A multivariate method based on solvent terminated dispersive liquid–liquid microextraction was developed for the determination of Cu²⁺ ions in aqueous samples. In the proposed approach, di-2-ethylhexylphosphoric acid, xylene and acetone were used as chelating agent, dispersive and extraction solvents, respectively. The effects of various factors on the extraction efficiency such as extraction and dispersive solvent volumes, salt addition and pH were studied using central composite design (CCD) and artificial neural networks coupled bees algorithm (ANN-BA). Upon comparison of these techniques, ANN-BA model was considered to be better optimization method due to its higher percentage relative recovery (about 5%) as compared to the CCD approach. The linear range and the limits of detection (S/N = 3) and quantitation (S/N = 10) were 0.22–140, 0.08 and 0.22 µg L⁻¹, respectively. Under the optimal conditions, the recoveries for real samples spiked with 0.1 and 0.3 mg L⁻¹ were in the range of 85–98%.

Solvent-terminated dispersive liquid-liquid microextraction (ST-DLLME) as a simple, fast, and low-cost technique was developed for simultaneous extraction of Cd²⁺ and Cu²⁺ ions in aqueous solutions. Multiobjective evolutionary algorithm based on decomposition with the aid of artificial neural networks (ANN–MOEA/D) was used for the first time in chemistry, environment, and food sciences to optimize several independent variables affecting the extraction efficiency, including disperser volume and extraction solvent volume, pH, and salt addition. To perform the ST-DLLME operations, xylene, methanol, and dithizone were utilized as an extraction solvent, disperser solvent, and chelating agent, respectively. Non-dominated sorting genetic algorithm versions II and III (NSGA II and NSGA III) as multiobjective metaheuristic algorithms and in addition central composite design (CCD) were studied as comparable optimization methods. A comparison of results from these techniques revealed that ANN-MOEA/D model was the best optimization technique owing to its highest efficiency (97.6% for Cd²⁺ and 98.3% for Cu²⁺). Under optimal conditions obtained by ANN-MOEAD, the detection limit (S/N = 3), the quantitation limit(S/N = 10), and the linear range for Cu²⁺ were 0.05, 0.15, and 0.15–1000 μg L⁻¹, respectively, and for Cd²⁺ were 0.07, 0.21, and 0.21–750 μg L⁻¹, respectively. The real sample recoveries at a spiking level of 0.05, 0.1, and 0.3 mg L⁻¹ of Cu²⁺ and Cd²⁺ ions under the optimal conditions obtained by ANN–MOEA/D ranged from 94.8 to 105%.