Both unit and integration testing are incredibly crucial for almost any software application because each of them operates a distinct process to examine the product. Due to resource constraints, when software is subjected to modifications, the drastic increase in the count of test cases forces the testers to opt for a test optimization strategy. One such strategy is test case prioritization (TCP). Existing works have propounded various methodologies that re-order the system-level test cases intending to boost either the fault detection capabilities or the coverage efficacy at the earliest. Nonetheless, singularity in objective functions and the lack of dissimilitude among the re-ordered test sequences have degraded the cogency of their approaches. Considering such gaps and scenarios when the meteoric and continuous updations in the software make the intensive unit and integration testing process more fragile, this study has introduced a memetics-inspired methodology for TCP. The proposed structure is first embedded with diverse parameters, and then traditional steps of the shuffled-frog-leaping approach (SFLA) are followed to prioritize the test cases at unit and integration levels. On 5 standard test functions, a comparative analysis is conducted between the established algorithms and the proposed approach, where the latter enhances the coverage rate and fault detection of re-ordered test sets. Investigation results related to the mean average percentage of fault detection (APFD) confirmed that the proposed approach exceeds the memetic, basic multi-walk, PSO, and optimized multi-walk by 21.7%, 13.99%, 12.24%, and 11.51%, respectively.