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The Open Automation and Control Systems Journal

Solving High Dimensional and Complex Non-convex Programming Based on Improved Quantum Artificial Fish Algorithm

Yang Hu, Tingsong Du, Jinhui Wu, Xianhui Liu, Deyi Li, Wenwu Li

Published Sep 16, 2014• 3 citations
Publisher

Abstract

An improved quantum artificial fish swarm algorithm is proposed in this paper.Based on that quantum computing have exponential acceleration for heuristic algorithm, by examining eight most recent patents and some literatures in the area of artificial fish swarm algorithm and quantum computing.The new algorithm uses qubits to code artificial fish and quantum revolving gate, preying behavior, following behavior and variation of quantum artificial fish to update the artificial fish for searching for optimal value.Then, apply the new algorithm, the basic artificial fish swarm algorithm and the global edition artificial fish swarm algorithm to the simulation experiment high dimensional and complex non-convex programming respectively.The simulation results show that the improved algorithm can escape from the local extremum effectively, and has higher convergence speed and precision.

DOI
10.2174/1874444301406010129

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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.
In view of the shortcomings of particle swarm optimization such as premature convergence to local optimization, particle swarm optimization algorithm based on quantum gate and particle swarm optimization algorithm based on quantum behavior are studied in this paper. The first algorithm uses the random observation method of quantum bit coding particles to simulate quantum particle collapse for generating a population and uses the quantum rotating gate to generate a new population. The adaptive mutation operator is used for ensuring the diversity of the population, effectively reducing the impact of local optimization; therefore, the robustness of the algorithm is improved. The second algorithm uses the probability density function of quantum computation to make the particles jump out of the local extreme points and fulfils the global search, which is more suitable for continuous optimization. The results of computational experiments show that both the two particle swarm optimization algorithms based on quantum technology have a good global convergence.
The Ant Colony Algorithm is an effective method for solving combinatorial optimization problems. However, in practical applications, there also exist issues such as slow convergence speed and easy to fall into local extremum. This paper proposes an improved Quantum Ant Colony Algorithm based on Bloch coordinates by combining Quantum Evolutionary Algorithm with Ant Colony Algorithm. In this algorithm, the current position information of ants is represented by the Bloch spherical coordinates of qubits; position update, position variation and random behavior of ants are all achieved with quantum rotation gate. Simulations of function extremum problem, TSP problem and QoS multicast routing problem were conducted, the results indicated that the algorithm could overcome prematurity, with a faster convergence speed and higher solution accuracy.
In order to improve the slow convergence speed and avoid falling into the local optimum in ant colony optimization algorithm, an improved quantum ant colony optimization (IMAQACO) algorithm based on combing quantum evolutionary algorithm with ant colony optimization algorithm is proposed for solving complex function problems in this paper.In the IMAQACO algorithm, the quantum state vectors are used to represent the pheromone, the adaptively dynamical updating strategy is used to control pheromone evaporation factor, the quantum rotation gate is used to realize the ant movement and change the convergence tend of quantum probability amplitude, quantum non-gate is used to realize ant location variation, so the IMAQACO algorithm has better global search ability and population diversity than ACO algorithm.In order to test the optimization performance of IMAQACO algorithm, several benchmark functions are selected in here.The tested results indicate that the IMAQACO can effectively improve the convergence speed and avoid falling into the local optimum, and has a stronger global optimization ability and higher convergence speed in solving complex function problems.