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Quantum Genetic Algorithm Based on Angle Coding of 3D

Decai Huang

Published Jan 1, 2012• 1 citation
OpenAlex

Abstract

In order to make full use of the quantum characteristics of the quantum state in the algorithm,and improve the search efficiency,reduce storage space,a new quantum genetic algorithm called 3D-AQGA was proposed.The algorithm describes quantum bit as a pair of angles in 3D spherical coordinate,makes full use of the quantum space motion characteristics,and introduces a kind of adaptive scheme to calculate the rotation angle size and direction which not only makes the process of chromosome's update and variation simplified,but also improves quantum characteristics,storage properties and time performance of the algorithm greatly.The simulation results show that the efficiency of the algorithm and the search ability are superior to the simple genetic algorithm and common quantum genetic algorithm.

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In order to make full use of the quantum characteristics of the quantum state in the algorithm,and improve the search efficiency,reduce storage space,a new quantum genetic algorithm called 3D-AQGA was proposed.The algorithm describes quantum bit as a pair of angles in 3D spherical coordinate,makes full use of the quantum space motion characteristics,and introduces a kind of adaptive scheme to calculate the rotation angle size and direction which not only makes the process of chromosome's update and variation simplified,but also improves quantum characteristics,storage properties and time performance of the algorithm greatly.The simulation results show that the efficiency of the algorithm and the search ability are superior to the simple genetic algorithm and common quantum genetic algorithm.
In order to decrease the storage quantity and increase the search efficiency,a new quantum genetic algorithm called AC-QGA is proposed,in which the chromosome is encoded by the angle in based on the qubit's polar coordinate representation in the two-dimensional Hilbert space.Thus,the representation of the gene-bit is changed from the complex number pair to a real number,and the storage quantity is decreased greatly.Meanwhile,the updating process of the chromosome and the mutation process of the gene-bit are simplified from the matrix multiplied by the vector to the angle addition or subtraction.The process of observing the chromosome is changed from probability comparison to angle comparison.The above-mentioned measures make the storage quality and the search efficiency of AC-QGA be increased greatly.The experiments show AC-QGA is very effective.
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.
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).
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.
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.
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.