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Journal of the University of Shanghai for Science and Technology

Solving Large-scale Traveling Salesman Problem by Quantum Ant Colony Algorithm

Ma Liang

Published Jan 1, 2012• 3 citations
OpenAlex

Abstract

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.

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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.
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.
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.
The quantum ant colony algorithm (QACO) is explored as a solution to the traveling salesman problem (TSP), targeting inefficiencies such as slow convergence and local optima entrapment found in traditional ant colony optimization (ACO) methods. By integrating quantum computing elements, specifically quantum rotation gates and qubits, into the ACO framework, QACO demonstrates enhanced efficiency and faster convergence. This paper delves into the foundational principles of quantum computing and their application to refine ACO, effectively solving the TSP. An in-depth analysis is provided, showcasing QACO's advantages over traditional ACO through empirical examples. These examples illustrate QACO's potential to improve path planning for applications within the rapidly growing e-commerce and logistics sectors. The integration of quantum mechanisms facilitates a more dynamic pheromone update process, which significantly reduces the likelihood of premature convergence and enhances solution quality in complex optimization scenarios. This advancement indicates a promising direction for future research in algorithmic optimization in both theoretical and practical applications.
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.
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 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.