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Journal of Chinese Computer Systems

Real-coded Quantum Differential Evolution Algorithm

Nay Ming Huang

Published Jan 1, 2013• 2 citations
OpenAlex

Abstract

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.

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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 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 increasing interest, in the last two decades, of evolutionary computation community in the combination of quantum computing and evolutionary computing, has led to the definition of a novel class of quantum-inspired evolutionary algorithms which exploit the concepts of quantum bits and quantum gates with the aim of improving the efficiency of current optimization methods. In this paper, a new method which hybridizes differential evolution with quantum computing is proposed. The method consists of two phases. In the first phase, it performs a new quantum-inspired evolutionary method until it does not get stuck into a local optimum, then, in the second phase, it runs differential evolution by using as initial population that obtained at the end of the first phase. Experiments on classical benchmark functions show that the hybridization outperforms standard methods by sensibly improving the fitness value and speeding up the convergence process.
In this paper, we propose a quantum differential evolution (QDE) algorithm for function optimization, which can improve the performance of differential evolution (DE) algorithm. First, the algorithm does some basic operations, such as mutation, crossover and selection of vectors. And then a quantum computing method is utilized to search the global optimal solutions, which avoids falling into the local minimums. Our experimental results show the proposed algorithm is feasible. And compared with other algorithms, the proposed algorithm is more effective. Furthermore it can improve the speed of convergence.
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 this paper,two aspects of the quantum-inspired evolutionary algorithm are improved:(1)Quantum chromosomes qubits in superposition and entangled states can not use the traditional cross-qubit operation,the full interference cross is designed for measured clas-sic chromosome,which could not undermine the inherent parallelism of quantum chromosome,and could increase the diversity of the chro-mosomes after the measurement,affect the direction of chromosome evolution,and effectively prevent premature;(2)The probability trigger is designed to start the quantum NOT gate for quantum variation.The experiments show that the improved quantum evolution opera-tor has better search ability than the previous algorithm over into a more stable convergence degree.