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Computer Engineering and Applications Journal

Hybrid quantum algorithm and its application in flow shop problem

Xie Jin-hua

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

Quantum Evolutionary Algorithm(QEA) is a distinctive type of algorithm for optimization currently,and the theoretical basis of QEA is quantum computation.The algorithm takes advantage of intervention and parallelism of quantum bit thoroughly,which enables QEA to solve combinatorial optimization problems.While solving scheduling problems,QEA has defects that it converges slowly and doesn’t use other immature individual.Hybrid Quantum Algorithm(HQA) is formed and it sucks Particle Swarm Optimization algorithm(PSO) and evolutionary computation into QEA.Classical flow shop problem is employed to test the algorithm,and the result shows that the hybrid algorithm overcomes the defects of QEA and it has universality to solve scheduling problems.

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Journal of the University of Shanghai for Science and Technology•Jan 1, 2009•1 citation
Quantum Evolutionary Algorithm(QEA) is a distinctive type of algorithm for optimization currently,and the theoretical basis of QEA is quantum computation.The algorithm takes advantage of intervention and parallelism of quantum bit thoroughly,which enables QEA to solve combinatorial optimization problems.While solving scheduling problems,QEA has defects that it converges slowly and doesn’t use other immature individual.Hybrid Quantum Algorithm(HQA) is formed and it sucks Particle Swarm Optimization algorithm(PSO) and evolutionary computation into QEA.Classical flow shop problem is employed to test the algorithm,and the result shows that the hybrid algorithm overcomes the defects of QEA and it has universality to solve scheduling problems.
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).The main idea of the first method called PSEQEA is to embed the evolutionary equation of PSO in QEA;while the main idea of the second method called QBPSO is to apply the quantum chromosomes of QEA to binary PSO(BPSO).The experiment results of the knapsack problem 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 BPSO 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).
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
This paper proposes a novel evolutionary algorithm inspired by quantum computing, called a quantum-inspired evolutionary algorithm (QEA), which is based on the concept and principles of quantum computing, such as a quantum bit and superposition of states. Like other evolutionary algorithms, QEA is also characterized by the representation of the individual, evaluation function, and population dynamics. However, instead of binary, numeric, or symbolic representation, QEA uses a Q-bit, defined as the smallest unit of information, for the probabilistic representation and a Q-bit individual as a string of Q-bits. A Q-gate is introduced as a variation operator to drive the individuals toward better solutions. To demonstrate its effectiveness and applicability, experiments were carried out on the knapsack problem, which is a well-known combinatorial optimization problem. The results show that QEA performs well, even with a small population, without premature convergence as compared to the conventional genetic algorithm.
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.
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.