Abstract The biosorption of lead and cobalt from an aqueous solution is studied using Rafsanjan pistachio shell (RPS) as a biosorbent. The amount of removed metal depends on four factors including pH of the aqueous solution, initial concentration of metal (C0), biosorbent dosage (DB), and temperature (T). An efficient set of experiments is obtained in a lab-scale batch study. Feed-forward neural network (FFNN) and genetic programming (GP) methods are used for process modeling. The FFNN formula is further improved using the grey wolf optimization (GWO) algorithm and it converges to the test observations with regression index (R2) of 0.9932 and 0.9908 for Pb(II) and Co(II). The GP formula also gives an R2 value of 0.9657 and 0.9518 for Pb(II) and Co(II) adsorptions respectively. Using the grey wolf optimization (GWO) method proves that at pH ​= ​5, C0 ​= ​10.2 ​mg/l, DB ​= ​0.8 ​g/l, and T ​= ​25 ​°C, the adsorption of Pb(II) and Co(II) together can be maximized up to 81.5% and 69.4%, respectively.

中文翻译：

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使用基于实验的 ANN 和 GP 模型以及灰狼优化器对具有 Rafsanjan 开心果壳的水中铅和钴的生物吸附进行建模和优化

摘要 使用 Rafsanjan 开心果壳 (RPS) 作为生物吸附剂研究了水溶液中铅和钴的生物吸附。去除金属的量取决于四个因素，包括水溶液的 pH 值、金属的初始浓度 (CO)、生物吸附剂剂量 (DB) 和温度 (T)。在实验室规模的批量研究中获得了一组有效的实验。前馈神经网络 (FFNN) 和遗传编程 (GP) 方法用于过程建模。FFNN 公式使用灰狼优化 (GWO) 算法进一步改进，它收敛到测试观测值，Pb(II) 和 Co(II) 的回归指数 (R2) 为 0.9932 和 0.9908。GP 公式还给出了 Pb(II) 和 Co(II) 吸附的 R2 值分别为 0.9657 和 0.9518。使用灰狼优化（GWO）方法证明，在pH=5时，