Technology in the financial sector is advancing at an accelerated rate as financial institutions seek to improve transaction speed and service convenience to customers. Several algorithms have been proposed to mitigate credit card fraud, such as swarm-based algorithms. These algorithms include, amongst others, the firefly algorithm (FA), which has gained a reputation for both efficiency and effectiveness as an optimization algorithm. There have been several variations of the algorithm, and these include, amongst others, compact L \(\acute{e}\) vy-flight FA, Yin-Yang FA and FA1 \(\rightarrow \) 3. The FA1 \(\rightarrow \) 3 has been shown to be very effective and efficient. On the other hand, L \(\acute{e}\) vy-flights have shown a lot of potential in real-life problems that are stochastic in nature. Therefore, this study proposes an algorithm to extend the FA1 \(\rightarrow \) 3 by merging it with L \(\acute{e}\) vy-flights in a bid to draw from the strengths of both existing variations. Furthermore a comparison of the three algorithms (original FA1 \(\rightarrow \) 3, updated FA1 \(\rightarrow \) 3 implementation and L \(\acute{e}\) vy-Flight based FA1 \(\rightarrow \) 3) is made based on experiments carried out on a credit card fraud data set. Although the original algorithm recorded the highest performance metrics, the proposed L \(\acute{e}\) vy based FA1 \(\rightarrow \) 3 algorithm proves to be more dependable.