This research paper focuses on the application of a new method for the simultaneous reconfiguration and the optimum placing of Soft Open Points (SOPs) in Radial Distribution Systems (RDS). The proposed Lévy Flight-based Improved Equilibrium Optimizer (LF-IEO) algorithm enhances the standard Equilibrium Optimizer (EO) by integrating several techniques to improve exploration and exploitation capabilities. SOPs are highly developed power electronics devices that can enhance distribution utility networks in terms of reliability and effectiveness. However, identifying their optimum place along with network reconfiguration is a challenging task that requires advanced computation techniques. The performance of the proposed LF-IEO algorithm has been first verified on several benchmark functions. Subsequently, it is implemented on a IEEE 33-Bus, 69-Bus, 118-Bus, and Algerian 116-Bus distribution network to solve the problem of simultaneous network reconfiguration and optimal SOP placement. For the Algerian 116-bus system case study, the algorithm achieved a significant 14.89% reduction in power losses, improved the minimum voltage, and generated substantial net annual savings of 74,426.40 $/year. To prove its superiority in terms of solution quality and robustness, the proposed LF-IEO approach was compared with several newly developed algorithms from the literature.