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A quantum-inspired ant colony algorithm for graph coloring problem

Ma Liang

Published Jan 1, 2013• 2 citations
OpenAlex

Abstract

A quantum-inspired ant colony algorithm(QACA) for the classic graph coloring problem is proposed based upon the combination of ant colony optimization and quantum computing.The quantum bits and quantum logic gates are introduced to the ant colony algorithm(ACA),and the disadvantage of getting into the local optimum can be effectively avoided.The computational speed of the algorithm is therefore significantly improved.Series of simulation instances of the graph coloring problem are tested.And the results show that the QACA is a feasible,effective and versatile method for solving the graph coloring problem.

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A quantum-inspired ant colony algorithm(QACA) for the classic graph coloring problem is proposed based upon the combination of ant colony optimization and quantum computing.The quantum bits and quantum logic gates are introduced to the ant colony algorithm(ACA),and the disadvantage of getting into the local optimum can be effectively avoided.The computational speed of the algorithm is therefore significantly improved.Series of simulation instances of the graph coloring problem are tested.And the results show that the QACA is a feasible,effective and versatile method for solving the graph coloring problem.
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
Quantum-inspired ant algorithm is a novel optimization method for solving real problems by using both the quantum information rules and the characteristics of ant colony optimization.This paper solves the classical TSP by quantum-inspired ant algorithm through series of typical instances.The computational results show the effectiveness and robustness of the algorithm in numerical simulation.It can find the satisfactory solutions with small size population and tiny relative error,even for medium or larger problem instances.
Based on the combination of the quantum theory and ant colony optimization,a novel algorithm,the quantum ant colony algorithm,was proposed.Ants's positions were represented by a group of quantum bits and the quantum rotation gates were designed to update the ants' positions for enabling the ants' movements.The classical TSP was successfully solved by using the quantum ant colony algorithm,taking series of typical instances as the examples.The computational results show the effectiveness and robustness of the algorithm in numerical simulations.The algorithm can find the satisfactory solutions with a small size of populations and minimal relative error.
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 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.
Quantum ant colony optimization (QACO) has drew much attention since it combines the advantages of quantum computing and ant colony optimization (ACO) algorithms and overcomes some limitations of the traditional ACO algorithm. However, due to the hardware resource limitations of currently available quantum computers, such as the limited number of qubits, lack of high-fidelity gating operation, and low noisy tolerance, the practical application of the QACO is quite challenging. In this paper, we introduce a hybrid quantum-classical algorithm by combining the clustering algorithm with QACO algorithm, so that this extended QACO can handle large-scale optimization problems, which makes the practical application of QACO based on available quantum computation resource possible. To verify the effectiveness and performance of the algorithm, we tested the developed QACO algorithm with the Travelling Salesman Problem (TSP) as benchmarks. The developed QACO algorithm shows better performance under multiple data set. In addition, the developed QACO algorithm also manifests the robustness to noise of calculation process, which is typically a major barrier for practical application of quantum computers. Our work shows that the combination of the clustering algorithm with QACO has effectively extended the application scenario of QACO in current NISQ era of quantum computing.