Quantum genetic algorithm based on Boltzmann selection mechanism

Abstract

In order to save computation time and avoid falling into local optima in quantum genetic algorithm (QGA), this paper proposes a quantum genetic algorithm based on Boltzmann selection mechanism (B_QGA). The proposed algorithm has several novel characteristics. Firstly, Quantum bits are encoded by angle and introduce the constant factor, aiming at enhancing calculated amount. Secondly, a new dynamic rotation angle adjustment strategy is presented to achieve updated chromosome, and individuals directly evolve to the current optimal solution with linear increasing rate, which greatly improve the rate of convergence and the ability of global search. Thirdly, instead of roulette selection mode, Boltzmann selection mechanism is employed for avoiding the local optimal problem. Finally, for the selected offspring's individuals, Hadamard door is proposed to perform mutation operation to sustain stability and diversity of population. The experiment results on three complicated continuous functions show the proposed algorithm is able to find the best solution in very short time and has excellent global search ability comparing to quantum genetic algorithm (QGA) and genetic algorithm (GA).