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Improved Quantum-Inspired Evolutionary Algorithm and Its Application to 3-SAT Problems

Xiaoyue Feng, Enrico Blanzieri, Yanchun Liang

Published Jan 1, 2008• 5 citations
Publisher

Abstract

An improved quantum-inspired evolutionary algorithm is presented in this paper. Quantum angle is adopted to present the quantum bit in the proposed algorithm. A novel quantum rotation gate strategy is adopted to adjust the direction of the quantum gate which is used to update the quantum population. The step size is adaptively adjusted rather than a fixed angle. Furthermore, the particle swarm optimization is added into the improved algorithm to accelerate the convergent speed and develop the local searching ability. To demonstrate the effectiveness and applicability of the proposed approach, several experiments are performed on the 3-SAT problems. The results show that it is feasible and effective to solve the 3-SAT problem using the proposed algorithm.

DOI
10.1109/csse.2008.1512

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An improved quantum-inspired evolutionary algorithm is presented in this paper. Quantum angle is adopted to present the quantum bit in the proposed algorithm. A novel quantum rotation gate strategy is adopted to adjust the direction of the quantum gate which is used to update the quantum population. The step size is adaptively adjusted rather than a fixed angle. Furthermore, the particle swarm optimization is added into the improved algorithm to accelerate the convergent speed and develop the local searching ability. To demonstrate the effectiveness and applicability of the proposed approach, several experiments are performed on the 3-SAT problems. The results show that it is feasible and effective to solve the 3-SAT problem using the proposed algorithm.
In this paper, quantum rotate gate is improved, which is the main operation in the population update of the traditional quantum evolutionary algorithm. A new rotation angle is defined, preventing the algorithm from easily falling into local optimum state in the middle and late term. Based on the characteristics of TSP, a modified quantum rotate gate is proposed in this paper to adaptively adjust the rotation angle, according to the evolution generations and the adapt to degree of the value to adaptive dynamic adjustment of the rotation angle, resulting a better global search capability. At the same time, in order to prevent the extramalisation of the probability amplitudes α and β falling into local optimal algorithm, this paper adopted the Hε gate on the probability amplitude of the rotation to make the corrective manipulation. The comparative experimental results showed that the algorithm's stability and accuracy have been greatly improved in solving the TSP problem, compared with the conventional quantum evolutionary algorithm.
In this paper, Quantum Rotate Gate is improved, which is the main operation in the Population Update of the traditional Quantum Evolutionary Algorithm. A new rotation angle is defined, preventing the algorithm from easily falling into local optimum state in the middle and late term. Based on the characteristics of TSP, a modified quantum rotate gate is proposed in this paper to adaptively adjust the rotation angle, according to the evolution generations and the adapt to degree of the value to adaptive dynamic adjustment of the rotation angle, resulting a better global search capability. At the same time, in order to prevent the extramalization of the probability amplitudes and falling into local optimal algorithm, this paper adopted the H ε gate on the probability amplitude of the rotation to make the corrective manipulation. The comparative experimental results showed that the algorithm's stability and accuracy have been greatly improved in solving the TSP problem, compared with the conventional quantum evolutionary algorithm.
In this paper, quantum rotate gate is improved, which is the main operation in the population update of the traditional quantum evolutionary algorithm. A new rotation angle is defined, preventing the algorithm from easily falling into local optimum state in the middle and late term. Based on the characteristics of TSP, a modified quantum rotate gate is proposed in this paper to adaptively adjust the rotation angle, according to the evolution generations and the adapt to degree of the value to adaptive dynamic adjustment of the rotation angle, resulting a better global search capability. At the same time, in order to prevent the extramalisation of the probability amplitudes α and β falling into local optimal algorithm, this paper adopted the Hε gate on the probability amplitude of the rotation to make the corrective manipulation. The comparative experimental results showed that the algorithm's stability and accuracy have been greatly improved in solving the TSP problem, compared with the conventional quantum evolutionary algorithm.
This paper proposes a new quantum particle swarm optimization algorithm with local attracting (LAQPSO), which is based on quantum-inspired evolutionary algorithm (QEA) and particle swarm optimization algorithm (PSO).In the proposed LAQPSO, a novel quantum bit expression mechanism called quantum angle is employed to encode the solution onto particle, and a new local attractor is proposed to determine the rotation angle of quantum rotation gate automatically.During the process of seeking the global solution, the magnitude of rotation angle is adjusted by an important parameter called contraction coefficient, which can quantitatively determine the tradeoff between exploration ability and exploitation ability.The simulation results for different contraction coefficients are helpful for selecting the key parameter.A set of benchmark functions are used to evaluate the performance of LAQPSO, QEA and QBPSO, and the results show that the proposed algorithm has a fast convergence rate and can effectively avoid premature convergence.
A quantum evolutionary computation (QEC) algorithm with particle swarm optimization (PSO) and two-crossovers is proposed to overcome identified limitations. PSO is adopted to update the Q-bit automatically, and two-crossovers are applied to improve the convergence quality in the basic QEC model. This hybrid strategy can effectively employ both the ability to jump out of the local minima and the capacity of searching the global optimum. The performance of the proposed approach is compared with basic QEC on the standard unconstrained scalable benchmark problem that numerous hard combinatorial optimization problems can be formulated. The experimental results show that the proposed method outperforms the basic QEC quite significantly.
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.