Title: Search performance analysis of qubit convergence measure for quantum-inspired evolutionary algorithm introducing on maximum cut problem

Authors: Yoshifumi Moriyama; Ichiro Iimura; Shigeru Nakayama

Addresses: Faculty of Administrative Studies, Prefectural University of Kumamoto, 3-1-100 Tsukide, Higashi-ku, Kumamoto, 862-8502, Japan ' Faculty of Administrative Studies, Prefectural University of Kumamoto, 3-1-100 Tsukide, Higashi-ku, Kumamoto, 862-8502, Japan ' Kagoshima University, 1-21-40, Korimoto, Kagoshima, 890-0065, Japan

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 the evolution from a global search to a local search and have shown superior search performance to the classical genetic algorithm. However, the population gets into a locally optimal solution and the solution search stagnates when the probability amplitudes of qubit excessively converge to |0⟩ or |1⟩. In this study, we have proposed a measure that can confirm convergence state of qubits. From the results of the computational experiment in the maximum cut problem, we have clarified that the proposed measure can estimate the state of the qubit, and the quality of the obtained solution is improved by applying the method for maintenance of diversity.

Keywords: quantum-inspired evolutionary algorithm; QEA; QEA with pair-swap strategy; QEAPS; qubit convergence measure; Noah's ark strategy; population-based incremental learning; PBIL; univariate marginal distribution algorithm; UMDA; estimation of distribution algorithms; EDAs; maximum cut problem.

DOI: 10.1504/IJCISTUDIES.2018.096185

International Journal of Computational Intelligence Studies, 2018 Vol.7 No.3/4, pp.231 - 252

Available online: 13 Nov 2018 *

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