Optimization of the square and squared-off cascades to separate stable isotopes using meta-heuristic algorithms

In this paper, the optimization of the square and squared-off cascades for the separation of stable isotopes with a certain number of gas centrifuges (GCs) using particle swarm optimization (PSO) and the whale optimization algorithm (WOA) was studied. For this purpose, the “SC-PSO” and “SC-WOA” codes for the square cascade (SC), and the “SOC-PSO” and “SOC-WOA” codes for the squared-off cascade (SOC) were developed. The performance of the PSO and WOA algorithms in the optimization of the square and squared-off cascades as an example for the separation of 124 Xe from nine stable isotopes of xenon up to an enrichment of 85% was compared. The recovery coefficient of 124 Xe isotope by the codes “SC-PSO”, “SC-WOA”, “SOC-PSO”, and “SOC-WOA” was obtained 86.14, 78.11, 92.84, and 83.41% respectively. The performance of the algorithms indicates the higher yield of the PSO algorithm in the optimization of SC and SOC. The efficiency of the PSO has been demonstrated by the Griewank test function compared with the WOA, the sine cosine algorithm (SCA), and the dragon-fly algorithm (DA) (PSO>WOA>SCA>DA). Furthermore, the results show that SOC performs better than SC.