rivers, Streams, Canals, Drains	Meets?	Soil (Infiltration and Other Irrigation)	Meets?
Arsenic	mg/L	0.4	Yes	0.2	Yes
Cadmium	mg/L	0.4	Yes	0.2	Yes
Cyanide	mg/L	3	Yes	2	Yes
Copper	mg/L	6	Yes	6	Yes
Chrome	mg/L	1.5	Yes	1	Yes
Mercury	mg/L	0.02	Yes	0.01	Yes
Nickel	mg/L	4	Yes	4	Yes
Lead	mg/L	0.4	Not	0.4	Not
Zinc	mg/L	20	Yes	20	Yes

Table 9. Permissible limits for metals and cyanides.

Parameter	Unit	Rivers, Streams, Canals, Drains	Meets?	Soil (Infiltration and Other Irrigation)	Meets?
Arsenic	mg/L	0.4	Yes	0.2	Yes
Cadmium	mg/L	0.4	Yes	0.2	Yes
Cyanide	mg/L	3	Yes	2	Yes
Copper	mg/L	6	Yes	6	Yes
Chrome	mg/L	1.5	Yes	1	Yes
Mercury	mg/L	0.02	Yes	0.01	Yes
Nickel	mg/L	4	Yes	4	Yes
Lead	mg/L	0.4	Not	0.4	Not
Zinc	mg/L	20	Yes	20	Yes

Table 10. Factors of interest to be studied.

Factor	Name	Levels	Categories
A:	Place	2	Field 1; Field 2
B:	Variety of cane	3	Mex 69-290; ATEMEX 96-40; ITV 92-1424
C:	Vinasse	2	With vinasse; Without vinasse
D:	Treatment	6	10, 20, 40, 60, 80, 100% 1

¹ The remaining volume of the extension is considered to be irrigation water.

Table 10. Factors of interest to be studied.

Factor	Name	Levels	Categories
A:	Place	2	Field 1; Field 2
B:	Variety of cane	3	Mex 69-290; ATEMEX 96-40; ITV 92-1424
C:	Vinasse	2	With vinasse; Without vinasse
D:	Treatment	6	10, 20, 40, 60, 80, 100% 1

¹ The remaining volume of the extension is considered to be irrigation water.

While the following output variables of interest are established: $y_1=$ pH (UpH), $y_2=$ MC—Microbiological Composition—(%), $y_3=$ K (mg/kg), $y_4=$ P (mg/kg), $y_5=$ N (mg/kg), $y_6=$ OM (%), $y_7=$ abundance (%), $y_8=$ diversity (%), and $y_9=$ equity (%). Factors, levels, variables, and units of measurement were established using the judgment technique of experts in sugarcane cultivation. Samples of the experimental runs were recovered from the farmland. For this, soil cores were randomly extracted from the experimental field with a 20 m separation between each soil core. As this is a study with the scope of analysis of microorganisms, each soil core had the dimensions of 15 × 15 × 20 cm (length × width × depth). Once the cores were extracted, they were immediately transferred to the laboratory for analysis.

Table 11. ANOVA.

Source of Variation 1	$\mathit{S}\mathit{S}$	$\mathit{\upsilon }$	$\mathit{M}\mathit{S}$	${\mathit{F}}_0$	Significant
A:	10.89	1	10.889	0.66
B:	9.53	2	4.764	0.29
C:	133.39	1	133.389	8.05	*
D:	119.94	5	23.989	1.45
BC:	6.86	2	3.431	0.21
BD:	231.64	10	23.164	1.40
CD:	53.28	5	10.656	0.64
BCD:	164.97	10	16.497	1.00
Error	580.11	35	16.575
Total	1310.61	71

¹ It represents the main factor and interactions. * Significant at 5%.

presents an Analysis of Variance (ANOVA) of the factors of interest. From ANOVA, it is identified with a confidence level of 95%, that vinasse is the main factor influencing the variation of the variables of interest. The approach used in this phase is considered sufficient since it allows for obtaining statistically robust results about the influence of the factors’ effects on the variables of interest.

3.4. Phase IV: Solving

The mathematical models that best represent each response variable were determined based on the data collected in Phase III. Various models were tested for each output variable ($y_i$). The best model for each variable was defined from the model’s fit, i.e., the coefficient of determination ($d^2$); this coefficient indicates the degree of variability of the dependent variable that is explained by the independent variable in the mathematical model (see

Table 12. Mathematical models of output variables.

Parameter	${\mathit{d}}^2$(%)	Equation
pH	87.57	$y_1=7.7020+0.1710x_{\mathrm{1,1}}-0.1710x_{\mathrm{1,2}}+0.0555x_{\mathrm{2,1}}-0.2783x_{\mathrm{2,2}}+0.223x_{\mathrm{2,3}}-0.1991x_{\mathrm{3,0}}+0.1991x_{\mathrm{3,1}}-0.107x_{\mathrm{4,1}}-0.298x_{\mathrm{4,2}}+0.201x_{\mathrm{4,3}}+\dots +0.444x_2{x}_3{x}_{\mathrm{4,3.1}.6}$
MC	99.51	$y_2=52.773-30.103x_{\mathrm{1,1}}+30.103x_{\mathrm{1,2}}+7.25x_{\mathrm{2,1}}+8.67x_{\mathrm{2,2}}-15.91x_{\mathrm{2,3}}-1.356x_{\mathrm{3,0}}+1.356x_{\mathrm{3,1}}+0.98x_{\mathrm{4,1}}+0.32x_{\mathrm{4,2}}-0.89x_{\mathrm{4,3}}+0.04x_{\mathrm{4,4}}-0.33x_{\mathrm{4,5}}-\dots -2.78x_2{x}_3{x}_{\mathrm{4,3.1}.6}$
K	97.96	$y_3=11.303+6.349x_{\mathrm{1,1}}-6.349x_{\mathrm{1,2}}+0.287x_{\mathrm{2,1}}-1.755x_{\mathrm{2,2}}+1.468x_{\mathrm{2,3}}+1.108x_{\mathrm{3,0}}-1.108x_{\mathrm{3,1}}-0.108x_{\mathrm{4,1}}-0.042x_{\mathrm{4,2}}-0.169x_{\mathrm{4,3}}-0.112x_{\mathrm{4,4}}+\dots +0.14x_2{x}_3{x}_{\mathrm{4,3.1}.6}$
P	90.26	$y_4=19.482-2.985x_{\mathrm{1,1}}+2.985x_{\mathrm{1,2}}+0.369x_{\mathrm{2,1}}+2.259x_{\mathrm{2,2}}-2.628x_{\mathrm{2,3}}+0.702x_{\mathrm{3,0}}-0.702x_{\mathrm{3,1}}-0.40x_{\mathrm{4,1}}-0.32x_{\mathrm{4,2}}+0.10x_{\mathrm{4,3}}+0.98x_{\mathrm{4,4}}+0.62x_{\mathrm{4,5}}-\dots -0.38x_2{x}_3{x}_{\mathrm{4,3.1}.6}$
N	82.40	$y_5=0.10713-0.01194x_{\mathrm{1,1}}+0.01194x_{\mathrm{1,2}}+0.00108x_{\mathrm{2,1}}+0.01245x_{\mathrm{2,2}}-0.01353x_{\mathrm{2,3}}+0.00051x_{\mathrm{3,0}}-0.00051x_{\mathrm{3,1}}-0.00630x_{\mathrm{4,1}}-0.00755x_{\mathrm{4,2}}-\dots +0.0030x_2{x}_3{x}_{\mathrm{4,3.1}.6}$
OM	79.71	$y_6=1.809-0.308x_{\mathrm{1,1}}+0.308x_{\mathrm{1,2}}+0.049x_{\mathrm{2,1}}+0.330x_{\mathrm{2,2}}-0.379x_{\mathrm{2,3}}+0.009x_{\mathrm{3,0}}-0.009x_{\mathrm{3,1}}-0.173x_{\mathrm{4,1}}-0.209x_{\mathrm{4,2}}-0.004x_{\mathrm{4,3}}+0.275x_{\mathrm{4,4}}+\dots +0.098x_2{x}_3{x}_{\mathrm{4,3.1}.6}$
abundance	95.27	$y_7=19.38-10.44x_{\mathrm{1,1}}+10.44x_{\mathrm{1,2}}+3.03x_{\mathrm{2,1}}-3.17x_{\mathrm{2,2}}+0.14x_{\mathrm{2,3}}-4.49x_{\mathrm{3,0}}+4.49x_{\mathrm{3,1}}+14.83x_{\mathrm{4,1}}+15.91x_{\mathrm{4,2}}-2.76x_{\mathrm{4,3}}-6.30x_{\mathrm{4,4}}-9.38x_{\mathrm{4,5}}-\dots -4.19x_2{x}_3{x}_{\mathrm{4,3.1}.6}$
diversity	88.90	$y_8=0.8687+0.1766x_{\mathrm{1,1}}-0.1766x_{\mathrm{1,2}}+0.1870x_{\mathrm{2,1}}-0.1489x_{\mathrm{2,2}}-0.0381x_{\mathrm{2,3}}+0.1248x_{\mathrm{3,0}}-0.1248x_{\mathrm{3,1}}+0.028x_{\mathrm{4,1}}+0.026x_{\mathrm{4,2}}+0.096x_{\mathrm{4,3}}-\dots +0.195x_2{x}_3{x}_{\mathrm{4,3.1}.6}$
equity	89.56	$y_9=0.6964+0.1566x_{\mathrm{1,1}}-0.1566x_{\mathrm{1,2}}+0.0383x_{\mathrm{2,1}}-0.0124x_{\mathrm{2,2}}-0.0259x_{\mathrm{2,3}}+0.0793x_{\mathrm{3,0}}-0.0793x_{\mathrm{3,1}}+0.0214x_{\mathrm{4,1}}-0.0948x_{\mathrm{4,2}}+0.0279x_{\mathrm{4,3}}-\dots +0.0942x_2{x}_3{x}_{\mathrm{4,3.1}.6}$

).

However, to identify the influence of factors on the soil, three categories of interest were established, on which three main functions involved in its behavior were defined. The mathematical models were integrated, with a tri-criterion objective function, as follows:

$${\mathit{FO}}_1: \mathrm{Soil} \mathrm{Fertility}, \mathrm{with} \mathrm{K} (f_1), \mathrm{P} (f_2), \mathrm{and} \mathrm{N} (f_3)$$

$$f_1=7.7020+0.1710x_{\mathrm{1,1}}-0.1710x_{\mathrm{1,2}}+\dots +0.444x_2{x}_3{x}_{\mathrm{4,3.1}.6}$$

$$f_2=19.482-2.985x\_\mathrm{1,1}+2.985x\_\mathrm{1,2}+\dots -0.38x\_2 x\_3 x\_\mathrm{4,3.1}.6$$

$$f_3=0.10713-0.01194x_{\mathrm{1,1}}+0.01194x_{\mathrm{1,2}}+\dots +0.0030x_2{x}_3{x}_{\mathrm{4,3.1}.6}$$

Subject to:

$$f_1\ge 80$$

$$f_1\le 250$$

$$f_2\ge 12$$

$$f_2\le 40$$

$$f_3\ge 10$$

$$f_3\le 20$$

$$x_{i,j.k.l}\ge 0;\hspace{1em}\hspace{1em}i,j,k,l=\mathrm{1,2},\dots ,3.1.6$$

FO₂: Soil Quality, with MC ($f_1$), OM ($f_2$), and pH ($f_3$)

$$f_1=52.773-30.103x_{\mathrm{1,1}}+30.103x_{\mathrm{1,2}}+\dots -2.78x_2{x}_3{x}_{\mathrm{4,3.1}.6}$$

$$f_2=11.303+6.349x_{\mathrm{1,1}}-6.349x_{\mathrm{1,2}}+\dots +0.14x_2{x}_3{x}_{\mathrm{4,3.1}.6}$$

$$f_3=35.924+23.757x_{\mathrm{1,1}}-23.757x_{\mathrm{1,2}}-\dots +2.64x_2{x}_3{x}_{\mathrm{4,3.1}.6}$$

Subject to:

$$f_1\ge 0.8$$

$$f_1\le 1$$

$$f_2\ge 0.025$$

$$f_2\le 0.04$$

$$f_3\ge 5$$

$$f_3<8.5$$

$$x_{i,j.k.l}\ge 0; i,j,k,l=\mathrm{1,2},\dots ,3.1.6$$

FO₃: Soil Health, with equity ($f_1$), abundance ($f_2$), and diversity ($f_3$)

$$f_1=1.809-0.308x_{\mathrm{1,1}}+0.308x_{\mathrm{1,2}}+\dots +0.098x_2{x}_3{x}_{\mathrm{4,3.1}.6}$$

$$f_2=19.38-10.44x_{\mathrm{1,1}}+10.44x_{\mathrm{1,2}}+\dots -4.19x_2{x}_3{x}_{\mathrm{4,3.1}.6}$$

$$f_3=0.8687+0.1766x_{\mathrm{1,1}}-0.1766x_{\mathrm{1,2}}+\dots +0.195x_2{x}_3{x}_{\mathrm{4,3.1}.6}$$

Subject to:

$$f_1\ge 0.75$$

$$f_1\le 0.80$$

$$f_2\ge 0.60$$

$$f_2\le 0.80$$

$$f_3\ge 0.75$$

$$f_3\le 1$$

$$x_{i,j.k.l}\ge 0; i,j,k,l=\mathrm{1,2},\dots ,3.1.6$$

The mathematical models were solved using MOGAs, a tool capable of exploring the space of solutions to complex problems. The model optimization process representing soil fertility, quality, and health is presented in Figure 5, Figure 6, and Figure 7, respectively.

Figure 5a–c illustrate the evolution of the multi-objective optimization process applied to the soil fertility model under ethanol vinasse treatment. Figure 5a, which shows the evolution of the individuals generated over generations, shows a progressive increase in the quality and diversity of solutions. This behavior indicates that the algorithm maintained an adequate search space exploration, avoiding premature convergence toward suboptimal solutions. The initial dispersal and subsequent concentration of individuals reflect a refinement process in the search for optimal combinations of parameters critical for fertility—K, P, and N―.

Figure 5b shows the genealogy of the evolutionary process of the algorithm for soil fertility, which is the relationship between individuals’—solutions—throughout the generations—blue, parent crossing; red, direct mutation―. It is generally observed that there is a balance between exploration—mutation—and exploitation—crossing—throughout the evolution of generations. This situation allows us to find several optimal solutions—Pareto Front―; therefore, genealogical evolution suggests that the algorithm better covers the multiple objectives. The MOGA then balances crossing and mutation, maintains population diversity, and better explores the space for solutions as evolution progresses.

Figure 5c represents the stopping criterion based on the model’s fitness function. It can be seen how, as the number of generations progresses, the variation in fitness is progressively reduced until it stabilizes. This stabilization suggests that the algorithm reached an equilibrium point where the solutions generated present marginal improvements that are smaller and smaller, thus validating that an approximation to the Pareto Front has been achieved. This pattern of evolution confirms the effectiveness of the model developed to identify strategies for the revaluation of vinasse that simultaneously optimize the leading indicators of soil fertility.

Figure 6a–c represent the evolutionary behavior of the multi-objective optimization process applied to the soil quality model under ethanol vinasse treatment. Figure 6a, corresponding to the evolution of individuals over generations, shows an initial dispersal pattern followed by a progressive concentration of solutions. This behavior suggests that the algorithm maintained an efficient exploration of the search space in early stages and then directed the exploitation toward high-quality regions, favoring optimal configurations of the soil—MC, OM and pH―.

Figure 6b shows the genealogy of the algorithm’s evolutionary process for soil quality. A high density of mutations is evident, which indicates an exploration of new solutions. Likewise, the algorithm maintains genetic diversity in the population throughout evolution, avoiding premature convergence. The high mutation rate allows an adequate exploration of the space of solutions in the face of a very complex Pareto Front, looking for various solutions in the feasible space.

Figure 6c shows the stop criterion based on stabilizing the fitness function. As generations pass, a sustained decrease in variability in fitness is observed, until a convergence phase is reached. This pattern indicates that the algorithm managed to stabilize the feasible solutions, guaranteeing the obtainment of a set of efficient alternatives that balance the physical properties of the soil. The evolution observed validates that the treatment with vinasse allows the identification of viable strategies to improve the structure and functionality of the soil, contributing to its resilience and long-term sustainability.

Figure 7a–c present the evolution of the optimization process applied to the agricultural soil health model. Figure 7a shows the evolution of the individuals generated over the generations. A progressive increase in the solutions’ equity, abundance, and diversity is observed, indicating that the algorithm managed to maintain a compelling exploration of the search space and avoid premature convergence toward local optima. This progressive evolution supports the efficiency of MOGA.

Figure 7b shows the genealogy of the health algorithm’s evolutionary process. During this process, the evolutionary genealogy of the individuals generated through crossbreeding and mutation operators showed a highly branched structure, which confirmed that adequate genetic diversity was maintained throughout the generations.

Figure 7c depicts the algorithm’s stop criterion as a function of the fitness function stabilization. The curve shows a gradual decrease in fitness variation over generations, indicating that the algorithm reached a convergence phase. This behavior validates the solutions balanced equity, abundance, and diversity, representing a robust Pareto Front.

3.5. Phase V: Evaluation

The Pareto Front of mathematical models is presented in Figure 8. Figure 8a–c show the behavior resulting from the multi-objective optimization applied to the mathematical models developed to evaluate the impact of ethanol vinasse on agricultural soil. Figure 8a, corresponding to the soil fertility model, shows a well-defined distribution of efficient solutions reflecting the optimal K, P, and N combinations. These results indicate that these three parameters are favored by incorporating vinasse. K increases the availability of sucrose, and according to the algorithm, the optimal value of K for sugarcane soil is 150–230 mg/kg. As for P, which is essential for root development and early productivity, the ideal range is between 25 and 35 mg/kg. N, a key component of proteins, sugar production, and photosynthesis, is optimal in the 17 to 19 mg/kg range. These configurations reflect how vinasse can improve nutrient availability without compromising the soil’s chemical balance, generating ideal conditions for crop development.

Figure 8b represents the Pareto Front associated with the soil quality model, considering the MC, OM, and pH. The optimal range of MC is 90% to 95%, in this range functional organisms predominate that due to microbial activity fortify the physical, chemical and biological properties of the soil. The results show that vinasse enriches the soil by transferring OM, which is incorporated into the porosity of the soil and improves the quality of the soil so that it is more fertile and healthy. This set of organic compounds improves the structure of the soil, increases its water retention capacity, and provides essential nutrients, with the optimal values being between 3.5% and 4%. According to the algorithm, the optimal soil pH for sugarcane cultivation should be around 6.5 UpH, allowing maximum nutrient availability. The soil tolerates a range of acidity and alkalinity between 6.5 and 7.5 UpH.

Figure 8c shows the Pareto Front corresponding to the health model based on biological variables such as equity, abundance, and diversity. In this study, it was identified that the optimal range for equity is 78% to 80%, where there is representation of different functional groups and ecological stability. Healthy soil must contain a proportion of beneficial microorganisms between 75% and 80%, which has an active microbial network and is helpful for mineralization, but it is not ideal for the development of sugarcane. Finally, considering that only healthy groups should have a large diversity of groups between 90 and 95%, this guarantees the appropriate synergy between the microbiota and the roots.

The approach used in this study based on the MOGAs is to demonstrate from a mathematical approach that there is a relationship between the study variables, and when treated with vinasse, it improves soil fertility, health, and quality. Thus, in the Pareto Fronts it is observed that the three functions that are used to characterize the space of optimal solutions show that their interrelation is a function of the incorporation of vinasse, influencing the improvement of fertility, quality, and health of sugarcane cultivation soil.

3.6. Phase VI: Dosage

From the previous phase, it was derived that the properties of the soil are improved with the incorporation of vinasse. Properly treated and dosed vinasse can regenerate soil fertility, quality, and health, in addition to being an input with the potential to enhance sugarcane crop yield. The analysis identified that sugarcane ethanol vinasse treated and supplied in a friendly way—this being one that is applied without negatively affecting the environment, in the appropriate dose―, has the potential to improve soil fertility, quality, and health; which translates into a better yield of sugarcane cultivation. This situation is associated with the fact that the treated vinasse, (a) due to its chemical composition promotes soil fertility, and that (b) due to its properties promotes soil health from microbial activity, so the combination (c) helps improve soil quality.

In this study, it was identified, through the DOEs and the evaluation of the behavior of the parameters in MOGAs, that the optimal dose of vinasse improves soil fertility, quality and health, i.e., vinasse treated and properly reincorporated into the crop soil enhances the physical, chemical and biological properties of the sugarcane soil, which, in turn, improves crop yield in tons per hectare; however, it is necessary to consider that this also depends on other factors, e.g., the variety of the type of sugarcane, the kind of soil, and climatological conditions. Therefore, the optimal ratio for the treatment of vinasse is a mixture formed by 40% vinasse and 60% irrigation water, i.e., a ratio of 1 to 1.5. So, the dose necessary to prepare the soil for the cultivation of sugarcane is 625 to 875 m³ per hectare, which is made up of a mixture of 40% vinasse and 60% water, i.e., 250 to 350 m³ of vinasse and 375 to 525 m³ of water per hectare, and that must be applied to the soil after the harvest of the crop is finished. It is recommended to apply the vinasse–irrigation water dose during the period of preparation of the soil, which lasts approximately one month, i.e., in the period between the harvesting of the sugarcane and before the planting of the cuttings—a piece of cane about 30 cm in length, with 3 to 6 buds, which is used to plant sugarcane―; this is because the dose is recommended as a biofertilizer to fortify the properties of the soil, while if it is applied directly during the development period of the crop, it has negative effects on the plant. This volume of vinasse is recommended according to its concentration, since a larger volume stresses the soil and a smaller volume does not strengthen it. So, the recommended dose in this study is a function of the components of the vinasse, the properties of the soil type and the ecosystem of the study area. Therefore, this dose is recommended because the water dilutes the components of the vinasse, thereby forming a biofertilizer with the ability to strengthen the soil, improving its physical, chemical and biological properties.

The validation of the findings of this study was carried out through the comparative analysis of two experimental fields of 1 ha each. In “Experimental Field 1”, sugarcane was grown in soil without vinasse treatment, while in “Experimental Field 2”, sugarcane was grown in soil with vinasse treatment at a rate of 40% vinasse and 60% irrigation water. The experimental fields were treated under the same care and production practices. Finally, the yield of sugarcane cultivation was compared, and it was identified that the yield of “Experimental Field 1” was 75 tons/ha, and the yield of “Experimental Field 2” was 93 tons/ha, which represents an increase of 24%.

Given the physical characteristics of the soil of the experimental field, which is of the leptosol type, this dose is recommended—40% vinasse and 60% irrigation water—to avoid salinity and soil erosion. Likewise, it is advisable to apply vinasse before planting the crop—i.e., vinasse should be applied to the soil and then the land should be prepared for planting—in dry seasons and before the beginning of the rainy season to avoid leaching of nutrients. This determination is based on the soil conditions of the crop under study and the components of the vinasse used in this study.

4. Discussion

By appropriate agricultural practices, treated vinasse incorporated into the farmland has the potential to regenerate soil conditions that have degenerated due to adverse factors. Specifically, in this study, it was shown that sugarcane ethanol vinasse improves the physical, chemical, and biological properties of the soil, i.e., it potentiates the fertility and health of the sugarcane soil, and thus, it can increase the yield of the agricultural crop. In this sense, it is agreed with Havlin and Heiniger (2020) [47] that adequate soil fertility management improves crop production. Soil fertility is supported by soil microbial activity through the aggregation and degradation of soil organic matter (SOM), and by the availability of nutrients, as mentioned by Alvarez et al. (2021) [48]. In addition, it is necessary to improve and maintain agricultural production through sustainable alternatives, as mentioned by Maharjan et al. (2020) [49].

It is a reality that multiple factors are affecting food availability; there is a socioeconomic imbalance between societies, which is reflected in the unequal distribution of food. In this situation, challenges are to be addressed, as farmland insecurity will be intensified by the conflict between food production and environmental sustainability, as mentioned by Kuang et al. (2022) [50]. Faced with this reality, it is agreed with Montgomery (2021) [51] that the adoption of regenerative agricultural practices contributes to improving soil health, supported by conservation agriculture as a cultivation system, which focuses on sustainably using natural resources while protecting biodiversity and increasing resilience to climate change.

In addition, in this study, it was identified that specifically, the incorporation of ethanol vinasse in the cropland (i) strengthens the N; which, being a component of chlorophyll and amino acids, is essential in plant growth; (ii) it increases the availability of P, which being part of the adenosine triphosphate (ATP) molecule provides energy to metabolic processes, which is why it is considered an essential nutrient for crop growth; and finally, (iii) OM is crucial for agriculture, as it improves soil conditions and contributes to crop growth. OM acts as a soil improver by increasing the soil structure, aeration, and fertility, which in turn promotes plant development. In addition, OM aids in nutrient uptake, reduces erosion, and maintains soil health. As it is embedded in the granular texture of the soil as a fine fraction, it improves the retention of water resources and increases the availability of nutrients; in addition to this, the availability of OM in the soil favors the growth and development of microorganisms, such as bacteria, actinomycetes and fungi, which are beneficial for the soil; however, it can also be unfavorable in high concentrations, mainly because it generates nutrient losses and acidifies the soil. So, the vinasse treated and incorporated into sugarcane cultivation land can improve soil fertility, health and quality. N, P, and K improve soil fertility when applied in the right dose, time, and place; in addition, OM is the basis for improving the conditions for achieving a healthy soil, while providing adequate conditions for the function of macroorganisms to improve crop growth. This finding coincides with what was mentioned by Rossetto et al. (2022) [52], in which the use of vinasse promotes the increase in the availability of P in the subsoil, and that it can be used throughout the sugarcane cultivation cycle.

From this study it is identified that vinasse can be used as a valuable resource if it is managed properly, but for nutrients and other organic compounds to be released, it is necessary that there are adequate conditions of temperature, humidity and the availability of microbes. If the released compounds are not within reach of the plant for uptake and growth, emissions to surface and groundwater, as well as to the atmosphere, are possible. It is a reality that the application of raw untreated vinasse affects the soil and the environment.

In this sense, it was identified that microorganisms are beneficial for the cropland in the form of (a) phytostimulators, by regulating growth and incorporating vitamins into crops from the strengthening of germination, rooting and plant growth, as mentioned by Bano et al. (2022), Liu et al. (2025), Ríos-Ruiz et al. (2025) [53,54,55]; (b) improvers, microbial activity the improves soil structure and consequently physicochemical properties, through the formation of aggregates, as cited by Q. Chen et al. (2024), Marzouk et al. (2025), and G. Wang et al. (2022) [56,57,58]; (c) bioremediators, microorganisms that have the ability to eliminate, e.g., pesticides and herbicides, as mentioned by Ayilara and Babalola (2023), Galic et al. (2024), Rafeeq et al. (2023), and Vermelho et al. (2024) [59,60,61,62]; and finally, (d) biofertilizers, by providing nutrients that improve crop growth and development, while at the same time controlling phytopathogens, coinciding with Fadiji et al. (2024), Pirttilä et al. (2021), Prisa et al. (2023), and G. Zhao et al. (2024) [63,64,65,66]. Microorganisms are critical to crop fertility and yield. Beneficial and pathogenic microorganisms compete for the nutrients available in the soil, while microorganisms decompose organic matter, which releases essential nutrients for crop growth; some bacteria and fungi fix the N for sugarcane, which is beneficial for it. However, a balanced population of microorganisms ensures the health and growth of sugarcane, while an excess of pathogens is harmful, since they compete for resources; so, if pathogens predominate they can displace beneficial populations, i.e., a balanced population is crucial for soil and crop health.

Given these findings, identified and analyzed, we agree with Carpanez et al. (2022) [67] that the controlled composition of vinasse-based fertilizer prevents excessive doses of nutrients from being applied to the soil; in this sense, irrigation water serves as a mechanism to control the concentration of vinasse because it dilutes its components and allows that, when they are reincorporated into the soil, they do not have a negative impact due to a high concentration. It is agreed with Tiefenbacher et al. (2021) [68] that the proper management of cropland improves soil fertility from the storage and sequestration of organic carbon. The optimal dose identified and recommended in this study ranges between 40%–60% of vinasse-irrigation water. With this relationship, the pollutant load of vinasse is reduced, without its revalued components degrading due to a greater dissolution.

In Mexico, during the 2023–2024 harvest, net milling was 44,026,929 tons distributed over 743,119 ha, considering 49 mills included in the seven regions; 799,271 L of alcohol are considered to have been produced [69]. However, considering that [36] mentions that 12 to 18 L of vinasse are produced for each liter of alcohol, it is estimated that during the 2023–2024 harvest, between 9,591,252 and 14,386,878 L were produced, or its equivalent of between 9,591,252 and 14,386,878 m³ of vinasse. Therefore, using the dose recommended in this article would allow the substitution of irrigation water with vinasse, which would represent a saving of water resources of between 185,779,750 and 278,669,625 m³. Then, the vinasse as wastewater generated from the production of alcohol, through the appropriate management, can be reincorporated in its entirety into sugarcane crops as a soil fortifying biofertilizer. In addition, vinasse could be supplied on crops grown in soils similar to that of sugarcane, e.g., sugar beets, corn, soybeans, and wheat. This strategy is presented as a promising scheme in sustainable management of ethanol production.

In this study, it has been identified that vinasse treated and incorporated into cropland reasonably has the potential to strengthen the soil by improving fertility and health. Therefore, it is highly beneficial that the waste generated from the production processes is reincorporated into the same chain from which it originated, thus closing the cycle and having the least negative impact on the environment. Therefore, the reuse of ethanol vinasse from revalued sugarcane is viable for use on sugarcane cultivation land. In this way and under this scheme, this study represents a model of sustainable production of sugarcane and ethyl alcohol, enabling regenerative agriculture by reintegrating vinasse as an improver of the properties of the sugarcane cultivation land. It is important to highlight that, during the process of recycling and reusing the vinasse that is generated from the production of ethanol, it is necessary to strictly control the management of this effluent through phytosanitary agents and thus protect the health of the environment and crops, avoiding the spread of pests, diseases and weeds.

So, given this scheme, we agree with Sydney et al. (2021) [28] that in the food processing industry, the by-products of a process are not considered as waste, but as inputs in parallel processes. This situation contributes to the achievement of the CE through the proper management and reuse of revalued waste as improvers of parallel value chains, which translates into fewer negative impacts on the environment, greater re-circularity and socioeconomic benefits.

Finally, the CE model is a scheme that promotes the revaluation of waste to be reincorporated into the same generation chain or another value chain of interest. This revaluation and integration of waste contribute to the achievement of sustainability.

5. Conclusions

Sugarcane ethanol vinasse is a highly polluting effluent if disposed of into the environment indiscriminately. Given this, the impacts of vinasse have been extensively studied; however, its potential as a farmland improver is not entirely clear. That is why, in this study, the impact that sugarcane ethanol vinasse has as an improver of the fertility and health of sugarcane cultivation land was analyzed; for this, how vinasse improves the physical, chemical and biological properties of the cropland was evaluated through Multi-Objective Genetic Algorithms; this is interesting and highly pertinent, as it allows for mapping the behavior and interaction of factors within the space of feasible solutions.

Despite being a highly polluting effluent without proper management, vinasse benefits the farmland if appropriately treated. In this study, it was identified that a rate of 40% vinasse and 60% irrigation water is an adequate ratio that maximizes the revaluation of the components of ethanol vinasse to the cropland while minimizing its negative impact on the environment. These results confirm the potential of vinasse as a regenerative input within regenerative agriculture and Circular Economy schemes. Therefore, this study evaluated vinasse as an improver of soil properties. At the same time, it would be interesting at a later stage to determine how this fortified soil influences sucrose production in terms of Brix and Pol degrees.

In this study, it has been shown that the computational approach based on MOGAs and the characterization of vinasse and agronomic criteria represents an essential contribution to the sustainable management of agroindustrial waste. In addition, this methodological approach marks an integrative approach between Artificial Intelligence and Sustainable Agriculture, a relevant and interesting scheme for researchers in the environmental, agricultural, and process optimization areas. Finally, this study has presented how revalued waste can improve the performance of the generating value chain; therefore, from a Circular Economy model, it contributes to the achievement of sustainability.