Abstract:Abstract: The goal of this study was to obtain an optimal nutrient solution formula of cucumber for substrate cultivation based on the comprehensive evaluation of cucumber yield, quality and fertilizer use efficiency. The concentrations of nitrogen (N), potassium (K), calcium (Ca) and magnesium (Mg) were designed by a five-level (1/2) quadratic orthogonal rotation combination design method to obtain a total of 23 treatments. The experiment was carried out in Yangling, Shaanxi of China (34°28′N, 108°07′E) from March 22 to July 10, 2018. The cucumber 'Bonai 526' was planted in substrate bags. The substrate had an organic matter content of 185.42 g/kg, a pH value of 7.28, and an electrical conductivity of 2.05 mS/cm. During the experiments, the cucumber yield was determined. The quality indexes including soluble protein, vitamin C and total soluble sugar content, organic acid and nitrate content were measured. The comprehensive evaluation score of cucumber yield and quality was calculated by a linear weighted model and then its relationship with concentrations of four elements was fitted by a quadratic regression model. The effect of two and three factors on the comprehensive score of cucumber yield and quality were analyzed. Subsequently, a multi-objective optimization model and a genetic algorithm were used to obtain the optimal nutrient solution formula. The results showed that the optimal treatments were different based on different yield and quality indexes, indicating that the comprehensive evaluation is necessary. Comprehensive evaluation scores of the 23 treatments were obtained and used for ranking. Different treatments of solution formula had significant effects on the comprehensive evaluation scores of cucumber yield and quality. A model was established to describe the relationship between comprehensive evaluation scores of cucumber yield and quality and the coding levels of N, K, Ca and Mg (R2=0.99, P<0.001). From the model, the coupling effects of four elements on comprehensive evaluation scores were explored and the results showed that the coupling effects of N and K, and N and Ca on the comprehensive evaluation scores of cucumber yield and quality was significant (P<0.05).The interaction between N and Ca coupling had a positive effect, whilst the interaction between N and K coupling had a negative effect. Similarly, the element use efficiency models of the four elements were also established with the R2 values between 0.710 and 0.944. The multi-objective optimization model and genetic algorithm evaluation method suggested that the optimal combination of N, K, Ca and Mg concentrations in nutrient solution was 14.83, 6.89, 3.55 and 4.17 mmol/L, respectively. Under the optimal conditions, the comprehensive scores of optimal cucumber yield and quality were 38.52×10-3 while the comprehensive scores of element use efficiency of N, K and Ca were 55.09%, 63.77% and 30.55%, respectively. The optimal nutrient solution formula was better than the commonly used Japanese Yamazaki cucumber special formula. The cucumber yield per plant, soluble protein, vitamin C and total soluble sugar content of the former were 21.07%, 40.91%, 53.33% and 11.48% higher than those obtained by the latter, while the organic acid and nitrate content of the former were significantly lower than those of the latter. The findings provide insightful guidance for high yield and quality of substrate-cultivated cucumber production, and further for the scientific management of nutrient solution in cucumber farming.