Optimization of anaerobic digestion poses many practical constraints. Therefore, a new approach was developed by integrating mathematical modeling and desirability analysis to determine optimum amounts of input factors. For this purpose, different proportions of co-digestion (grapefruit waste:cow manure) and pretreatments (NaOH and H₂O₂) were tested on the basis of a combined D-optimal experimental design. Different models were developed for certain slurry properties and CH₄ production (responses) depending on the input factors. To improve the models, Box-Cox transformation was used to transform the models into more accurate formats. The improved models were then used in desirability analysis, and optimum ranges were determined instead of optimum absolute values in three cases of given constraints, (i) constraints of the slurry properties, (ii) increase in CH₄ production, and (iii) constraints on all the responses (more important for plant efficiency). The optimum ranges were extracted for the desirability levels with values greater than 0.9 × (maximum desirability value). For the constraints given in all the responses, the optimum range of grapefruit waste:cow manure proportion was 2.5%:97.5% to 25%:75%, the optimum range of NaOH pretreatment was 0.3–2.64%, and the optimum range of H₂O₂ was range experimented except for 1.32–1.68%. Similar trends were determined for the other cases of constraints. To clarify the method of desirability analysis, the overlaying method was used to determine regions of interest according to some predefined constraints. Simultaneous consideration of range optimization and region of interest showed that (i) an amount greater than 25% grapefruit waste in the digestion decreased the CH₄ production significantly, and (ii) plant efficiency was improved with all amounts of H₂O₂ except 1.32–1.68%, and with amounts of 0.3–1.2% and 1.8–2.64% of NaOH. As shown the optimum ranges are more common for practical use in plants.

厌氧消化的优化存在许多实际限制。因此，通过整合数学建模和合意性分析来确定输入因子的最佳数量，开发了一种新方法。为此，在组合的D最佳实验设计的基础上，测试了不同比例的共消化（柚子废料：牛粪）和预处理（NaOH和H ₂ O ₂）。针对某些浆料特性和CH ₄开发了不同的模型生产（响应）取决于输入因素。为了改进模型，使用Box-Cox转换将模型转换为更准确的格式。然后将改进的模型用于合意性分析，并在三种给定的约束条件下确定最佳范围，而不是确定最佳绝对值：（i）浆料特性的约束，（ii）CH _4的增加生产；以及（iii）对所有响应的约束（对于工厂效率而言更为重要）。提取大于0.9×（最大期望值）的期望水平的最佳范围。对于所有响应给出的限制条件，葡萄柚废料：牛粪的最佳比例为2.5％：97.5％至25％：75％，NaOH预处理的最佳范围为0.3–2.64％，H的最佳范围₂ O ₂除1.32–1.68％外，均进行了范围实验。对于其他约束条件，也确定了类似的趋势。为了阐明合意性分析的方法，根据一些预定义的约束条件，使用叠加方法确定了感兴趣的区域。同时考虑范围优化和目标区域显示：（i）消化中葡萄柚废料的量大于25％会显着降低CH _4的产生，并且（ii）除1.32以外的所有H ₂ O ₂量均可提高植物效率。–1.68％，以及NaOH的0.3–1.2％和1.8–2.64％。如图所示，最佳范围是在植物中实际使用的更常见的范围。