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Open Journal of Optimization

Quantum-Inspired Bee Colony Algorithm

Guorui Li, Sun Mu, Panchi Li

Published Jan 1, 2015• 7 citations
Publisher

Abstract

To enhance the performance of the artificial bee colony optimization by integrating the quantum computing model into bee colony optimization, we present a quantum-inspired bee colony optimization algorithm. In our method, the bees are encoded with the qubits described on the Bloch sphere. The classical bee colony algorithm is used to compute the rotation axes and rotation angles. The Pauli matrices are used to construct the rotation matrices. The evolutionary search is achieved by rotating the qubit about the rotation axis to the target qubit on the Bloch sphere. By measuring with the Pauli matrices, the Bloch coordinates of qubit can be obtained, and the optimization solutions can be presented through the solution space transformation. The proposed method can simultaneously adjust two parameters of a qubit and automatically achieve the best match between two adjustment quantities, which may accelerate the optimization process. The experimental results show that the proposed method is obviously superior to the classical one for some benchmark functions.

DOI
10.4236/ojop.2015.43007

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To enhance the performance of the artificial bee colony optimization by integrating the quantum computing model into bee colony optimization, we present a quantum-inspired bee colony optimization algorithm. In our method, the bees are encoded with the qubits described on the Bloch sphere. The classical bee colony algorithm is used to compute the rotation axes and rotation angles. The Pauli matrices are used to construct the rotation matrices. The evolutionary search is achieved by rotating the qubit about the rotation axis to the target qubit on the Bloch sphere. By measuring with the Pauli matrices, the Bloch coordinates of qubit can be obtained, and the optimization solutions can be presented through the solution space transformation. The proposed method can simultaneously adjust two parameters of a qubit and automatically achieve the best match between two adjustment quantities, which may accelerate the optimization process. The experimental results show that the proposed method is obviously superior to the classical one for some benchmark functions.
To solve the problems of slow convergence speed and easily getting into local optimal value for Artificial Bee Colony(ABC) algorithm,a new quantum optimization algorithm was proposed by combining quantum theory and artificial colony algorithm.This algorithm expanded the quantity of the global optimal solution and improved the probability of achieving the global optimal solution by using Bloch coordinates of quantum bit encoding food sources in the artificial colony algorithm;then food sources were updated by quantum rotation gate.This paper put forward a new method for determining the relationship between the two rotation phases in the quantum rotation gate.When the ABC algorithm searched as the equal area on the Bloch sphere,it was proved that the size of the two rotation phases in the quantum rotation gate approximated to the inverse proportion.This avoided blind arbitrary rotation and made the search regular when approaching the optimal solutions.The experiments of two typical optimization issues show that the algorithm is superior to the common Quantum Artificial Bee Colony(QABC) and the simple ABC in both search capability and optimization efficiency.
To enhance the performance of the intelligent optimization algorithm, a new model of performing search on the Bloch sphere is proposed. Then, by integrating the model into the artificial fish swarm optimization, we present a quantum-inspired artificial fish swarm optimization algorithm. In proposed method, the fishes are encoded with the qubits described on the Bloch sphere. The vector product theory is adopted to establish the axis of rotation, and the Pauli matrices are used to construct the rotation matrices. The four fish behaviors, such as moving, tracking, capturing, aggregating, are achieved by rotating the current qubit about the rotation axis to the target qubit on the Bloch sphere. The Bloch coordinates of qubit can be obtained by measuring with the Pauli matrices, and the optimization solutions can be presented through the solution space transformation. The highlight advantages of this method are the ability to simultaneously adjust two parameters of a qubit and automatically achieve the best match between two adjustment quantities, which may accelerate the optimization process. The experimental results show that the proposed method obviously outperforms the classical one in convergence speed and achieves better levels for some benchmark functions.
To enhance the performance of quantum-behaved PSO, some improvements are proposed. First, an encoding method based on the Bloch sphere is presented. In this method, each particle carries three groups of Bloch coordinates of qubits, and these coordinates are actually the approximate solutions. The particles are updated by rotating qubits about an axis on the Bloch sphere, which can simultaneously adjust two parameters of qubits, and can automatically achieve the best matching of two adjustments. The optimization process is employed in the n-dimensional space [-1, 1]n, so this approach fits to many optimization problems. The experimental results show that this algorithm is superior to the original quantum-behaved PSO.
To improve the efficiency of particle swarm optimization, a quantum particle swarm optimization algorithm is proposed on the basis of analyzing the search process of particle swarm optimization algorithm. In the proposed algorithm, particles are endoded by qubits described on the Bloch sphere, each particle occupy three locations of the search space, and each location represents a optimization solution. By employing the search method of general PSO to adjust the two parameters of qubit, the qubits rotation are performed on the Bloch sphere, which can simultaneously update three locations occupied by a qubit and quickly approach the global optimal solution. The experimental results of standard test function extreme optimization and fuzzy controller parameters optimization show that the proposed algorithm is superior to other similar algorithm in optimization ability and optimization efficiency.
To design a novel intelligence algorithm for discrete optimisation problem, a simple quantum-inspired bee colony algorithm (SQBCA) is proposed. The proposed SQBCA applies the quantum computing theory to bee colony optimisation (BCO), which is an effective discrete optimisation algorithm. Then the proposed simple quantum-inspired bee colony algorithm is used to solve benchmark functions and multiuser detection problems of code division multiple access (CDMA) system. By hybridising the bee colony optimisation and quantum computing theory, the quantum state and binary state of the quantum bees can be well evolved by simulated quantum rotation gate and simulated quantum not gate. The new robust multiuser detection based on SQBCA can search the global optimal solution. Simulation results for CDMA systems are provided to show that the proposed robust multiuser detection method is superior to the multiuser detection based on previous intelligence algorithms.
To improve the efficiency of particle swarm optimization,a quantum particle swarm optimization algorithm is proposed on the basis of analyzing the search process of particle swarm optimization algorithm.In the proposed algorithm,particles are endoded by qubits described on the Bloch sphere,each particle occupy three locations of the search space,and each location represents a optimization solution.By employing the search method of general PSO to adjust the two parameters of qubit,the qubits rotation are performed on the Bloch sphere,which can simultaneously update three loations occupied by a qubit and quickly approach the global optimal solution.The experimental results of standard test function extreme optimization and fuzzy controller parameters optimization show that the proposed algorithm is superior to other similar algorithm in optimization ability and optimization efficiency.