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Jisuanji gongcheng

Convergence Analysis of Double Chains Quantum Genetic Algorithm

Yang Guo-weia

Published Jan 1, 2012• 3 citations
OpenAlex

Abstract

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.

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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 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 this paper, we present a novel quantum-inspired genetic algorithm with expanded solution space. Based on the double chains quantum genetic algorithm (DCQGA), we have expanded the solution space by increasing the number of solution space transformation functions. And we propose a novel method for quantum rotation gate's update by using the sign function and the gradient of objective function. With this method we can automatically determine the direction of quantum rotation gate and adaptively adjust the magnitude of quantum rotation gate. Through experimenting on 2 benchmark problem in the optimization literature: Rosenbrock function and Schaffer's F6 function, we demonstrate that our expanded solution space quantum genetic algorithm (ESSQGA) has achieved more satisfactory results than DCQGA and common genetic algorithm.
To address training of process neural networks based on the orthogonal basis expansion, a double chains quantum genetic algorithm based on the probability amplitudes of quantum bits is proposed. In this method, the probability amplitudes of each qubit are regarded as two paratactic genes, each chromosome contains two gene chains, and each of gene chains represents an optimization solution. The number of genes is determined by the number of weight parameters. Taking each qubit in the optimal chromosome as the goal, individuals are updated by quantum rotation gates, and mutated by quantum non-gates to increase the diversity of population. Taking the pattern classification of two groups of two-dimensional trigonometric functions as an example, the simulation results show that the proposed method is effective and efficient.
The current quantum evolution algorithms have slow convergence rate and poor robustness. In order to overcome the two shortages, a novel self-adaptive quantum genetic algorithm is proposed. Firstly, the new algorithm adopts an encoding method which is based on the Bloch spherical coordinates. Secondly, in the process of searching the optimal solution, a self-adaptive factor is introduced to reflect the relative change rates which are relative to the difference of the best individual's objective fitness between the parent generation and the child generation. The convergence rate and direction of the algorithm can be improved by adjusting the factor. The rules of updating the rotation angle and are constructed. Finally, using hadamard gate of the quantum in the mutation strategy, it can enhance the diversity of population. The simulation results of the optimizing problem of the multidimensional complex functions show that the new algorithm has not only avoided effectively the premature and improved the convergence rate, but also boosted strikingly efficiency and stability robustness of the algorithm.