The cultivation of the mushrooms not only lessens the environmental effects of the wastes used as substrate but also provides an economically viable alternative for producing high-quality and beneficial food and precious metabolites (Israilides and Philippoussis, 2003). Shiitake, Lentinula edodes (Berk.) Pegler, has been cultivated for thousands of years. L. edodes is one of the best-known medicinal and edible mushrooms worldwide, especially in East Asia, due to its widespread use in food and traditional medicines (Xu et al., 2014; Mahdizadeh et al., 2021; Ahmad et al., 2023). This valuable medicinal mushroom is used to treat influenza, tumors, high blood pressure, heart disease, obesity, age-related sexual dysfunction, liver problems, diabetes, fatigue, weakness, high cholesterol, and respiratory diseases (Bisen et al., 2010; Ahmad et al., 2023). Shiitake is nourishing and appetizing as a food and exhibit several pharmacological properties, including antiviral, immunomodulatory, antifungal, antibacterial, antiviral and anticancer effects (Bisen et al., 2010; Diallo et al., 2020; García-Cruz et al., 2020; Ahmad et al., 2023). The lignan-rich fraction extracted from L. edodes mycelial culture medium is promising for the treatment of AIDS and hepatitis B (Bisen et al., 2010).

The preferred substrate for L. edodes is hardwood sawdust supplemented with rice bran, wheat bran and millet powder (Philippoussis et al., 2007). Bagasse substrate supplemented with rice bran improved mushroom quality and biological efficiency of shiitake (Rossi et al., 2003). Bagasse is an important solid residue in the sugarcane industry, and hundreds of millions of tons of bagasse are produced worldwide every year (Mahmud and Anannya, 2021). The use of bagasse (Selman-Housein et al., 2000) and other agricultural residues (Devi et al., 2017), including wheat bran, is crucial from both environmental and economic perspectives. Beech sawdust is obtained in abundance from the timber industry (Jahedi et al., 2023). The reuse of these solid wastes is also crucial for environmental reasons (Gordić et al., 2014; Jahedi et al., 2023). In this study, different ratios of bagasse (B), beech sawdust (BS), and wheat bran (WB) were used as growing substrates to determine the compatibility of agricultural and industrial residues for shiitake production. The ratio of substrate components should be optimized to achieve the best running of L. edodes. A detailed analysis of the effects of the ratio of growing substrate components on the running length (RL) and running rate (RR) of L. edodes and their optimal quantity selection would lay the foundation for the commercialization of the conversion of agro-industrial residues into foods with therapeutic active ingredients. However, optimizing the ratio of growing substrate components to achieve the maximum running is expensive and time-consuming. Evaluating the relationship between the input variables “ratios of substrate components (B, BS, and WB) and running time” and the output variables “RL and RR of L. edodes” could simplify the optimization of the growing substrate for production of this valuable medicinal and edible mushroom. Analyses of biological data have been conducted using multivariate statistical methods, including multiple linear regression (MLR), stepwise regression (SR), principal component regression (PCR), ordinary least squares regression (OLSR), and partial least squares regression (PLSR; Wold, 1966; Farhadi et al., 2020; Salehi et al., 2020b). Growth is a highly nonlinear and complex biological process involving multiple interconnected signaling and biochemical pathways (Olas et al., 2020). The optimal conditions for a complex process can be accurately predicted using efficient nonlinear computational algorithms (Struik et al., 2005; Gallego et al., 2011). Traditional prediction and modeling methods, including regression models, have negligible nonlinear fitting and prediction capabilities (Farhadi et al., 2020; Salehi et al., 2020a,b). Artificial intelligence (AI) is used to address issues that cannot be explained using traditional computing techniques. One of the key aspects of AI is artificial neural networks (ANNs), which discover multifactorial nonlinear relationships between the output and input data (Farhadi et al., 2020; Hesami et al., 2020; Hesami and Jones, 2020; Salehi et al., 2020a; Jahedi et al., 2023). ANNs are brain-inspired systems that mimic the human brain’s ability to sense and think in a simplified manner to process information and recognize patterns in systems that involve ambiguity and uncertainty (Patnaik, 1999; Agatonovic-Kustrin and Beresford, 2000). ANNs learn through experience and gain intelligence by discovering hidden patterns and relationships (Agatonovic-Kustrin and Beresford, 2000). Response surface methodology (Kovalchuk et al., 2017), multivariate adaptive regression splines (Akin et al., 2020), and multilayer perceptron-genetic algorithm (MLP-GA; Jahedi et al., 2023) have been used for culture media optimization in plant and fungal research. Multilayer perceptron (MLP) is an effective tool in solving complicated non-linear problems, handles the massive data set well, quickly predicts after training, and obtains the same accuracy even with small data. Disadvantages of MLP include that the degree to which the dependent variable influences each independent variable is unknown, some hyperparameters of the MLP, such as the number of hidden neurons and layers, must be tuned, which requires time and power, model performance depends on the training quality, and the MLP is sensitive to feature scaling (Pedregosa et al., 2011). MLP, one of the most well-known feedforward neural networks, exhibits superior prediction accuracy compared to traditional statistical methods for calculating mathematical functions for analyzing and interpreting various unpredictable data sets (Salehi et al., 2020a; Jahedi et al., 2023). However, there are numerous problems in designing and training ANNs. Due to a large number of hidden neurons, the training time increases and data overfitting occurs. Low accuracy rates are caused by a few hidden neurons (Matignon, 2005). In addition, one of the main problems is the allocation of weights in the MLP structure which directly affects the model performance. Network topology and learning algorithm parameters control the weights. Learning rates, the number of memory taps, and the number of hidden nodes and layers are the network factors that can influence ANN performance (Tahmasebi and Hezarkhani, 2009). To address these issues, ANNs have been combined with other optimization techniques, such as genetic algorithms (GA; Plumb et al., 2005; Salehi et al., 2020a).

GA, developed by Holland (1992), is a popular evolutionary algorithm that excels in finding answers to problems and has been used to optimize bioprocesses (Osama et al., 2015; Farhadi et al., 2020; Salehi et al., 2020a; Jahedi et al., 2023). The GA is a search algorithm inspired by genetics and natural selection (Holland, 1992). GAs apply biologically inspired operators, including crossover, mutation, and selection, to obtain high-quality optimization solutions (Katoch et al., 2021). The principles of GA are the creation of the initial population of search solutions (chromosomes), followed by selecting the superior search solutions for crossover using a roulette wheel selection method and determining the best solution (optimal value, fittest chromosome) among them (Holland, 1992). GA obtains solutions improving over time, requires no derivative information, displays superior parallel capabilities, optimizes continuous functions and discrete functions, and multi-objective problems, is the best option for a wide range of optimization problems, and can handle a broad search space. However, GA is not an efficient method for solving simple problems and ones with available derivative information. Additionally, GAs may be computationally costly, especially when working with large problem spaces or complex fitness evaluations. Also, the quality of the final solution found using GA to a problem is not guaranteed (Sivanandam and Deepa, 2008). This study attempted to automatically determine the optimal number of neurons using GA to improve the prediction accuracy and determine the optimized values of the inputs “(B, BS, and WB ratio)” for the maximum mycelial RL and RR of shiitake (L. edodes). Furthermore, the performances of the regression and MLP-GA models were evaluated in terms of the prediction accuracy of the output variables optimized for the maximum mycelial RL and RR of L. edodes, and the most important inputs (factors) were detected for the highest RL and RR of shiitake.

Shiitake (L. edodes) strain VM230 was obtained from the culture collection of the Plant Pathology Department at Tarbiat Modares University (Mahdizadeh et al., 2021).

Forecasting the optimal ratio of substrate components is essential to enhance shiitake production and reduce costs. This is the first report to establish a mathematical model for the prediction of the RL and RR of L. edodes according to the ratios of growing substrate components (B, WB, and BS) and running time, as well as the optimization of growing substrate composition to achieve the maximum RL and RR. An accurate modeling system is required to forecast the optimal ratio of substrate components (B, BS, and WB) and running time for the maximum RL and RR of L. edodes. Various regression models and MLP-GA modeling were used to examine the relationships among the four input variables “ratios of B, WB, and BS and running time” and the output variables “RL and RR,” and the prediction probability of RL and RR using the studied input variables. Such mathematical forecasts have not yet been reported for valuable medicinal and edible mushrooms. Previous studies (Salehi et al., 2020a,b, 2021; Jahedi et al., 2023) have also indicated that MLP-GA models have superior accuracy compared with regression models (Figures 4, 5; Table 4). R-squared (Table 4), a measure of the fit of regression models for the testing subset, showed that these models could describe 71 and 52% variability in the RL and RR of shiitake, respectively, for unseen data. The results of the present study suggest that the developed MLP-GA models correctly predicted the RL and RR of L. edodes (R² = 0.97 and 0.92, respectively; Table 4) in the testing subset, which was not utilized in the MLP-GA training process. The closeness of the errors of the training and testing subsets (Table 4), as well as the small number of hidden neurons confirmed the absence of overlearning during training and the good generalizability of the developed MLP-GA models for unseen data (Lou and Nakai, 2001; Farhadi et al., 2020; Salehi et al., 2020a, 2021). From the statistical metrics including R² and RMSE of the training and testing subsets (Table 4), it can be inferred that the tansig activation function worked well for modeling throughout the experiment. Furthermore, the small RMSE values (Table 4) show the great potential of the developed MLP-GA models for predicting the parameters (output variables). Mycelium running is a colonization of the substrate thoroughly by fungal hyphae. The fungus first colonizes the entire substrate and then creates new hyphae by lateral branching, increasing the density and surface area of the colony. Fungi thrive in both nutrient-rich and nutrient-poor culture media. However, their lateral branching occurs only in the nutrient-rich medium, like what is observed in sparse and dense growth of fungal hyphae on water agar and potato dextrose agar. This could explain why the optimum substrate compositions for RL and RR are different.

Regardless of previous studies on the effects of growing substrate composition and running time on RL and RR of L. edodes, the question remains: which input variables are most important for RL and RR of L. edodes? As mentioned previously, sensitivity analysis showed that running time was the most important variable affecting mycelial RL of L. edodes (Table 5). The RR of L. edodes is important for commercial cultivation. Sensitivity analysis revealed that WB ratio was the most important factor affecting RR of L. edodes (Table 5). Shiitake running is a complex bioprocess that requires reliable methods for the model development and optimization. The MLP-GA has been successfully used to solve problems in various areas that are highly challenging and for which there is no known answer (Eftekhari et al., 2018; Salehi et al., 2020a; Jahedi et al., 2023). The growing interest in ANNs is primarily due to their ability to solve problems in various domains, their ability to model complex and nonlinear relationships, their ability to predict relationships on unseen data, and the fact that they do not require the specification of statistical data distribution (Mahanta, 2017). Due to the high prediction performance of the testing subset (Table 4), the established MLP-GA correctly predicted the RL and RR of L. edodes.

In this study, the RL and RR of L. edodes were modeled and optimized using mathematical methods for the first time. The high degree of fit between the forecasted and actual values of the output variables (the RL and RR of L. edodes) confirmed the superior performance of the developed MLP-GA models. This study presents MLP-GA as a useful mathematical tool for predicting and optimizing complex systems such as the growth of medical mushrooms, and the RL and RR of L. edodes in response to the composition of the growing substrate.

The original contributions presented in the study are included in the article/Supplementary material, further inquiries can be directed to the corresponding author.

NS: Conceptualization, Investigation, Methodology, Project administration, Resources, Supervision, Writing – review & editing. MS: Conceptualization, Formal analysis, Investigation, Methodology, Validation, Visualization, Writing – original draft, Writing – review & editing. SF: Formal analysis, Investigation, Software, Visualization, Writing – review & editing. AA: Investigation, Methodology, Writing – review & editing. VM: Resources, Writing – review & editing.