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 is another type of cascade called an 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. In this study, it is used to find the parameters of the optimum cascade. In this work, three test cases are considered to compare ideal and optimum cascades. The first test case includes two distinct symmetrical separation cascades. In the first cascade, the minimum total flow for the ideal type ۳ cascade and its corresponding optimum cascade is obtained as ∑L⁄P=۱۷۶.۷۱۲۸, and in the second one for the ideal type ۱ cascade and its corresponding optimum cascade, it is obtained as ∑L⁄P=۲۰۲.۷۸۲۸. The results show that for symmetric separation, the ideal cascade coincides with the optimum cascade. In test case ۲, the minimum total flows for the ideal type ۱ cascade of non-symmetrical separation elements and its corresponding optimum cascade (CPSO) are obtained as ∑L⁄P=۴۷۷.۶۱۷۰ and ∑L⁄P=۲۲۸.۶۹۹۷, respectively. In test case ۳, for the ideal type ۲ cascade of non-symmetrical elements and its corresponding optimum cascade, the minimum total flows are obtained as ∑L⁄P=۲۹۹.۹۹ and ∑L⁄P=۱۹۱.۶۵۸۴, respectively.