The need to develop an ICT-based mechanism for detecting and preventing fraudulent financial transactions from large volumes of available financial datasets, such as credit cards, motivated this study. Existing methods are either based on machine learning algorithms or on meta-heuristic optimization algorithms to achieve the aforementioned goals. The convergence of an algorithm is one of its most important characteristics as it is possible to analyze and prove whether an algorithm converges using mathematical theoretical knowledge. Therefore, an appropriate strategy for improving the speed of convergence randomization of a nonlinear optimization algorithm must be implemented. In this paper, a nonlinear convergence factor based on tangent trigonometric function is proposed and embedded into the existing Firefly Algorithm (FA). Using credit card transaction datasets from a Nigerian financial institution's website, the goal is to find the best global solution and improve convergence search speed. When compared to state-of-the-art methods, the proposed improved FA has a high randomized convergence speed with a success rate of 3724±573 (100%). Finally, when it comes to problems like detecting credit card payment fraud with a greater emphasis on convergence speed, the proposed algorithm has an excellent success rate for finding global optima.