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Journal of Computer Applications

Ant colony optimization of quantum harmonic oscillators

Meng Yu

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

The authors analyzed the current problems of ant colony algorithm and the advantages of improved algorithm,and then found that the physical properties of quantum harmonic oscillators would guarantee the convergence of final algorithm.Changing process of the quantum harmonic oscillators from high energy state to low energy state and increment of pheromone had a corresponding relationship,and thereby updated pheromone,and physically it provided the algorithmic theoretical basis.Quantum rotation door changed the transfer rules of city.Mutations by Pauli matrix allowed ants have a wider space.Integrating the above advantages of quantum harmonic oscillator,the authors proposed a quantum harmonic oscillator ant colony algorithm,and achieved better optimization path in the Traveling Saleman Problem(TSP) problems.

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The authors analyzed the current problems of ant colony algorithm and the advantages of improved algorithm,and then found that the physical properties of quantum harmonic oscillators would guarantee the convergence of final algorithm.Changing process of the quantum harmonic oscillators from high energy state to low energy state and increment of pheromone had a corresponding relationship,and thereby updated pheromone,and physically it provided the algorithmic theoretical basis.Quantum rotation door changed the transfer rules of city.Mutations by Pauli matrix allowed ants have a wider space.Integrating the above advantages of quantum harmonic oscillator,the authors proposed a quantum harmonic oscillator ant colony algorithm,and achieved better optimization path in the Traveling Saleman Problem(TSP) problems.
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.
For the low efficiency and poor performance of the ant colony algorithm in solving TSP problems, a new quantum ant colony algorithm proposed. The models of probability selection and pheromone are redefined, integrated with the quantum information intensity factor; The factor updated by quantum rotating gate according to iteration process; Some important parameters are self-adapted controlled at the same time; And 3-opt is used to further local optimization. Stimulation shows the performance is greatly improved.
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.
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.
The algorithm in this paper is based on the combination of Quantum Evolutionary algorithm (QEA) and Ant Colony System (ACS), a new algorithm, Quantum Ant Colony Algorithm (QACA) is proposed in this paper. The core is that Q-bit and quantum rotation gate adopted in QEA are introduced into ACS to represent and update the pheromone respectively, so it has better diversity and global search capacity. The experimental result demonstrates that QACA can get better solutions to some Traveling Salesman Problems (TSP) than the solutions given in TSPLIB
The algorithm is based on the combination of quantum evolutionary algorithm(QEA) and ant colony system(ACS),a new algorithm,quantum ant colony algorithm(QACA) is proposed.The core is that Q-bit and quantum rotation gate adopted in QEA are introduced into ACS to represent and update the pheromone respectively,so it has better diversity and global search capacity.The ex-perimental result demonstrates that QACA can get better solutions to some traveling salesman problems(TSP) than the solutions given in existing bibliographer,it indicate that the algorithm is effective to solve TSP.