Enhancing isotopic separation cascades by single and multi-objective solutions using Moth Flame optimization algorithm

• A unified framework for single and multi-objective optimization of isotopic separation cascades is proposed. • Moth Flame Optimization (MFO) is applied in both Single-Objective (SOMFO) and Multi-Objective (MOMFO) forms. • Explicit Pareto fronts from MOMFO visualize trade-offs between NSEs/TF and separation accuracy. • The proposed SOMFO outperforms classical methods (GWO, RCGA) across all three test cases. The design of optimum isotopic separation cascades is a critical economic challenge in nuclear fuel cycle. This study presents a unified framework for cascade optimization by applying the Moth Flame Optimization (MFO) algorithm to both single-objective and multi-objective formulations. In the single-objective approach, the goal is to minimize a composite function that simultaneously targets the reduction of the number of separation elements (NSEs) or total flow (TF) in cascade and the deviation of output concentrations from their target values. For the multi-objective approach, these goals are treated as distinct objectives to generate a set of Pareto-optimal solutions. The performance of both methodologies was rigorously evaluated across three distinct test cases, including comparisons with literature algorithms. The results demonstrated that the proposed single-objective approach consistently identifies solutions that either dominate or are highly competitive with those from other methods. Furthermore, the Pareto fronts obtained from multi-objective formulations provides designers a clear visualization of the trade-offs involved, enabling more informed decision making. It is concluded that the MFO algorithm constitutes a suitable tool for optimal design of separation cascades.