Individuality for Quantum-Inspired Individuals Based on Nonuniform Convergence Speed in Maximum Cut Problem

摘要

The quantum-inspired evolutionary algorithm (QEA) and QEA with a pair-swap strategy (QEAPS) have quantum-inspired individuals, where each gene is represented by a quantum bit (qubit). QEA and QEAPS iterate the evolution using the unitary transformation of probability amplitudes in each qubit, and can automatically shift the evolution from a global search to a local search. Here, the convergence speed depends on the rotation angle of each qubit toward either the 0〉 or 1〉 state vector, and the probability amplitude diverges or the population is likely to fall into a local solution if the rotation angle is too large. If the rotation angle is too small, the convergence speed may become low and the search performance will degrade. In this study, we introduce nonuniform convergence speeds into the quantum-inspired individuals and regard the convergence speed as the individual feature (individuality) of each quantum-inspired individual. Introducing the proposed individuality can eliminate the cumbersome process required to design a rotation angle while ensuring the quality of the obtained solution.