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Solving TSP By Quantum-inspired ant Algorithm

Ma Liang

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

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.

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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.
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.
A novel self-adaptive Ant Colony Optimization algorithm based on Quantum mechanism for Traveling salesman problem(TQACO) is proposed. Firstly, initializing the population of the ant colony with superposition of Q-bit, Secondly, using self-adaptive operator, namely in prophase we use higher probability to explore more search space and to collect useful global information; otherwise in anaphase we use higher probability to accelerate convergence. This mechanism offers the ability to escape from local optima and can self-regulate the production of diverse antibodies. Because of the quantum superposition and rotation it can maintain quite nicely the population diversity than the classical evolutionary algorithm, because of the self-adaptive operator it can obtain more optimal solution and the solution quality is improved significantly. TSP benchmark instances Chn144 results demonstrate the superiority of TQACO in this paper.
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 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.
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.