Multi-objective optimization of germination process parameters of browntop millet (Brachiaria ramosa) grains for improved bioactive compound production using response surface methodology and genetic algorithm approaches

Abstract

Background

Browntop millet (Urochloa ramosa syn. Brachiaria ramosa) is a nutrient-rich minor millet known for its resilience to harsh environments and potential as a functional food ingredient. Germination is a bioprocess that can enhance its nutritional value by increasing bioactive compounds and reducing antinutritional factors. The present study investigated the effects of germination conditions on the accumulation of bioactive compounds and the reduction of phytic acid and tannins in browntop millet grains.

Results

A Box–Behnken design was employed with three independent variables—soaking time (8–16 h), germination temperature (25–45 °C), and germination time (24–72 h). Response surface methodology (RSM) and a genetic algorithm (GA) were applied to model and optimize responses, including total phenolic content, total flavonoid content, antioxidant activity, ascorbic acid, γ-aminobutyric acid (GABA), and antinutritional factors. Statistical analysis indicated that the RSM empirical model predicted experimental results with high accuracy. Optimization based on the desirability function identified 12 h soaking, 33 °C germination temperature, and 48 h germination time as optimal conditions. Under these conditions, the maximum levels obtained were: total phenolic content 16.30 mg GAE/100 g, total flavonoid content 2.63 mg QUE/100 g, antioxidant activity 81.33%, ascorbic acid 4.00 mg/100 g, GABA 16.38 mg/100 g, phytic acid 0.32 mol/kg, and tannins 0.19 mg/100 g.

Conclusions

Germination under optimized conditions significantly enhanced the nutritional and functional quality of browntop millet by increasing antioxidant and bioactive components while reducing antinutritional factors. The Box–Behnken design combined with RSM provided more accurate and efficient optimization compared to the genetic algorithm, demonstrating its suitability for modelling germination-based biofortification in functional grains.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12870-025-08067-4.

Introduction

Germination occurs when dormant grains absorb water and, under suitable conditions, activate their metabolism, leading to growth and development. This process involves both biochemical reactions and physical changes within the grain. During germination, seeds reactivate their metabolism, enabling the initial root and shoot to emerge [1, 2]. It is a complex and efficient method for enhancing the nutritional and functional properties of grains and legumes. Germination also reduces levels of anti-nutritional compounds like phytic acid, tannins, and trypsin inhibitors, as these substances are partially washed-out during soaking [3]. It can induce significant changes in whole grains, affecting their phenolic content, antioxidant properties, levels of unsaturated fatty acids, and γ-aminobutyric acid (GABA). This process may improve the nutritional and health-promoting qualities of the grains [4–6]. During germination, many dormant enzymes within dry seeds are activated, breaking down complex storage compounds such as starch, proteins, and fats into simpler, more digestible forms. This enhances nutrient availability for both the developing plant and human consumption [7–10]. The process results in the formation of new cells, altering the seed’s biochemical composition, physical structure, viscosity, and nutritional and functional traits [11]. Germination causes notable phytochemical and physical transformations in various grains, influenced by grain type and germination conditions. These changes reflect variations in nutrient levels, involving processes like nutrient redistribution, degradation of certain substances, and accumulation of others [12, 13]. It occurs in different phases: first, dry seeds rapidly absorb water until fully hydrated, activating hydrolytic enzymes that release stored compounds, nutrients, and bioactive substances [14]. Second, water intake becomes more controlled, with a significant increase in metabolic activity. In the third phase, water absorption intensifies, leading to cell elongation and signalling the end of germination [15, 16]. When dry seeds absorb water, they quickly become metabolically active, initiating processes like breakdown, storage, and nutrient redistribution. These changes enhance the nutritional content, biochemical qualities, and sensory appeal of seed-based foods [17, 18]. Germination markedly increases amylase activity in millet, breaking down large starch molecules into smaller ones and changing the grain’s structure. This softens the grains, making processing easier and improving taste, flavor, and digestibility [19]. Germinated grains are generally easier to digest and safer to eat than non-germinated grains, making them preferable for consumption [20–22].

Browntop millet, scientifically known as Brachiaria ramose and commonly called Dixie signal grass, is an ancient minor millet from the grass family Poaceae. Browntop millet is gluten-free and rich in protein, fibre, vitamins, and minerals, but it also contains antinutritional factors, like all other millets. It is often recommended for individuals with diabetes because of its low glycemic index, which helps regulate blood sugar. Incorporating it into a regular diet can reduce the risk of diabetes, improve kidney and liver function, and prevent gastric ulcers [23]. Germination results in breakdown of storage macromolecules, reduction of antinutritional factors, and accumulation of health-promoting bioactive compounds such as phenolics, flavonoids, ascorbic acid, and γ-aminobutyric acid (GABA). These compounds contribute to the antioxidant and therapeutic potential of sprouts, making them valuable functional foods. The accumulation and synthesis of bioactive compounds and the reduction of antinutritional factors are highly dependent on germination conditions such as soaking time, germination temperature, and germination time, which interact with each other in a complex and nonlinear manner. Therefore, optimizing these parameters is crucial to achieving the maximum nutritional benefits of sprouts.

Response surface methodology has been extensively employed in food and bioprocess optimization. The goal is to formulate a mathematical model to estimate a response and reduce the number of experiments conducted. A statistical technique called analysis of variance will be used to identify the factors that have a significant impact on the response [24, 25]. The quadratic equation developed using RSM may not fully capture the complex and nonlinear behaviour of biological processes such as germination.

They are well-positioned for problems that are difficult for traditional optimization techniques, which are commonly used when an optimization problem exhibits discontinuity, non-differentiability, or dimensionality in problems [26, 27]. In a standard genetic algorithm (GA), a population of potential solutions evolves over several generations. Each solution, typically expressed as a chromosome, is assigned a fitness value, which measures the quality of the solution according to a fitness function. The GA implements genetic operators, selection, crossover, and mutation to explore the search space and exploit the best parts (Fig. 1). Eventually, the population converges towards the optimum or near-optimum solutions.

Fig. 1.

Process flowchart of Genetic Algorithm

In the present study, an integrated RSM–GA approach was employed to optimize germination conditions for maximizing the accumulation of bioactive compounds such as total phenolic content (TPC), total flavonoid content (TFC), antioxidant activity, ascorbic acid, and GABA, while minimizing phytic acid and tannins in browntop millet sprouts. Initially, RSM was used to establish a second-order quadratic model representing the relationships between process parameters (soaking time, germination temperature, and germination time) and the responses. The RSM-predicted model was subsequently optimized using GA to identify global optima beyond the limitations of the quadratic model. This dual optimization framework aims to enhance the understanding of process–response interactions and establish a predictive strategy for maximizing the functional and nutritional quality of germinated browntop millet sprouts.

Materials and methods

Chemicals and reagents

For the experimental study work, all required chemicals are procured from Loba Chemie (Mumbai, India) and Sigma-Aldrich (Steinheim, Germany) Company. The chemicals and reagents, which are used during the research study work include gallic acid (GAE), sodium carbonate, methanol, Folin-Ciocalteu reagent, 2,2- diphenyl-1-picrylhydrazyl (DPPH), quercetin (QUE), sodium nitrite, aluminium chloride, sodium hydroxide, sodium hypochlorite, hydrochloric acid, potassium thiocyanate, ferric chloride, γ-aminobutyric acid, meta-phosphoric acid, L-ascorbic acid, 2,6-dichlorophenolindophenol, boric acid, phenol reagent, Folin Denis reagent, and tannic acid.

Raw material

Seeds of browntop millet germplasm BRO-08 were obtained from the Indian Institute of Millet Research, Hyderabad, and cultivated in the agricultural farms of Lovely Professional University, Phagwara, Punjab, India, in the period of May-October 2024, (supplementary file). The seeds after harvesting were cleaned to eliminate foreign materials like stones, dirt, and damaged seeds. The cleaned seeds were then stored in a dry place for further experiments.

Soaking and germination

20 g of browntop millet grains were washed thoroughly, followed by soaking and germination under different conditions, viz., soaking time (8–16 h), germination temperature (25 –45 °C), and germination time (24–72 h) as given by experimental design. The seed-to-water ratio was fixed at 1:5 (w/w) for all batches. After soaking, water was removed, and seeds were surface dried with blotting paper and kept for germination in a germination chamber at a relative humidity of 70%. The tray was covered with a damp cloth and kept in a dark, humid environment, with water sprayed at regular intervals to maintain moisture. Once germination was complete, the samples were dried in a hot air oven at 40 °C until they reached equilibrium moisture content, then ground into flour. The germinated millet flour was stored at 4 °C for further analysis. All the experiments were conducted in triplicate according to Nguyen et al. [28], with slight modifications according to previous studies.

Determination of bioactive compounds and antioxidant activity

Preparation of extracts

The germinated sample was extracted with the method of Bennour et al. [29]. Powdered dried powder (5 g) was extracted by maceration with 100 mL of 70% methanol for 48 h at room temperature on an orbital shaker. The solution was filtered with Whatman No.1 filter paper, and the filtrate was evaporated to obtain a dry extract using a rotary evaporator under reduced pressure at 40 °C for 6 h.

Determination of total Phenol Content (TPC)

TPC was analysed using Folin-Ciocalteau method of Ukpong et al. [30]. The absorbance was taken at 760 nm. The values were reported as mg gallic acid equivalent (GAE) per gram of dry matter.

Total Flavonoid Content (TFC)

The aluminium chloride method given by Sharma & Sharma [31] was used to analyse TFC. The absorbance of the reaction solution was measured at 415 nm, and the results were represented as mg quercetin equivalent (QUE) per gram of dry matter.

Determination of antioxidant activity

The total antioxidant activity was evaluated using the procedure outlined by Hussain et al. [32], and the capacity of the sample extracts to scavenge the DPPH free radical was determined. In brief, 10 µl of ethanolic extracts were added with 2 ml of DPPH solution and then kept in the dark for incubation for 30 min, and the resulting solution was measured by using a spectrophotometer at 517 nm. The inhibition % was calculated using the following equation.

Ascorbic acid content

The ascorbic acid content was measured by the method explained by Upadhyay et al. [33] with slight modifications. A germinated browntop millet powdered sample (3 g) was extracted at room temperature using 1% meta-phosphoric acid. The obtained filtrate (5 ml) was combined with the 10 ml of dichlorophenol indophenol dye, and the absorbance was read immediately at 518 nm against a blank. The ascorbic acid content was estimated using the calibration curve of standard L-ascorbic acid, and results were presented in mg/g flour dry matter.

γ-amino Butyric acid (GABA)

GABA was extracted from germinated browntop millet flour samples, following the protocol used by Sharma et al. [34]. 3 g of germinated BTM flour sample was extracted with 30 mL of 70% ethanol for 25 min on orbital shaker. The supernatant layer was centrifuged for 15 min at 4000 rpm to extract GABA from the agitated mixture. The extraction was performed twice, and the supernatants were collected and evaporated at 40 °C under vacuum. A reagent solution blend was made by mixing 200 µl of 0.2 M borate buffer and 1000 µl of 6% phenol reagent, along with the concentrated extract in the test tube. 400 µl of 7.5% NaOCl was then added to the entire mixture and heated for ten minutes in a water bath. The sample was cooled, and the absorbance of the extracted sample was determined at 630 nm using a spectrophotometer, and the solvent was taken as a blank. The standard curve of GABA was generated at various concentrations in the range of 10–50 µg/mL.

Phytic acid

Phytic acid was quantitatively determined according to the method followed by Dey et al. [35]. 2 g of the grounded sample was soaked in 100 mL of 2% HCl for 3 h and then filtered through Whatman No. 1 filter paper. 25 mL of the filtrate was placed in a 100-mL conical flask, and an indicator consisting of 5 mL of 0.3% ammonium thiocyanate solution was added. Distilled water (53.5 mL) was added to the mixture after setting it to proper acidity; this was titrated with a standard iron (III) chloride solution, having about 0.00195 g of iron per milliliter, till a brownish-yellow color appeared, which remained for 5 min.

where: T = titre value; M = Molar mass of phytate.

Tannins

The tannin content was estimated as per the method of Srivastava et al. [36]. This method is commonly employed to determine the tannin content in samples and is based on the color change observed in the presence of tannins, which is then quantified spectrophotometrically. 10 g of the sample was boiled along with 75 mL of water for 30 min. The sample was then centrifuged at 2000 rpm for 20 min, and the supernatant was collected separately. Folin Denis reagent (5 mL) from Sigma-Aldrich and sodium carbonate (10 mL) were added to the sample extract. The resulting solution was diluted to a total volume of 100 ml using distilled water. After allowing the solution to incubate for 30 min, its absorbance was measured at a wavelength of 700 nm. A set of standard solutions of tannic acid (20, 40, 60, 80, and 100 µg/mL) was prepared for constructing the calibration curve. The total tannin content was expressed in terms of mg of tannic acid/g of extract.

Experimental design by response surface methodology

The germination of browntop millet was carried out using various combinations, and experimental work was carried out using the Design Expert (version 16), a statistical software package. The Box Behnken model was used [37, 38], which dictated 17 experimental runs. The independent variables, such as soaking time (A), germination temperature (B), and germination time (C), including seven responses, total phenolic content, total flavonoid content, antioxidant activity, phytic acid, tannins, ascorbic acid, and γ-aminobutyric acid, in germinated seeds. Analysis of variance (ANOVA) and second-order polynomial coefficients were obtained after model fitting. A second-order polynomial empirical model was built based on experimental data.

Optimization approach using genetic algorithm

In this study, a Genetic Algorithm (GA) was applied to identify the optimal combination of germination conditions, specifically soaking time, germination temperature, and germination duration, that enhances beneficial nutritional attributes while suppressing anti-nutritional compounds in the germinated sample. The Algorithm was developed and executed in the Python programming environment, making use of the DEAP (Distributed Evolutionary Algorithms in Python) framework, which is well-suited for building evolutionary models. All computational tasks and code executions were performed on the Google Colab platform, enabling efficient implementation and testing in a cloud-based environment.

Chromosome structure

The optimization focused on three independent variables such as soaking time (h) for 8 to 16 h, germination temperature (°C) varied between 25 °C and 45 °C and germination time (h) was set within the interval of 24 h to 72 h. Each individual (chromosome) was encoded as a vector of three integer values, with each gene representing one of the process variables.

Objective functions

The performance of each candidate solution was assessed using multiple objectives. The desirable targets included maximizing the concentrations of Total Phenolic Content (TPC), Total Flavonoid Content (TFC), Antioxidant Activity, Ascorbic Acid, and Gamma-Aminobutyric Acid (GABA). Additionally, the algorithm was designed to minimize the Phytic Acid and Tannin.

These objectives reflect the dual aim of enhancing functional properties while reducing anti-nutritional factors.

Fitness evaluation

To evaluate the quality of each solution, a nearest-neighbor approach was employed. For each individual in the population, the Euclidean distance between its decision variables and all experimental data points was calculated.

The fitness vector for each individual was defined as follows:

Here, the negative signs for phytic acid and tannin indicate that lower values are preferred for these attributes.

Genetic algorithm configuration

In this study, an evolutionary optimization framework was implemented using a population size of 50 individuals evolved over 50 generations. The optimization employed the NSGA-II (Non-dominated Sorting Genetic Algorithm II) as the selection method to efficiently handle multi-objective decision-making. Genetic variation among solutions was introduced using a two-point crossover operator with a crossover probability of 0.5. Mutation was performed using a uniform integer mutation operator, applied with a mutation probability of 0.2, corresponding to a 20% chance of mutation per gene. These parameter settings ensured an appropriate balance between exploration and exploitation throughout the optimization process.

Performance of developed models

The performance of models obtained from RSM and GA tools was analyzed by comparing the statistical parameters. The statistical parameters, viz., coefficient of determination (R²) and root mean square error (RMSE), were determined by regression analysis in data analysis from Excel 2019. The higher the value of R² and the lower the value of RMSE, the better fit of the model.

Similarly, absolute error (MAE) and absolute average deviation (AAD) were calculated.

Optimization and model validation

Different approaches were used to optimize germination conditions for a developed RSM model, viz., with a desirability function and with a genetic algorithm. Design-Expert 16.0 software was used to obtain the best combination of independent variables with responses with the help of numerical optimization of process variables. The desired goal was set to maximize the values of TPC, TFC, Antioxidant activity, ascorbic acid, and GABA, and minimize antinutritional factors, phytic acid, and tannins for optimization. The desirability function (D(x)) was computed using software. The value of the desirability function ranges from zero to one. The program of the software seeks to find the values of variables, which can result in the maximum value of the desirability function.

For GA, the second-order polynomial model equations generated from RSM were employed in GA for multi-objective optimization. The objective was set to maximize TPC, TFC, Antioxidant activity, ascorbic acid, and GABA, and minimize antinutritional factors, phytic acid, and tannins for optimization. The error percentage was estimated to explain the fit of the model.

Results

Optimization of germination variables for bioactive compounds and antinutrients

All experiments were conducted according to the experimental design (Table 1) to determine the optimal germination conditions for enhanced production of bioactive compounds. The effect of all three independent variables, viz., soaking time, germination temperature and germination time, was observed on the responses, such as total phenolic content, total flavonoid content, antioxidant activity, tannin content, phytic acid content, ascorbic acid content, and γ-aminobutyric acid content, as shown in Table 1. The estimated coefficients and F-statistics for all variables and responses are provided in Table 2. The predicted results were obtained by a model-fitting technique in Design Expert software version 16.0, and the values were compared with experimental values. The observed values are shown in Table 1. Fitting data to various models has generated regression equations. Besides RSM, a genetic algorithm (GA) technique was also used to enhance optimization by exploring trade-offs between different responses. Unlike RSM, which produces a single optimum solution based on desirability, GA generates a series of Pareto-optimal solutions that balance nutritional increase with a decrease of antinutritional variables.

Table 1.

Effect of independent variables on dependent variables after germination, experimental and predicted values:

Process Variables			Experimental values							Predicted values
A	B	C	TPC (mg GAE/100 g)	TFC (mg QUE/100 g)	Antioxidant activity (%)	Ascorbic acid (mg/100 g)	GABA (mg/100 g)	Phytic acid (mol/kg)	Tannin (mg tannic acid/100 g)	TPC (mg GAE/100 g)	TFC (mg QUE/100 g)	Antioxidant activity (%)	Ascorbic acid (mg/100 g)	GABA (mg/100 g)	Phytic acid (mol/kg)	Tannin (mg tannic acid/100 g)
12	35	48	15.57	2.72	84.35	3.90	16.95	0.31	0.19	16.22	2.66	80.13	4.06	16.04	0.33	0.20
16	35	24	10.29	1.24	62.25	2.96	8.13	0.25	0.18	10.19	1.23	60.57	2.89	8.30	0.25	0.18
8	45	48	8.44	1.96	38.89	2.08	7.48	0.19	0.15	8.55	1.89	39.08	2.20	8.19	0.21	0.15
16	45	48	7.67	1.59	44.14	2.71	7.04	0.15	0.13	7.61	1.52	43.72	2.84	7.55	0.17	0.14
8	35	72	10.20	1.71	42.62	2.05	8.47	0.23	0.17	10.31	1.73	44.30	2.12	8.30	0.26	0.17
12	45	24	11.19	1.17	54.39	3.87	8.62	0.26	0.18	11.36	1.26	56.49	3.81	7.93	0.26	0.18
12	35	48	16.27	2.77	81.96	4.25	15.80	0.31	0.19	16.22	2.66	80.13	4.06	16.04	0.33	0.20
16	35	72	11.15	2.53	61.94	2.45	8.51	0.25	0.18	11.43	2.54	64.23	2.51	8.53	0.28	0.18
12	25	24	12.38	1.59	78.06	2.25	12.21	0.27	0.19	12.59	1.54	79.93	2.44	12.75	0.28	0.19
12	35	48	16.72	2.58	81.00	3.95	16.13	0.33	0.20	16.22	2.66	80.13	4.06	16.04	0.33	0.20
12	35	48	16.11	2.69	80.64	4.05	15.78	0.31	0.20	16.22	2.66	80.13	4.06	16.04	0.33	0.20
12	25	72	14.19	2.20	62.99	3.31	9.69	0.27	0.19	14.02	2.12	60.89	3.37	10.38	0.30	0.19
8	35	24	10.06	2.31	75.45	1.53	13.90	0.25	0.18	9.77	2.29	73.16	1.47	13.88	0.25	0.18
8	25	48	8.54	2.07	56.64	1.48	15.88	0.19	0.15	8.61	2.14	57.06	1.35	15.36	0.19	0.15
16	25	48	11.19	2.19	59.94	0.25	0.17	2.65	11.35	11.08	2.26	59.75	2.53	10.64	0.25	0.17
12	35	48	16.41	2.53	72.73	0.32	0.19	4.15	15.57	16.22	2.66	80.13	4.06	16.04	0.33	0.20
12	45	72	11.93	1.37	52.21	0.24	0.17	3.35	5.50	11.71	1.42	50.34	3.16	4.95	0.26	0.17

A soaking temperature (h), B, Germination temperature (°C), C Germination time (h)

Table 2.

Analysis of variance and regression analysis of Box-Behnken design for bioactive compounds and antinutritional factors after germination of Browntop millet

Estimated coefficients										F values
Variables	DF	TPC	TFC	Antioxidant activity	Phytic acid	Tannins	Ascorbic acid	GABA	TPC		TFC	Antioxidant activity	Phytic acid	Tannins	Ascorbic acid	GABA
Model	9	16.22	2.66	80.13	0.316	0.193	4.06	16.05	105.38*		45.04*	24.09*	39.33*	14.11*	44.08*	42.94*
A	1	0.38	-0.06	1.84	0.005	0.001	0.45	-1.34	7.50**		2.81	1.72	1.82	0.37	47.60*	23.19*
B	1	-0.88	-0.25	-8.50	-0.018	-0.008	0.29	-2.56	40.16*		42.56*	36.98*	22.27*	10.98**	19.44*	85.02*
C	1	0.44	0.19	-6.30	-0.005	-0.002	0.07	-1.34	10.14**		24.95*	20.30*	1.82	0.51	1.09	23.13*
AB	1	-0.85	-0.12	0.49	-0.025	-0.010	-0.14	1.02	18.70*		5.28***	0.06	22.73*	9.76**	2.11	6.75**
AC	1	0.18	0.47	8.13	0.005	0.002	-0.26	1.45	0.80		78.77*	16.91*	0.91	0.50	7.66**	13.68*
BC	1	-0.27	-0.10	3.22	-0.005	-0.003	-0.40	-0.15	1.84		3.86***	2.66	0.91	0.61	18.04*	0.15
A²	1	-4.62	-0.17	-15.79	-0.068	-0.024	-1.39	-2.43	578.46*		10.81**	67.14*	177.00*	58.23*	234.67*	40.32*
B²	1	-2.63	-0.53	-14.44	-0.053	-0.020	-0.44	-3.18	187.04*		106.41*	56.18*	107.52*	39.25*	23.69*	68.88*
C²	1	-1.17	-0.54	-3.78	-0.003	0.006	-0.42	-3.86	36.76*		108.93*	3.85***	0.34	3.95***	21.85*	101.67*
Lack of Fit	3	NS	NS	NS	NS	NS	NS	NS	0.68		1.22	0.56	1.88	0.44	2.61	3.54
C.V. %		3.22	5.3	6.17	4.07	3.64	6.20	6.78
R2		0.99	0.98	0.97	0.98	0.95	0.98	0.98
Adj. R2		0.98	0.96	0.93	0.96	0.88	0.96	0.96
Pred. R2		0.95	0.86	0.82	0.81	0.73	0.81	0.79

A Soaking Time, B Germination Temperature, C Germination Time

* Significant at p ≤ 0.01

** Significant at p ≤ 0.05

*** Significant at p ≤ 0.1

Second-order polynomial equations and statistical analysis

Based on the Box-Behnken experimental design, the empirical relationship between the independent variables and the investigational results obtained was indicated by a second-order polynomial equation with linear, interaction, and quadratic terms. The equations generated by the software in coded factors are presented below.

Regression analysis and analysis of variance (ANOVA) were used to test the capability and fitness of the models, and F-test was conducted to evaluate the significance of each independent variable. The analysis of variance results in Table 2 show F-values for TPC, TFC, antioxidant activity, phytic acid, tannins, ascorbic acid, and GABA as 105.38, 45.04, 24.09, 39.33, 14.11, 44.08, and 42.94, respectively, suggesting that the model is significant at p < 0.01.

Coefficient of determination (R²) and adjusted-R² were calculated to verify the adequacy and fitness of the model. The values of R² were found to be in the range of 0.95 and 0.99 for all the responses, which means that 95–99% of the experimental data was well fitted. The high value of adjusted-R² supports a high association between the experimental and anticipated values (Table 2).

Effect of independent variables on TPC

TPC of the germinated browntop millet grains was analyzed as per the experimental design and was found to be in the range of 7.67 to 16.72 mg GAE/100 g. Three-dimensional response plots were used to describe the effect of the independent variables on the total phenolic content. These plots demonstrated the significance of two variables at a time on the response while the third variable was maintained as constant. The final empirical equation obtained for total phenols is given below:

The non-significant lack of fit suggests that the model aligns well with the data. The independent variables for total phenolic content were quadratic with a good regression coefficient accounted for 0.99 of total variation in TPC. The experimental data were analyzed by multiple regression analysis and coefficients of model were used for the significance levels. The linear, interaction and quadratic effects of each independent variables are shown in Table 2. It is evident that two linear (A, C) were significant at the level of (p ≤ 0.05), whereas one linear (B), interaction (AB) and quadratic variables (A², B², C²) were significant at (p ≤ 0.01). Soaking time showed a positive (p < 0.05) linear effect on total phenolic content. As shown in the Fig. 2 (a), the phenolic content initially increases and then decreases, reaching a maximum of 16.72 mg GAE/100 g after soaking for 12 h. Similar patterns of increase and decrease have been reported for foxtail sprouts [39] and finger millet [40]. The enzyme responsible for extracting and releasing phenolics gets activated at the start of soaking, raising the TPC values. Additionally, soaking helps loosen the seed structure and release bound phenolics. As a result, polyphenol content rises early in soaking. However, as soaking continues, free phenolics leach out, leading to a decrease in total phenolic content [34]. Germination temperature initially increased, then a decrease in TPC content occurs, as shown in Fig. 2 (a).

Fig. 2.

The 3D graph depicting the effect of soaking time, germination temperature and germination time on the (a) total phenolic content and (b) flavonoid content of sprouts

Effect of independent variables on TFC

TFC levels ranged from 1.17 to 2.77 mg QUE/100 g, with the maximum value achieved after 12 h of soaking, germination at 35 °C for 48 h, and the lowest value acquired after 12 h of soaking at 45 °C for 24 h. A shorter germination time (24 h) results in reduced TFC content, whereas a longer duration (more than 48 h) results in lower flavonoid content. At temperatures above 40 °C, the TFC decreases, regardless of the duration of germination, indicating that flavonoids are sensitive to heat (Fig. 2b). In contrast, germination at moderate temperatures improves TFC over time. Flavonoid production is generally stimulated during germination as part of the plant’s natural defence process [41]. The findings show that favorable germination conditions promote flavonoid accumulation. The linear, interactive, and quadratic effects of independent variables on TFC are given in Table 2 along with coefficients and significance level. The empirical equation obtained for total flavonoids is given below:

Effect of independent variables on antioxidant activity

Antioxidant activity ranged from 38.89% to 84.35%. The non-significant lack of fit suggests that the model is a good fit for the data. Regression equation (R²) accounted for 0.95 of total variation in antioxidant activity. The highest activity was observed with 12 h of soaking, a germination temperature of 35 °C, and 48 h of germination. The study by Kainama et al. [42] reveals that higher antioxidant activity is linked to increased levels of phenolic compounds and flavonoids, which effectively neutralize free radicals. The outer layers of millet grains, particularly the pericarp and aleurone, are where the phenolic and flavonoid antioxidants are concentrated. As germination progresses and the cell wall softens, these substances are easily released or made available (Gowda et al. [43]. Sprouting is an effective way to enhance the antioxidant properties of grains. The best conditions for maximizing this activity are at moderate temperatures, between 25 °C and 35 °C, with extended germination periods up to 48 h. The combination of temperature and time helps increase antioxidant content, making germination beneficial for improving seed health and nutritional value (Fig. 3a). Longer germination periods boost antioxidant activity only when the temperature remains low to moderate. At higher temperatures, longer germination does not significantly impact antioxidant levels because most antioxidants are already degraded. As shown in Table 2, the total antioxidant capacity of germination was significantly affected by two linear variables (B, C), an interaction term (AC), and quadratic variables (A², B²) at (p ≤ 0.01), and one quadratic variable (C²) was significant at (p ≤ 0.1). The empirical equation for antioxidant activity is provided below:

Fig. 3.

The 3D graph depicting the effect of soaking time, germination temperature and germination time on the (a) antioxidant activity (b) ascorbic acid content of sprouts

Effect of independent variables on ascorbic acid

The ascorbic acid ranged from 1.48 to 4.25 mg/100 g. The independent variables for ascorbic acid content were quadratic with a good regression coefficient (R² = 0.98) and lack of fit was found not significant. The significant differences in linear, interaction, and quadratic variables are shown in Table 2. Two linear variables (A, B), one interaction (BC), and all quadratic variables (A², B², C²) were highly significant (p ≤ 0.01), while the interaction (AC) was significant at (p ≤ 0.05). The highest ascorbic acid content was obtained with a moderate range of time and temperature (12 h soaking at 35 °C for 48 h), and a moderate range during 16 h of soaking for 48 h at 25 °C to 35 °C. The lowest content was observed with 8 h of soaking for 24 to 48 h at 25 °C to 35 °C (Fig. 3b). Temperatures above 40 °C may cause degradation. The final predictive equation for ascorbic acid is provided below.

Effect of independent variables on γ-aminobutyric acid (GABA)

The γ-aminobutyric acid was found in the range of 5.50 to 16.95 mg/100 g. The R² value was found 0.98, this means that the model is highly reliable in predicting the outcome. The significant difference was observed in linear, interaction, and quadratic variables, that is, all linear (A, B, C), one interaction (AC) and all the quadratic variables (A², B², C²) at the level of (p ≤ 0.01), and interaction (AB) have shown the significant at (p ≤ 0.05). GABA is synthesized during germination as a stress response to changes in temperature and oxygen levels. The results indicate that moderate soaking and germination conditions are optimal for GABA production, which is linked to improved seed nutritional quality (Fig. 4).

Fig. 4.

The 3D graph depicting the effect of soaking time, germination temperature and germination time on GABA content of sprouts

Effect of independent variables on antinutritional compounds (phytic acid and tannins)

The phytic acid and tannins content range from 0.15 to 0.33 mol/kg and 0.13 to 0.20 mg tannic acid/100 g, respectively. It was found that high germination temperatures above 35 °C showed a clear reduction in both phytic acid and tannins. Germination time alone contributed marginally, but when combined with higher temperatures, it significantly increased the antinutritional reduction, e.g., the greatest reduction was phytic acid (Fig. 5a), and tannins (Fig. 5b) were at 48 h and 45 °C or greater. The reduction in phytic acid is good for increasing the nutritional values of the seeds. The slight reduction measured is just what would be expected from partial degradation of tannins during seed sprouting. The final empirical equation for phytic acid and tannins are given below:

Fig. 5.

The 3D graph depicting the effect of soaking time, germination temperature and germination time on the (a) phytic acid and (b) tannin content reduction of sprouts

Germination usually changes the physical structure, nutritional value, and biochemical activity of foods. The negative linear and quadratic coefficients of temperature (B and B²) in all models demonstrate that the phytic acid and tannin break more quickly at higher germination temperatures, and the coefficients of interaction demonstrate that temperature increases the soaking time. It does alter the amounts of various strong anti-nutrients, including tannin and phytic acid, which directly enhance mineral bioavailability in the body and thus improve the nutritional value of food products [44, 45]. Germination time had a lesser effective impact than temperature exhibited on the amount of this antinutritional compound, its concentration decreased over time as germination duration increased, particularly at elevated temperatures (Fig. 5b), the same trend was also noted in other studies for instance, 65.80 ± 0.44 to 32.17 ± 0.56 mg/100 g in finger millet [10] and for cowpea 308.83 ± 5.21 to 19.07 ± 3.06 mg per 100 g dry matter [46].

Genetic algorithm

At the end of the optimization, the final population was analysed to extract non-dominated solutions that offered optimal trade-offs between nutritional enhancement and anti-nutritional reduction.

The genetic algorithm (GA) effectively identified optimal combinations of germination parameters that enhance nutritional quality while minimizing anti-nutritional factors. After 50 generations of evolutionary search using a population of 50 individuals, the algorithm converged towards a set of non-dominated solutions, reflecting optimal trade-offs among competing objectives.

Among the Pareto-optimal solutions, one particular combination stood out in terms of both nutritional enhancement and reduction of undesired components. The optimal set of germination conditions was as follows in Table 3:

Table 3.

Optimized values given by the genetic algorithm:

Independent Variables	Optimized Value
Soaking Time	12 h
Germination Temperature	33.38 °C
Germination Duration	51 h
Response Variables	Optimized Value
Total Phenolic Content (TPC)	16.62 mg GAE/100 g
Total Flavonoid Content (TFC)	2.66 mg QUE/100 g
Antioxidant Activity	80.08%
Ascorbic Acid	4.06 mg/100 g
GABA (γ-Aminobutyric Acid)	16.03 mg/100 g
Phytic Acid	0.32 mol/kg
Tannin	0.19 mg/100 g

These results indicate that the selected germination parameters favor the biosynthesis and accumulation of health-promoting compounds, such as phenolics and GABA, which are known for their antioxidant, anti-inflammatory, and neuroprotective properties. The increase in ascorbic acid content further contributes to the antioxidant capacity of the germinated product, supporting its potential as a functional food ingredient [47].

Interpretation of trade-offs

An important aspect of this study was the simultaneous optimization of multiple, sometimes conflicting, objectives. For instance, while longer germination times generally promote the accumulation of certain phytochemicals, they can also lead to increased levels of anti-nutritional factors if not adequately controlled. The GA effectively navigated these trade-offs, as demonstrated by the reduction in phytic acid and tannin content in the optimized solution.

The observed decrease in phytic acid is particularly noteworthy, given that this compound can impair mineral absorption by forming insoluble complexes with dietary minerals [48]. Likewise, the lower tannin levels contribute to improved protein digestibility and palatability. Thus, the optimization process not only enhanced the functional value of the germinated product but also improved its overall nutritional bioavailability.

The predicted and observed values indicated that both RSM and GA were successfully able to represent the response patterns for the different germination conditions in Table 4. RSM shows a closer agreement with the experimental results, suggesting RSM is more accurate for prediction. The observed values also follow the overall trends with the GA modelling, but with less accuracy relative to the RSM predictions. RSM is the more suitable option for accurate predictions, but GA is still proven to be useful for assessing optimization.

Table 4.

Predicted and observed values under optimized germination conditions of Browntop sprouts

Responses	RSM			GA
	Predicted Values	Experimental Values	Error%	Predicted Values	Experimental Values	Error%
TPC, mg GAE/100 g	16.30	15.90	2.45	16.10	15.19	5.65
TFC, mg QUE/100 g	2.68	2.63	1.87	2.58	2.20	14.7
Antioxidant activity, %	81.33	81.26	0.09	80.00	78.06	2.42
Ascorbic acid, mg/100 g	4.0	3.90	2.5	3.95	3.51	11.14
GABA, mg/100 g	16.38	16.00	2.32	15.78	14.60	7.48
Phytic acid, mol/kg	0.32	0.31	3.12	0.31	0.27	12.9
Tannins, mg/100 g	0.19	0.18	5.23	0.19	0.18	5.26

Comparison of statistical parameters of developed RSM and GA models

The performance of both models was compared based on statistical parameters presented in Table 5. For a better model fit, R² should be maximum, while the RMSE, MAE, and AAD should be minimum. From Table 5, it can be observed that the R² value of the RSM model for TPC, TFC, antioxidant activity, ascorbic acid, GABA, phytic acid, and tannin was 0.99, 0.98, 0.97, 0.98,0.98, 0.93, and 0.93, respectively, whereas R² of the GA model was 0.96, 0.88, 0.91, 0.96, 0.95, 0.84, and 0.84, respectively. For each response variable, the experimental and predicted values were compared to assess the predictive ability of the RSM and GA models (Fig. 6). The validity of both models in explaining the relationship between germination conditions and response variables was confirmed by the significant linear correlation that was found between the predicted and experimental values for every response. For total phenolic content (TPC), the RSM model exhibited an excellent fit with R² of 0.99, while the GA model achieved R² of 0.96. Similarly, for total flavonoid content (TFC), RSM R² 0.98 showed better agreement with experimental data compared to GA (R² = 0.88). The antioxidant activity and ascorbic acid responses also showed very high predictability in both models, with R² values of 0.97 and 0.98 for RSM, and 0.91 and 0.96 for GA, respectively. These results suggest that RSM effectively attained the quantitative relationships for bioactive enhancement, while GA performed comparably but exhibited slightly higher prediction variability due to its stochastic search mechanism. For GABA, both models confirmed a strong correlation, with R² of 0.98 (RSM) and R² of 0.95 (GA), indicating that the germination conditions influencing GABA synthesis were well-predicted. In contrast, for the antinutritional factors, the results showed different trends. For phytic acid, GA achieved a higher predictive accuracy (R² = 0.92) compared to RSM (R² = 0.87), suggesting GA’s advantage in modelling nonlinear and complex reduction kinetics. However, for tannins, RSM provided a stronger fit with R² of 0.93 than GA with R² of 0.84, reflecting that the polynomial surface adequately represented tannin degradation behaviour.

Table 5.

Statistical parameters analysis for model fit

Response	R 2		RMSE		MAE		AAD		PE
	RSM	GA	RSM	GA	RSM	GA	RSM	GA	RSM	GA
TPC	0.99	0.96	0.25	0.59	0.2	0.44	1.58	4.30	0.04	3.66
TFC	0.98	0.88	0.07	0.18	0.06	0.14	3.02	8.15	0.24	4.30
Antioxidant activity	0.97	0.91	2.54	4.36	1.88	3.43	2.83	6.00	0.14	2.65
Ascorbic Acid	0.98	0.96	0.12	0.18	0.11	0.15	4.00	5.72	0.02	2.63
GABA	0.98	0.95	0.50	0.80	0.43	0.63	4.26	6.95	0.07	5.50
Phytic acid	0.93	0.84	0.005	0.007	0.002	0.01	5.56	4.70	5.56	3.42
Tannins	0.93	0.84	0.005	0.007	0.002	0.004	1.38	2.54	1.38	0.05

Fig. 6.

Experimental vs. predicted value fitting plots of RSM and GA models for different responses

The R² of the RSM model for all responses was higher than that of the GA model. Similarly, the absolute fit of the model is indicated by RMSE and AAD values, which represent the percentage deviation of the predicted value from the observed value. The RSM model demonstrated lower MSE, MAE, and AAD values compared to the GA model. RSM predicted results are closer to the experimental results than those of GA.

The percent error comparison (Fig. 7) further supports the reliability of the developed models. RSM demonstrated consistently lower error percentages across most of the responses, confirming its higher prediction accuracy and model stability. In contrast, GA showed slightly higher variation in certain responses, such as TFC and antioxidant activity, though it performed comparatively better for phytic acid prediction, capturing its nonlinear behaviour more effectively. RSM demonstrated consistently lower and narrower error distributions, with most values below 10% and very few outliers. In contrast, GA displayed higher variability, with large deviations especially for TFC, Antioxidant activity, and GABA, where errors exceeded 20–30% in some cases. For TPC, Phytic acid, and Tannins, both models gave reasonably accurate predictions, although RSM maintained better precision. These findings suggest that while GA can approximate experimental responses, its predictions are less stable than RSM. Overall, RSM proved more robust and reliable, making it a more suitable method for modelling and optimizing germination conditions in this study.

Fig. 7.

Percent error comparison between RSM and GA predictions against experimental values

Optimization and validation of germination process conditions

The optimized conditions for the germination process were obtained through the desirability function and GA approach for maximum bioactive compound production and minimizing antinutritional factors. Based on the desirability function, the optimal conditions obtained were soaking time 12 h, germination temperature 33 °C, and germination time of 48 h with a desirability function of 0.94. The predicted results for TPC, TFC, antioxidant activity, ascorbic acid, GABA, phytic acid, and tannins obtained were 16.30 mg GAE/100 g, 2.68 mg QUE/ 100 g, 81.33%, 4.00 mg/100 g, 16.38 mg/100 g, 0.32 mg/100 g, and 0.19 mg/100 g, respectively.

In GA, the Pareto optimization was terminated after achieving 50 iterations. The input value for each Pareto optimal solution was obtained (Fig. 8). The validation curves for all responses (TPC, TFC, antioxidant, ascorbic acid, GABA, phytic acid, and tannins) show a steady decline in RMSE values across successive epochs, indicating progressive improvement in model prediction accuracy during optimization. Each response reached its minimum RMSE between epochs 49–50, demonstrating that the GA achieved convergence without signs of overfitting. The first solutions obtained by GA were selected as optimal germination conditions. The optimized conditions are given in Table 3. From the error analysis, it was found that overall, 2.5% error and 11% error for all responses were obtained for optimization based on the desirability function and GA, respectively (Table 4). Hence, it can be considered that optimum germination conditions provided by RSM were more reliable and accurate in comparison to GA.

Fig. 8.

Best performance validation curves with epoch numbers for (A) TPC, (B) TFC, (C) Antioxidant activity, (D) Ascorbic acid, (E) GABA, (F) Phytic acid, and (G) Tannins

Discussion

Effect of sprouting on total phenolic content, flavonoid content and antioxidant activity

Germination activates pathways for phenolic production, triggering critical enzymes involved in the process [6]. The phenylalanine pathway is vital for producing phenolic compounds in plants, with the enzyme phenylalanine ammonia lyase (PAL) playing a key regulatory role. During germination, PAL activity often increases, leading to higher levels of polyphenol. This phenolic accumulation is mainly observed in germinated seeds such as beans, cereals, and pseudocereals [49]. Throughout germination, enzymes like cellulase break down the cell wall, releasing bound polyphenols and increasing free phenolic acids. Fundamentally, cell wall breakdown enhances the availability of these compounds [50, 51]. Similar trends in germination have been reported in finger millet, where TPC increased from 122 ± 0.03 to 140 ± 0.01 mg GAE/100g [10], in brown rice from 0.5 to 1.3 mg GAE/g dry weight by Ukpong et al. [30] and in barnyard millet and little millet from 99.07 to 194.43 mg GAE/100 g and 111.77 to 220.89 mg GAE/100 g, respectively [52]. A decline in TPC values at higher temperatures may be linked to enzyme denaturation, limiting new phenol synthesis. Additionally, higher temperature activates polyphenol oxidase, which degrades and oxidizes existing phenolic compounds. The interactive effect of soaking time and germination temperature showed a significant effect on TPC value, similar to the linear effect. Longer soaking hours and higher germination temperature showed a decline in phenolic content. The millet grain’s pericarp, testa, aleurone layer, and endosperm all contain phenolic acids (Malathi et al. [6]. The most well-known secondary metabolites created during sprouting are phenolic compounds. According to studies, several phenolic synthesis pathways are activated during germination, which permits the activation of important enzymes that regulate the process [7]. Germination time shows a significant positive (p < 0.05) effect on TPC values at the linear level. This is because of the activation of PAL during germination, which remains active as germination progresses and continues to accumulate polyphenols [39]. The interactive effect of germination time with soaking time and germination temperature in non-significant, as reported in the Table 2. Temperature significantly influences phenolic levels, with higher sprouting temperatures leading to a reduction in phenolics. Notably, the influence of germination temperature differed between studies. While it was observed a favorable germination temperature of 35 °C, Rico et al. [53] reported the most favorable phenolic accumulation at a temperature of 21–23 °C for 48 h. This variability may indicate that both grain type and germination conditions have a significant influence on findings, further highlighting the need to perform controlled studies and optimize treatments.

The accumulation of flavonoid content primarily depends on germination temperature, responsible for activates the enzyme system responsible for flavonoid synthesis. Higher temperatures can deactivate flavonoids and increase the risk of oxidative degradation caused by polyphenol oxidase, thereby reducing their content. During germination, total flavonoid contents may increase; for example, in foxtail millet, levels rose from 628.93 ± 2.15 to 658.51 ± 3.72 mg QUE/100 g [31], while in lima beans, levels increased from 20.16 ± 0.05 to 33.63 ± 0.14 mg QUE/100 g, and in adzuki beans, from 25.38 ± 0.18 to 34.47 ± 0.31 mg QUE/100 g [54]. Quinoa showed an increase from 6.23 ± 0.26 to 11.52 ± 0.92 QE/g [55], and chickpeas from 54 to 130 mg QUE/100 g [56]. As the germination period lengthens, bioactive compounds decrease; this reduction in sprouted grains is mainly due to phenolic compound degradation during soaking. Endogenous phenolic enzymes are active during germination, causing hydrolysis and loss during soaking. Conversely, sprouting and roasting can positively impact phenolic compound bio accessibility, with a 67% increase observed after sprouting [57]. It has been reported that polyphenol oxidase and peroxidase are activated early in germination, which may cause a decrease in TFC [4, 58]. These enzymes oxidize a wide range of hydrogen donors, including flavonoids, phenolic acids, and polyphenols [59]. This oxidation process accounts for the decline in TFC levels during germination.

Antioxidant levels were observed to be higher after germination when compared to ungerminated grains. This increase in antioxidant activity is most likely attributed to biochemical reactions that occur during germination, which accelerate the formation of secondary metabolites and the release of bound phenolic and flavonoid compounds. These changes help to improve the grain’s antioxidant properties [59]. Similar trend is reported for different millets, the DPPH free radicals were scavenged from 18.42 ± 0.41% to 24.97 ± 0.22% in foxtail millet [31], 72.22 ± 1.93% to 78.88 ± 1.92% in finger millet [60], and 61.69% to 94.07% in kodo millet [35]. Similarly, the antioxidant potential of lentils dropped as the germination period increased [53, 61].

Biosynthesis of ascorbic acid and GABA during germination

An increase in ascorbic acid can be partly attributed to the enzymatic hydrolysis of starch by amylases in sprouted grains, which enhances the bioavailability of glucose. Since ascorbic acid is synthesized from glucose, mannose, and galactose was described by Saithalavi et al. [62] some minor millets have shown similar results to our study, indicating that germination increases ascorbic acid levels. For example, small, kodo, and proso millet ranged from 1.33 ± 0.18 to 1.73 ± 0.10, 0.84 ± 0.15 to 1.73 ± 0.10, and 7.68 ± 0.04 to 9.45 ± 0.16, respectively [63]. In cowpea, levels increased from 0.08 ± 0.14 to 3.03 ± 0.31 mg per 100 g dry matter [45]. The activity of the key enzyme in ascorbic acid biosynthesis depends on the activation of L-galactono-γ-lactone dehydrogenase, which catalyses the oxidation of L-galactono-1,4-lactone to ascorbic acid [53, 64] possibly contributing to the increase in ascorbic acid during sprouting [53]. This confirms that the accumulation of ascorbic acid in millets during germination is due to the reactivation of its biosynthesis [65].

γ-aminobutyric acid (GABA) is one of the most important secondary metabolites synthesized during germination. GABA is an inhibitory neurotransmitter in the central nervous system, which gives antihypertensive, anti-diabetic, and anticancer effects, relieves pain and anxiety, acts on the pancreas to formulate, and acts as a diuretic. Therefore, many scientists consider GABA-rich food sources and enriched food products [66]. GABA was significantly enriched during the sprouting process, with an increase of 0.00715 ± 0.001 to 0.0385 ± 0.004 g/100 g in foxtail millet, and the study revealed that overall, there was a 29% increase after germination [34]. Higher contents of glutamic acid decarboxylase (GAD) are encouraging the formation of GABA from glutamic acid during steeping and germination [67–69]. During the soaking operation, a large amount of water was used, and this could exert some forms of abiotic stress (water stress) on the grains, which enhances the production of GABA during germination [70].

Effect of germination on phytic acid and tannin content

Phytic acid is regarded as an anti-nutrient since it forms insoluble complexes with important dietary minerals like calcium, magnesium, iron, and zinc, thereby lowering their bioavailability in humans and animals [6]. The germination of seeds activates the enzyme phytase, which thereby breaks down phytate and decreases phytic acid [71]. Results from the present study indicate that the activation of the endogenous phytases, enzymes that break down phytic acid to lower inositol phosphates and free phosphorus, as represented in sprouted lentils, takes place at longer sprouting times, and can achieve reductions of up to 50% in the level of this component [53]. It is possible that the reduction in phytate was achieved through a combination of phytate degradation and phytase enzyme synthesis during germination [72, 73].

Compared to phytic acid, tannins exhibit smaller decreases because some tannins-protein complexes are not broken during early germination, preventing a complete breakdown. Tannins are considered polyphenols, and tannins decrease amino acids in cereals and pulses by attaching to carbonyl groups of proteins [74]. Germination activates several catabolic enzymes, especially polyphenol oxidase, which catalyse the disintegration of polyphenolic compounds during germination. Therefore, tannins are hydrolysed by polyphenol oxidase enzymes and lead to a decrease of tannins in germinated grains [75, 76]. The considerable reduction of tannins during the germination process may contribute to the significant increase of these phenolic acids [28]. According to some studies, similar results have been reported, that is, for kodo millet and barnyard millet from 4.94 to 2.74 mg TAE/ 100 g and 1.594 mg/100 g to 0.657 mg/ 100 g, respectively [35, 77]. The tannic acid of kodo millet appeared to be significantly decreased with more germination. The absence of, or low level of, tannin during germination might be due to leaching of the tannins into the water [35]. Germination was reported to demonstrate activation of polyphenol oxidase enzymes, which are responsible for the degradation of polyphenol compounds, in a number of cereals, and in some instances, pearl millet [78].

Validation and predictive performance of GA and RSM

To further validate these analyzed biochemical changes in germination, the validation and predictive performance of the RSM and GA models were evaluated. Both RSM and GA produced statistically reliable predictive models, with RSM showing slightly better performance in most of the responses, while GA outperformed RSM for certain non-linear degradations such as phytic acid. The close alignment between experimental and predicted values confirms that the developed models can effectively describe and predict the impact of soaking time, germination temperature, and germination time on the production of bioactive compounds and degradation of antinutritional compounds during sprouting. Validation curves of all the responses (total phenolic content, total flavonoid content, antioxidant, GABA, phytic acid and tannins), reveal a gradual decrease in the values of RMSE with each passing epoch which is an indication of progressive increase in the accuracy of the model prediction as it is being optimized. All the responses found their minimum RMSE during epochs 49–50, and it indicates that the GA has reached convergence without any evidence of overfitting. The low final RMSE values (0.20–0.29) confirm the robustness and reliability of the developed GA model in accurately predicting both bioactive and antinutritional responses under varying germination conditions.

Conclusion

In this study, browntop millet grains were germinated as per Box Behnken design. The experimental design was subjected to predictive modelling using RSM and GA. Optimization was done using desirability function and GA approaches. The results indicated the significant effect of independent variables such as soaking time, germination temperature and germination time on different responses. It was noticed that RSM model had given a more accurate prediction owing to higher R² and smaller value of RMSE, MAE and AAD. The GA was induced, with the only aim of testing this optimization, and of finding that a model-free approach, globally, can also indicate the same direction. RSM performed better in our study and was more predictive and in agreement with experiment values. GA had reached the same optimal area with slightly lower accuracy which confirmed the fact that RSM was the most credible and precise model for optimization. Also, further optimization showed that desirability function provided the nearest value of responses to the experimental value in comparison to GA. Finally, the optimized conditions can therefore be used to produce the browntop millet sprouts with maximum bioactive components for added health benefits.

Authors’ contributions

Puneet Kang: Writing original draftSushma Gurumayum: Writing review and editingSrikanta Kumar Meher: Statistical analysisVikas Nanda: Supervision, Conceptualisation, Writing review and editing.Gholamreza Abdi: Writing review and editingSawinder Kaur: Supervision, Conceptualisation, Writing review and editing.

Data availability

Data will be made available on request.

Declarations

Ethics approval and consent to participate

This article does not contain any studies with human or animal subjects.

Consent for publication

Not applicable (NA).

Competing interests

The authors declare no competing interests.