The field of Quantum Genetic Algorithm (QGA) has seen extensive efforts to develop reasonable algorithmic designs mainly due to its potential as well as the intrinsic difficulty to reproduce the necessary processes with the limited amount of quantum resources available, although it still remains one of rather theoretical concepts of approach to achieving quantum optimization. In this paper, we propose a dynamic encoding scheme that combines quantum adaptive search with iterative approximation of the search region. The method reuses the same quantum index register while updating the classical coordinate mapping associated with its basis states, thereby increasing local coordinate resolution without globally refining the entire continuous domain. Through noiseless statevector simulations on benchmark functions, we compare the proposed method with selected QGA variants in terms of final optimization accuracy and simulated qubit usage. The results show improved optimization performance under similar maximum qubit constraints, establishing a simulation-level resource advantage.