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Advanced materials research

A Novel Quantum Genetic Algorithm for Continuous Function Optimization

Hao Li, Shi Yong Li

Published Sep 23, 2013• 0 citations
Publisher

Abstract

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.

DOI
10.4028/www.scientific.net/amr.816-817.907

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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.
Aiming at the issue that quantum genetic algorithm is not suitable for continuons function optimization,an improved quantum genetic algorithm is proposed.This algorithm directly compares the quantum chromosomes with the current best solution to determine the rotating angle of the rotating gate.Every individual in population evolves with different rates to complete local search and global search simultaneously.Mutation operation is used to prevent the premature convergence.After analyzing the algorithm and its global convergence,this algorithm is applied to solve the function extremum and to optimize the PID controller parameters,and it is compared with the standard genetic algorithm and the quantum genetic algorithm.Experimental results illustrate that the proposed algorithm has better performance.
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.
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.
Due to frequent decoding operations, the efficiency of optimization is severely reduced when the binary quantum genetic algorithm based on qubits measure is applied to the continuous space optimization.To solve this problem, a quantum genetic algorithm based on phase encoding is proposed.In this method, the chromosomes are encoded by the phase of qubits, evolved by quantum rotation gates, and mutated by quantum Pauli-Z gates.As the optimization process is performed in 0,2πn, which has nothing to do with specific issues, therefore, the proposed method has good adaptability for a variety of optimization problems.With application of function extremum optimization, the simulation results show that the approach is superior to common quantum genetic algorithm and simple genetic algorithm in both search capability and optimization efficiency.
In order to save computation time and avoid falling into local optima in quantum genetic algorithm (QGA), this paper proposes a quantum genetic algorithm based on Boltzmann selection mechanism (B_QGA). The proposed algorithm has several novel characteristics. Firstly, Quantum bits are encoded by angle and introduce the constant factor, aiming at enhancing calculated amount. Secondly, a new dynamic rotation angle adjustment strategy is presented to achieve updated chromosome, and individuals directly evolve to the current optimal solution with linear increasing rate, which greatly improve the rate of convergence and the ability of global search. Thirdly, instead of roulette selection mode, Boltzmann selection mechanism is employed for avoiding the local optimal problem. Finally, for the selected offspring's individuals, Hadamard door is proposed to perform mutation operation to sustain stability and diversity of population. The experiment results on three complicated continuous functions show the proposed algorithm is able to find the best solution in very short time and has excellent global search ability comparing to quantum genetic algorithm (QGA) and genetic algorithm (GA).
A quantum genetic algorithm based on real number encoding and gradient of fitness function is proposed in this paper.Chromosomes comprised of quantum bits are updated by quantum rotating gates,and are mutated by quantum non-gate.A convenient method to choose the direction of rotation angle of quantum rotation gate is proposed.The computation formula of the rotation angle value is constructed by the gradients of fitness function.In this method,two probability amplitude of each quantum bit are regarded as two coordinate genes;each chromosome contains two chains of genes;and each chain of genes represents an optimization result.This method can accelerate convergence process and increase successful probability with the same number of chromosomes.Its application to fuzzy controller parameters optimization illustrates that the approach is superior to common quantum genetic algorithm in searching ability.