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Systems engineering and electronics

Ant colony algorithm and application based on quantum space

Jiyin Li

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

Aimming at the low convergent rate of the ant colony algorithm(ACA)and the disadvantage of falling into local extremum easily,this paper proposes a method of combining quantum evolutionary algorithms with ACA,which regards two probability amplitudes of quantum bits as current location of ant.When the number of ants is the same,the proposed algorithm makes the search space double and uses the quantum gate to realize the variation operation.Compared with the traditional algorithms,it has better population diversity in the optimization process and effectively avoids the prematurity and stagnation phenomenon of ACA.This method can be used in image segmentation.The experimental results show that this method is effective to solve the slow convergence rate and easy to fall into local extremum problems of ACA,and segmentation speed and precision have been improved greatly.

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Aimming at the low convergent rate of the ant colony algorithm(ACA)and the disadvantage of falling into local extremum easily,this paper proposes a method of combining quantum evolutionary algorithms with ACA,which regards two probability amplitudes of quantum bits as current location of ant.When the number of ants is the same,the proposed algorithm makes the search space double and uses the quantum gate to realize the variation operation.Compared with the traditional algorithms,it has better population diversity in the optimization process and effectively avoids the prematurity and stagnation phenomenon of ACA.This method can be used in image segmentation.The experimental results show that this method is effective to solve the slow convergence rate and easy to fall into local extremum problems of ACA,and segmentation speed and precision have been improved greatly.
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.
Aiming at the shortcoming of optimization problems in continuous space based on ant colony optimization which is easy to fall into local optimums and has a slow convergence rate,a novel quantum ant colony optimization algorithm is presented.In this algorithm,each ant position is represented by a group of quantum bits;a new quantum rotation gates are designed to update the position of the ant so as to enable the ant to move.Some quantum bits are mutated by quantum non-gate so as to increase the variety of ant positions.It not only proves the convergence of the proposed algorithms through theoretical analysis,but also demonstrates that the algorithm can double searching space,maintain better population diversity,rapider convergence speed and global optimal ability than the classical ant colony algorithm by simulation experiments.
To tackle the shortcoming of ant colony optimization which can only be applied to discrete problems and hold a slow convergence rate,a novel method for solving optimization problems in continuous space is presented.In this algorithm,each ant carries a group of quantum bits which represent the position of the ant.Firstly,the target where the ant is going to move is selected according to the selection probability based on pheromone information and heuristic information.Secondly,quantum bits of the ant are updated by quantum rotation gates so as to enable the ant to move.Some quantum bits are mutated by quantum non-gate so as to increase the variety of ant positions.Finally,pheromone information and the heuristic information are updated according to the new position of each ant arrived at.In this algorithm,both probability amplitudes of a quantum bit are regarded as position information belonging to an ant,a double searching space is acquired for ant colony which hold the same number of ants.At last,the availability of the algorithm is illustrated by two application examples of function optimization and weight optimization of neural networks.
Ant Colony Algorithm(ACA) demonstrates the superiority in solving TSP,and Quantum Evolution Algorithm (QEA) has the performance of high efficiency on combinational optimization problems,so combining the thought of ACA with QEA,a novel quantum ant colony algorithm for TSP is proposed.In this algorithm,the pheromone on each path is encoded by a group of quantum bits,and a new pheromone representation is designed,called quantum pheromone.The quantum rotation gate and the best tour are applied to update the pheromone so as to accelerate its convergence speed.To avoid the search falling into local optimum,the strategy of quantum crossover is designed to improve the information structure of population.Simulation results show that the algorithm has fast convergence speed and global optimal ability,and the algorithm is more effective than ACS.
Aiming at the disadvantage of optimization problems based on traditional ant colony optimization (ACO)which easily falls into local optimums and has worse performance in convergence,the paper unifies the quantum evolutionary algorithm (QEA) and the ant colony algorithm,in this algorithm,pheromone is represented by quantum bits and updated by a new quantum rotation gate adjustment srrategy.And this paper applies separately this algorithm and the traditional ACO to traveling salesman problem(TSP),The simulation results show that the algorithm of this paper has excellent global optimization properties and quicker convergence than the traditional ACO.
Aiming at the shortcoming of ant colony optimization of being only suitable for discrete problems and holding a slow convergence speed, a novel algorithm for continuous optimization problems is presented. In this algorithm, each ant carries a group of qubits which represents the position of its own. First, the destination to which ant want to move is selected according to the select probability based on pheromone information and heuristic information. Then, the ant's own qubits are updated by quantum rotation gates so as to move. Some ants' qubits are mutated by quantum non-gate so as to increase the diversity of positions. Finally, both information of the pheromone and the heuristic are updated according to the new position of each ant. In this algorithm, both probability amplitudes of a qubit are regarded as position information, a double searching efficiency is acquired for ant colony which hold the fixed number of ants. The availability of the proposed algorithm is illustrated by simulation examples of function extremum optimization.