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Control theory & applications

Quantum ant colony algorithm for continuous space optimization

Shiyong Li

Published Jan 1, 2008• 19 citations
OpenAlex

Abstract

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.

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Computer Engineering and Applications Journal•Jan 1, 2013•0 citations
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.
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 ant colony optimization which was only suitable for the discrete optimization and the problem of slow convergence,this paper proposed a suitable quantum ant colony optimization algorithm for continuous optimization. The locations of ant were directly encoded by the phase of qubits in the proposed algorithm. First,determined the destination to move according to the select probability constructed by the pheromone information and heuristic information,and then updated the qubits of ant by quantum rotation gates to achieve ant moving,and mutated by quantum Pauli-Z gates to increase diversity of ants. Finally,updated the pheromone information and the heuristic information in the new location of ants. As performed the optimization in [0,2π]n ,which had nothing to do with the specific issues,hence,the proposed method had good adaptability for a variety of optimization problems. With applications of function extremum and controller parameters optimization,the simulation results show that the proposed algorithm is superior to the continuous quantum ant colony algorithm and the standard genetic algorithm in both search capability and optimization efficiency.
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 shortcoming of ant colony optimization which was only suitable for the discrete optimization and the problem of slow convergence,a suitable quantum ant colony optimization algorithm for continuous optimization was proposed.The locations of ant were directly encoded by the phase of qubits in the proposed algorithm.First,the destination to move was determined according to the select probability constructed by the pheromone information and heuristic information,then the qubits of ant were updated by quantum rotation gates to achieve ant moving,and mutated by quantum Pauli-Z gates to increase diversity of ants.Finally,the pheromone information and the heuristic information were updated in the new location of ants.As the optimization is performed in[0,2π]~n,which has nothing to do with the specific issues,hence,the proposed method has good adaptability for a variety of optimization problems. With applications of function extremum and clustering optimization,the simulation results show that the proposed algorithm is superior to the common ant colony optimization algorithm and the standard genetic algorithm in both search capability and optimization efficiency.
According to extension of ant colony optimization converging slowly and easily falling into the local optimum,some improved strategies were presented.First,a group of quantum bits which represent the position of the ant increased the diversity of the solution.Secondly,some quantum bits were mutated by a quantum non-gate so as to avoid ants involving in the local optimum.Thirdly,quantum bits of the ant were updated by quantum rotation gates and Gaussian kernel functions so as to find the optimization in continuous space.Lastly,in order to obtain the optimal solution quickly and increase the direction,the weight of each solution in the memory was improved by the importance of the weight.The simulation and comparison on the many two-dimensional and multi-dimensional continuous functions prove the effectiveness of the algorithm.
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.