The Kula Field is the youngest volcanic center in western Türkiye, and consists of various well-preserved volcanic products. Although many geological studies have been conducted in the region, geophysical anomalies have not been studied in detail. Therefore, we analyzed the aeromagnetic anomalies of these volcanic products by performing inversion studies with a recently proposed global optimizer. This study is the first attempt to use success-history-based adaptive differential evolution algorithm (SHADE) for inverting magnetic anomalies. To reduce the computational cost, we introduced the E-SHADE scheme by incorporating an exponential population reduction strategy into the optimizer. A synthetic anomaly study revealed the mathematical nature of the handled inverse problem. Some pre- and post-inversion analyses showed the efficiency of the proposed algorithm. Additionally, we observed that the E-SHADE algorithm produced better results than a commonly used derivative-based local optimizer. Nine profile data sets including magnetic anomalies of some volcanic cones in the Kula region were inverted. It was determined that the basaltic intrusions that allow the mantle material to uplift rapidly are not very deep in the subsurface. Therefore, it is possible that the three-phased volcanism may become active again and generate new alkaline basaltic lava flows in a new phase through these shallow dykes.