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Acta Mechanica

Quantum evolutionary algorithm with rotational gate and $$H_\epsilon $$-gate updating in real and integer domains for optimization

Mohammad Kamalinejad, Hamed Khajeh Arzani, Ali Kaveh

Published Jun 1, 2019• 11 citations
Publisher
DOI
10.1007/s00707-019-02439-2

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Quantum evolutionary algorithm with rotational gate and HϵH_\epsilon Hϵ​-gate updating in real and integer domains for optimization
Parameter estimation of chaotic systems is essentially a multidimensional optimization problem.To estimate the unknown parameters of chaotic systems precisely,we present an effective hybrid quantum-inspired evolutionary algo-rithm(HQEA),in which the real-valued quantum angle is used to express the Q-bits of chromosome,and the probability of each Q-bit is considered the position information of the chromosome.Combining the quantum differential evolutionary algorithm(QDE) which uses differential evolution to update the state of Q-bits with the real-coded quantum evolutionary algorithm(RQEA) which employs quantum rotation gate to update the state of Q-bits,we make a balance between the global exploration and the local exploitation.In addition,the HQEA performs the quantum non-gate operation in which the Q-bits selected from the current best chromosome with a certain probability are transformed to get rid of the premature local optimum.The experimental results of benchmark function tests show that the HQEA algorithm greatly improves the global optimization performance as well as the reliability performance.Numerical simulation results of the Lorenz system also demonstrate its effectiveness.
In order to optimize the numerical functions with the continuous solution space, a new phase angle encoded quantum evolutionary algorithm(PAQEA) is proposed based on the quantum computing and real encoded evolutionary algorithm. In PAQEA, a quantum chromosome with probabilistic representation can represent all the feasible solution probabilistically, and the dynamic quantum rotation gate is used to update chromosomes. Thus, the population diversity and directional evolution realize a good balance between exploration and exploitation. Theoretical analysis shows that the PAQEA is a global convergence algorithm. Simulation results show that the algorithm is suitable for the optimization of complex numerical functions, and has the characteristics of rapider convergence, powerful global search capability and better stability.
For improving convergence rate and preventing prematurity in quantum evolutionary algorithm, an allele real-coded quantum evolutionary algorithm based on hybrid updating strategy is presented. The real variables are coded with probability superposition of allele. A hybrid updating strategy balancing the global search and local search is presented in which the superior allele is defined. On the basis of superior allele and inferior allele, a guided evolutionary process as well as updating allele with variable scale contraction is adopted. And H ε gate is introduced to prevent prematurity. Furthermore, the global convergence of proposed algorithm is proved by Markov chain. Finally, the proposed algorithm is compared with genetic algorithm, quantum evolutionary algorithm, and double chains quantum genetic algorithm in solving continuous optimization problem, and the experimental results verify the advantages on convergence rate and search accuracy.