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Journal of Computers

Improved Quantum Ant Colony Algorithm based on Bloch Coordinates

Xiaofeng Chen, Xingyou Xia, Ruiyun Yu

Published May 18, 2013• 2 citations
Publisher

Abstract

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.

DOI
10.4304/jcp.8.6.1536-1543

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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.
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.
Aiming at the Traveling Salesman Problem based on ant colony optimization which is easy to fall into local optimums and has a slow convergence rate,a hybrid quantum ant colony optimization algorithm is presented.In this algorithm,the pheromone on each path is encoded by a group of quantum bits,the quantum rotation gate and ant's tour are used to update the pheromone so as to accelerate its convergence speed.To avoid the search falling into local optimum,the new neighborhood exchange strategy is designed to improve solution efficiency.Some cases from the TSP library(TSPLIB)are used to experiment,the results show that the algorithm has rapider convergence speed and higher accuracy than the classical ant colony algorithm.
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.
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.
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.