Primary or raw quantum circuits are challenging to directly implement on real quantum devices due to the qubit count restrictions and coupling limits. To matches hardware layouts between logic gates and physical gates sequences, the Adaptive Genetic Algorithms technique was used for this transformation, where a link can be created between algorithms and hardware using quantum circuit mapping as the linkage agent. Though, most mapping algorithms currently in use employ deterministic systems, which often result in less flexibility, insufficient diversity, and challenges in finding a balance between mapping quality and multiplicity, even while they guarantee a given level of mapping quality. This paper proposes a Quantum Circuit Mapping Based on an Improved Genetic Algorithm (QCMGA) to tackle these challenges by enhancing the workability of mapping schemes on actual hardware and overall optimization performance. This approach advances an adaptive fitness performance to strongly assess the quality of mapping schemes and uses a range of crossover tactics and selection processes to improve algorithm performance. Furthermore, QCMGA familiarizes an initialization approach based on neighbourhood gate distributions and designs a mutation mechanism specifically personalized to the structural features of quantum circuits, enhancing algorithm robustness and diversity while further increasing search efficiency and meeting the speed from a structural perspective. The applications of adaptive genetic algorithms circuits in various aspects have been highlighted and discussed in this work.