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Advances in intelligent systems research/Advances in Intelligent Systems Research

Generalized Quantum Genetic Algorithm of Multidimensional Space

Xiaofeng Zhang, Wei Miao, Guifang Sui, Guowei Yang

Published Jan 1, 2014• 0 citations
Publisher

Abstract

Quantum coding plays an important role in quantum genetic algorithm and affects the optimizing efficiency of algorithm, However, there are some defects in existing quantum genetic algorithm: the quantum coding scheme reduces the stability of the algorithm, making the algorithm easily occurs premature convergence and falls into local extremums.Therefore, coding scheme of multi gene chain is extended in a four dimensional space and multidimensional space based on an improved algorithm.Through simulation experiments of function extremum, combine double and triplestranded coding scheme, in accordance with the characteristics of qubits and the normalization condition.Through the experiment, study the effect of multiple genes encoding scheme chain on the performance of the algorithm.The results show that the optimal results of the algorithm can be better and the precision of solution can be higher by increasing the genetic chain.It is an effective strategy to improve the performance of algorithm.

DOI
10.2991/lemcs-14.2014.168

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Quantum coding plays an important role in quantum genetic algorithm and affects the optimizing efficiency of algorithm, However, there are some defects in existing quantum genetic algorithm: the quantum coding scheme reduces the stability of the algorithm, making the algorithm easily occurs premature convergence and falls into local extremums.Therefore, coding scheme of multi gene chain is extended in a four dimensional space and multidimensional space based on an improved algorithm.Through simulation experiments of function extremum, combine double and triplestranded coding scheme, in accordance with the characteristics of qubits and the normalization condition.Through the experiment, study the effect of multiple genes encoding scheme chain on the performance of the algorithm.The results show that the optimal results of the algorithm can be better and the precision of solution can be higher by increasing the genetic chain.It is an effective strategy to improve the performance of algorithm.
Quantum genetic coding method plays an important role in improving the efficiency of optimization algorithm. The existing quantum genetic algorithm has some defects, that quantum encoding scheme is tend to reduce the stability, so that the algorithm is prone to premature convergence and falls into local minima. Therefore, the chain of multiple genes encoding scheme is used to extend in the multi-dimensional space for improving this algorithm. By function extremum and simulation of neural network weights optimization, according to the characteristics of qubits and the normalization condition, double and triple chain binding coding schemes are proposed. By experiments on multiple genes encoding scheme chain, the performance of the algorithm is tested. It shows that the algorithm can get better results by increasing the higher accuracy of solution chain genes. It is an effective strategy to improve the performance of genetic coding.
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.
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 solve the problems of optimization efficiency and inferior local search of quantum genetic algorithm whose coding is based on bloch coordinates,this paper proposes two improvements,combines local search with global search which is based on comparative population,and expands the search space from one sphere to three-sphere according to the characteristics of three chains.With the application of function extreme optimization of multi-variables,simulation results show that the improved algorithm has lower generation,higher efficiency,diverse populations,and it proves that the improvement is efficient.
Aiming at the problems that the Quantum Genetic Algorithm(QGA) easily falls into local extremum,an improved QGA algorithm of quantum revolving gate is proposed.In order to achieve the goal of optimization solving,quantum bit probability amplitude is applied to the chromosome encoding,and quantum rotation gate is used to chromosome updating.The theoretical derivation proves that the proposed algorithm converges with probability 1,and the algorithm converges strongly to 1?e.Comparing with double QGA,simulation results show that the algorithm increases complexity,the average time extension,but convergence times increase,convergence times of the function 1 increases from 3 to 7,and convergence times of the function 2 increases from 8 to 9.
Aimed at the problem of large storage capacity and easily falling into local optimum,a novel improved quantum genetic algorithm is presented.The algorithm adopts an angle-coding method to reduce the storage space of chromosomes.For the quantum chromosomes are distributed averagely in space of initial value,small interval method is used to initialize quanta swarm.It uses the improved quantum rotation gates to renew the population and realizes adaptive search by the adjustment strategy of dynamic quantum step and uses the operation of quantum crossover and quantum mutation to prevent the premature problem.Through the typical multi-peak function optimization test,it shows that the algorithm has the faster convergence rate,the stronger global optimization ability and the shorter computing time.The algorithm can be used for multi-peak function optimization problem.