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Journal of the University of Shanghai for Science and Technology

Application study on hybrid quantum algorithm in traveling salesman problem

Chunming Ye

Published Jan 1, 2009• 1 citation
OpenAlex

Abstract

A novel method of coding was brought forward and the essence of evolutionary algorithm(EA) and particle swarm optimization algorithm(PSO) was put into consideration in terms of the characteristics of Traveling Salesman Problem(TSP),and a distinctive hybrid quantum algorithm(HQA) was constructed.The breakthrough was taken as the means of updating the individual to improve the capability of HQA.Still further,the updating of inertial weight was guided dynamically,and the decision that individual would turn out to be attractive or repulsive in the next iteration was made.This new algorithm is called improved hybrid quantum algorithm(IHQA).The result of the test manifests that both two algorithms are of strong capability in optimum-searching,and IAQA performs better.

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A novel method of coding was brought forward and the essence of evolutionary algorithm(EA) and particle swarm optimization algorithm(PSO) was put into consideration in terms of the characteristics of Traveling Salesman Problem(TSP),and a distinctive hybrid quantum algorithm(HQA) was constructed.The breakthrough was taken as the means of updating the individual to improve the capability of HQA.Still further,the updating of inertial weight was guided dynamically,and the decision that individual would turn out to be attractive or repulsive in the next iteration was made.This new algorithm is called improved hybrid quantum algorithm(IHQA).The result of the test manifests that both two algorithms are of strong capability in optimum-searching,and IAQA performs better.
Hybrid quantum algorithm(HQA) was put forward to solve traveling salesman problems.On the basis of quantum computing,displacement decoding was designed which enables the algorithm to overcome the difficulties in route configuration.Evolutionary mode and best tracing and keeping mode,derived from particle swarm optimization algorithm,were adopted,dynamic inertia weight was configured to update quantum angles effectively,and local optimization was taken to carry out lean search.The capability of HQA to solve traveling salesman problems was demonstrated by the results of several examples.
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.
Inspired by the idea of hybrid optimization algorithms, this paper proposes two hybrid quantum evolutionary algorithms (QEA) based on combining QEA with particle swarm optimization (PSO) to improve the performance of QEA . The main idea of the first method called PSEQEA is to embed the evolutionary equation of PSO in the evolutionary operator of QEA; while the main idea of the second method called PSSQEA is to replace the evolutionary operator of QEA using the evolutionary equation of PSO which is redefined the meanings of the original evolutionary equations. The experiment results of the knapsack problem, the function optimization problems and multiuser detection problem show that the both of the proposed methods not only have simpler algorithm structure, but also perform better than conventional QEA and PSO in terms of ability of global optimum
Managers have focused a lot on the aid of computers since the introduction of scientific management concepts into production process.Job Shop scheduling problem(JSP) is a simplified model which results from many exact production scheduling problems.The tremendous solution space brings big challenge.On the basis of Q-bit coding,two types of decoding are designed, quantum angles can be adjusted intelligently with the help of Particle Swarm Optimization algorithm(PSO) and Hybrid Quantum Algorithm(HQA) is constructed.However,when HQA is employed to solve JSP,the effect is not satisfactory.Under the HQA structure,some optimization mechanisms are introduced,which dramatically improve the capability of the algorithm,and the new algorithm is denoted as Improved Hybrid Quantum Algorithm(IHQA).
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.