FP-AK-QIEA-R implements and evaluates a new quantum-inspired evolutionary algorithm based on the concept of quantum superposition for initialization. This model is based on QIEA-R for initialization, and for next iterations, it uses probability density functions where the best individuals are rewarded; then, the sampling process gets closer to the best region. FP-AK-QIEA-R was evaluated in real domain problems such as benchmark functions, protein folding, and it obtained excellent results. This work evaluates the algorithm in a binary domain, and several experiments were performed on the knapsack problem, showing good results for the experiments.