Formulation of Nutrient Solutions Using Simulated Annealing

Modern agriculture requires optimizing available resources to maximize production while minimizing environmental impact without increasing economic costs. Hydroponic agriculture replaces soil with inert media that provide physical support for plants but do not supply nutrients. In this type of agricultural production, fertilization with nutrient solutions is essential, as they supply the 15 elements necessary for proper plant development. These solutions consist of mixtures of different amounts of fertilizers dissolved in water. In this context, a method based on a simulated annealing algorithm is proposed, a metaheuristic that optimizes fertilizer quantities in grams to achieve target concentrations in parts per million for six macronutrients and nine micronutrients. The algorithm addresses a multi-objective optimization problem, balancing two competing goals: first, maximizing the accuracy of the fertilizer balance to achieve the required nutritional levels, and second, minimizing the total cost of the fertilizer mixture. The algorithm’s fitness function weights the total cost of the fertilizers used and the total relative error between the concentrations obtained and those desired, allowing the relative importance of cost and accuracy in the nutrient solution to be adjusted. The results of three experiments with varying nutrient levels are presented for a 1000-L water tank. The first experiment consisted of three macronutrients and two micronutrients. The second configuration added three macronutrients and two micronutrients, for a total of ten nutrients. Finally, five micronutrients were added to complete the 15 essential nutrients for plants. It is important to note that there are several methods for calculating micronutrients that contribute to precision agriculture, increasing the complexity of finding a solution that meets established nutritional requirements. The nutrient concentrations in parts per million required for tomato cultivation during the vegetative development stage. To balance nutrient accuracy and solution cost, we applied weighting factors of 0.65, 0.75, 0.85, 0.90, 0.95, and 1.0 for accuracy. The corresponding weights for cost were calculated as the complement of these values (totaling 1). By favoring nutrient accuracy with a weighting of 1, accuracies of 0.00500, 0.02618, and 0.03077 parts per million were achieved in each experiment, respectively. Meanwhile, the lowest cost is 2.06, 2.72, and 2.70 USD for the aforementioned experiments.