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Journal of Jilin University(Science Edition)

Quantum Shuffled Frog Leaping Algorithm for Continuous Space Optimization Problems

Panchi Li

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

A quantum shuffled frog leaping algorithm was proposed which combines with the quantum theory.In this algorithm,the individuals are expressed with Bloch spherical coordinates of qubits,the individual update is realized with the rotation of qubits in Bloch sphere,and the local search capabilities within the subgroup is improved with adaptive chaotic rotation angle operator.Then,to avoid premature convergence,the mutation of individuals is achieved with Hadamard gates.Above operations extend the search of the solution space effectively.Results of experiments show that compared with the SFLA,PSO and GA,the algorithm has a higher optimization capability and efficiency,and is more suitable for high-dimensional optimization of complex functions.

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A quantum shuffled frog leaping algorithm was proposed which combines with the quantum theory.In this algorithm,the individuals are expressed with Bloch spherical coordinates of qubits,the individual update is realized with the rotation of qubits in Bloch sphere,and the local search capabilities within the subgroup is improved with adaptive chaotic rotation angle operator.Then,to avoid premature convergence,the mutation of individuals is achieved with Hadamard gates.Above operations extend the search of the solution space effectively.Results of experiments show that compared with the SFLA,PSO and GA,the algorithm has a higher optimization capability and efficiency,and is more suitable for high-dimensional optimization of complex functions.
To improve the efficiency of Particle Swarm Optimization(PSO),a quantum particle swarm optimization algorithm combined with quantum theory on the basis of Bloch sphere was proposed.In Bloch spherical coordinates,the particle automatically updated rotation angle and particle position,without setting the rotation angle in the form of look-up table(or setting fixed value of the interval),making up for the deficiency of quantum evolutionary algorithm and quantum genetic algorithm on the basis of Bloch sphere,and the algorithm is more generalizable.Using quantum Hadamard gate to realize the variation of particle enhanced the diversity of population,and prompted particle jump out of local extreme value.The simulation results of the typical function optimization problem show that the algorithm is stable with high precision and fast convergence rate,and it is practical.
Aiming at the search speed and accuracy of the shuffled frog leaping algorithm not high, the idea of variation was integrated into the shuffled frog leaping algorithm. A new improved shuffled frog leaping algorithm was proposed which was called quantum frog leaping algorithm. The positions of frog are encoded by the probability amplitudes of quantum bits, the movements of frog are performed by quantum rotation gates, which achieve particles searching. Through the experiments on six standard functions, simulation results show the proposed algorithm has high searching efficiency and precision, Moreover, QSFLA as a promising optimization algorithm has strong convergence and high stability.
A quantum binary shuffled frog leaping algorithm (QBSFLA) is proposed through integrating the theories of the quantum evolutionary algorithm and the shuffled frog leaping algorithm (SFLA). Firstly, the superposition state characteristic of quantum makes the separate individual expresses more states, and the probability expression characteristic makes individuals' states are expressed with certain probability for increasing the diversity of the population potentially. Then, SFLA is used to regulate the phrase of the quantum bit to achieve a balance of the local and global search and improve the run speed. The experi-mental results of three 0-1 knapsack problems solved by QBSFLA with the greedy algorithm show that QBSFLA has several advantages such as fast convergence, powerful global search ability and good stability.
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.
In the existing quantum intelligent optimization algorithms,almost all of the individuals are encoded by qubits described on plane unit circle.Since there is only one adjustable parameter,quantum properties have not been fully embodied,which limits the improvement of the optimization ability further.To address this issue,a chaos quantum immune algorithm based on Bloch sphere is proposed.In the proposed algorithm,the antibodies are encoded by qubits described on Bloch sphere,the axis of rotation is designed by using Pauli matrix,the clone of the excellent antibodies is performed by rotating qubits on Bloch sphere,and the local searching is achieved by employing the chaos variables in the rotation angles.The global searching is achieved by the mutations of the inferior individuals based on the Hadamard gates.The simulation results show that the proposed algorithm is superior to other quantum intelligent optimization algorithms in both search capability and optimization efficiency.
To enhance optimization ability of quantum potential well-based particle swarm optimization algorithm,a quantum particle swarm optimization algorithm based on Bloch spherical search is proposed by analyzing the design of quantum potential well-based particle swarm optimization algorithms.Firstly,particles are expressed with qubits,axis of rotation is established with Pauli matrix,the angle of rotation is obtained with a model of Delta potential well,and search is realized with rotation of qubits in Bloch sphere.Then,to avoid premature convergence,mutation of particles is achieved with Hadamard gates.Such rotation makes current qubit approximates target qubit along with the biggest circle on Bloch sphere,which accelerates optimization process.It shows that the proposed algorithm is superior to the original one in optimization ability.