Hybrid quantum genetic algorithm with adaptive rotation angle for the 0-1 Knapsack problem in the IBM Qiskit simulator

Abstract

A Hybrid Quantum Genetic Algorithm with an Adaptive Rotation Angle (HQGAAA) for the 0-1 knapsack problem is presented. This novel proposal uses the Deutsch-Jozsa quantum circuit to generate quantum populations, which synergistically works as haploid recombination and mutation operators taking advantage of quantum entanglement providing exploitative and explorative features to produce new individuals. Furthermore, the created individuals are updated using an adaptive rotation angle operator that helps refine new individuals to converge to the optimal solution. We performed comparative tests with other quantum evolutionary algorithms and the classical genetic algorithm to demonstrate that this proposal performed better with the tested problem. Results showed that quantum algorithms performed similar but better than the classic genetic algorithm regarding accuracy. Moreover, statistic tests demonstrated that our proposal is faster than the other quantum algorithms tested.