Investigation on introducing qubit convergence measure to QEA in maximum cut problem

Abstract

The quantum-inspired evolutionary algorithm (QEA) and QEA with a pair-swap strategy (QEAPS), where each gene is represented by a quantum bit (qubit), and the qubit is updated by a unitary transformation in both algorithms. QEA and QEAPS can automatically shift from a global search to a local search and have shown superior search performance to the classical genetic algorithm. However, it is important to appropriately manage the convergence speed of qubits. In this study, we have proposed a measure that can confirm convergence state of qubits, and applied the measure to a method for keeping diversity. From the results of the computational experiment in the maximum cut problem, we have clarified that the proposed measure can confirm the state of the qubit, and the discovery rate of the optimal solution improves with to apply the method for maintenance of diversity.