Study of ideal and optimum cascades using Co-evolutionary Particle Swarm Optimization algorithm

Ideal cascades for binary mixtures of isotopes are specified by no-mixing at confluent points and minimum total flows. Studies show that there are another types of cascades called the optimum cascade. These cascades have total flows lower than ideal cascades while separation factors are greater than unity and mixings are allowed. In this paper, using a Co-evolutionary Particle Swarm Optimization (CPSO) algorithm, the ideal and optimum cascades are compared in different operating regimes. The CPSO is a metaheuristic algorithm that uses the concept of co-evolution to deal with constrained engineering optimization problems. With the use of the CPSO algorithm, the weighting coefficients of the objective function are adjusted in a self-tuning manner. In this study, it is used to find the parameters of the optimum cascade. Ideal cascades are first classified into four types based on the various relationships between the number of stages of enriching and stripping sections. Three test cases are considered to compare ideal and optimum cascades. The first test case includes two examples of ideal cascades of symmetrical separation stages. In the first example, the total flow for the ideal type 3 cascade and its corresponding optimum cascade is obtained as ∑ 𝐿 𝑃⁄ = 176.7128 , and in the second example for the ideal type 1 cascade and its corresponding optimum cascade, it is obtained as ∑ 𝐿 𝑃⁄ = 202.7828 . The results show that for the ideal cascades of symmetrical separation stages, the ideal cascade coincides with the optimum cascade. In test case 2, the total flow for the ideal type 1 cascade of non-symmetrical separation stages and its corresponding optimum cascade (CPSO) is obtained as ∑ 𝐿 𝑃⁄ = 477.6170 and ∑ 𝐿 𝑃⁄ = 228.6997 , respectively. In test case 3, for the ideal type 2 cascade of non-symmetrical separation stages and its corresponding optimum cascade, the total flows are obtained as ∑ 𝐿 𝑃⁄ = 299.99 and ∑ 𝐿 𝑃⁄ = 191.6584, respectively. The results show that for ideal cascades of non-symmetrical separation stages, the non-mixing condition does not coincide with the condition of the minimum total flow.