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.
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.
In order to optimize the complex functions,a real-coded quantum evolutionary algorithm is proposed based on the relational concepts and principles of quantum computing.Real-coded triploid chromosomes,whose alleles are composed of a component of the independent variable vector and a pair of probability amplitudes of the corresponding states of a qubit,are constructed to keep the population diversity.The complementary double mutation operator,which is designed according to the probability amplitudes of a qubit fulfilling the normalization conditions,and the quantum rotation gate are used to update chromosomes and realize a good balance between exploration and exploitation.Simulation results on benchmark functions show that the algorithm is well suitable for the complex function optimization,and has the characteristics of rapider convergence,more powerful global search capability and better stability.
For optimzing complex functions with high-dimension, a real-coded quantum evolutionary algorithm (RCQEA) is proposed on the basis of the concept and principles of quantum computing such as qubits and superposition of states. Firstly, in this algorithm, real-coded triploid chromosomes, whose alleles are composed of real variable and a pair of probability amplitudes of the correspinding states of one qubit, are constructed to keep the diversity of solution. Secondly, complementary double mutation operator (CDMO), which is designed according to a pair of probability amplitudes of the correspinding states of one qubit satisfying the normalization condition, as well as quantum rotation gate (QRG) are used to update chromosomes, which can treat the balance between exploration and exploitation. Thirdly, discrete crossover (DC) is employed to expand search space. Finally, "Hill-climbing" selection (HCS) is adopted to accelerate the convergence speed. Simulation results on 4 benchmark complex functions with high-dimension show that RCQEA is not only effective, efficient, but also very adaptive to the dimensions, and has the characteristics of rapider convergence, more powerful global search capability and better stability.
The double chains quantum genetic algorithm based on real coded and gradient of objective function increases the diversity of population,expands the search field about space,accelerates the algorithm evolutionary process,avoids the premature convergence phenomenon,is an effective optimization algorithm,but does prove theoretically convergence.This paper gives the corresponding theorem on the basis of previous work,theoretically proves the convergence of the algorithm by the theorem,and discusses the effects of the quantum coding and quantum rotation gate in terms of the algorithm convergence and optimization efficiency by simulation example.Results show that his research enriches and improves the double chains quantum genetic theory.
In order to improve the efficiency of the quantum genetic algorithm,this paper proposed a quantum genetic algorithm based on a expanded multi-chain coding scheme.The algorithm took qubit as chromosome.Each chromosome generated multiple and parallel gene chains which were mapping to multiple optimized solutions by separating qubit into multiple and parallel genes.The expanded genes chains expanded the searching space effectively and increased evolutionary rate for quantum genetic algorithm.It introduced the dynamic adjusting rotation angle mechanism to quantum rotation gate to guide individual evolution and used quantum not-gate to prevent algorithm occurring premature convergence.The method further improved searching efficiency.In the simulation experiment,analysed the influence for the algorithm with different variation probability([0,0.1,…,0.9,1])and used different code schemes to optimize extremal function.The simulation experiment result shows that it can obviously improve the efficiency of quantum genetic algorithm by adding gene chain,and the quantum genetic algorithm based on a expanded multi-chain coding scheme is efficient.
Quantum evolutionary algorithm is a novel and efficient algorithm which inspired by the ideas of quantum computing,and it has excellent results on the computational efficiency and avoid falling into local extremum problems.Therefore,the combination of quantum mechanics and intelligent optimization algorithms will further expand the application areas of intelligent optimization algorithms to improve the optimization algorithm problem-solving ability.For this,the introduction of quantum computation to the differential evolution algorithm,we proposed a new evolutionary algorithm-quantum differential evolution algorithm.This method is the probability of quantum bits used in the real-coded chromosomes,with the quantum mutation,quantum crossover and quantum choose operation to achieve the update of chromosomal location,and using the quantum NOT gate to swap two probability amplitude of quantum bits,it can prevent the premature algorithm,while the algorithm converges faster.The function extreme value and TSP problems as an example to verify the effectiveness of the proposed algorithm.
In this paper, a novel quantum genetic algorithm is proposed. This algorithm compares the probability expectation of the quantum chromosome with the best binary solution to determine rotation angle of rotation gate. Different individual in population evolve with different rate to complete local search and global search simultaneously. Hε gate is used to prevent the algorithm from premature convergence. After analyzing the algorithm and its global convergence, applying this approach to the optimization of function extremum, and comparing with the simple genetic algorithm and the quantum genetic algorithm, the simulation result illustrates that the algorithm has the characteristic of quick convergence speed and high solution precision.