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World Congress on Intelligent Control and Automation

A Novel Quantum Evolutionary Algorithm and Its Application

Hui Gao, Guanghui Xu, Zheren Wang

Published Jan 1, 2006• 14 citations
Publisher

Abstract

Based on the probability amplitude ratio of the corresponding states of quantum bits, the rotation angle of quantum rotation gate is calculated adaptively and a new quantum rotation gate is constructed. A novel quantum evolutionary algorithms (NQEA), whose core is that the designed quantum rotation gate is used as evolutionary strategy is introduced, rapid convergence and good global search capability characterize the performance of NQEA, and NQEA is able to possess the two characteristics of exploration and exploitation, simultaneously. NQEA is applied on the physical distribution vehicle routing problem - a typical combinatorial optimization problem, the results show that NQEA is superior to the previous quantum evolutionary algorithm as well as other conventional genetic algorithms

DOI
10.1109/wcica.2006.1713048

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Based on the probability amplitude ratio of the corresponding states of quantum bits, the rotation angle of quantum rotation gate is calculated adaptively and a new quantum rotation gate is constructed. A novel quantum evolutionary algorithms (NQEA), whose core is that the designed quantum rotation gate is used as evolutionary strategy is introduced, rapid convergence and good global search capability characterize the performance of NQEA, and NQEA is able to possess the two characteristics of exploration and exploitation, simultaneously. NQEA is applied on the physical distribution vehicle routing problem - a typical combinatorial optimization problem, the results show that NQEA is superior to the previous quantum evolutionary algorithm as well as other conventional genetic algorithms
The method of calculating rotation angle of quantum rotation gate plays an important role to the performance of quantum evolutionary algorithm (QEA). This paper proposes an improved quantum evolutionary algorithm (IQEA), whose core is that a new approach of adaptive calculating rotation angle of quantum rotation gate is designed on the basis of the probability amplitude ratio of the corresponding states. Rapid convergence and good global search capability characterize the performance of IQEA. Based on a typical combinatorial optimization problem - 0/1 knapsack problems, the influence of the relative parameter to the performance of IQEA is demonstrated, and then comparing experiments have been done. The results show that IQEA is superior to the previous quantum evolutionary algorithm.
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In this paper, we propose a novel quantum-inspired evolutionary algorithm, called NQEA, for solving combinatorial optimization problems. NQEA uses a new Q-bit update operator to increase the balance between the exploration and exploitation of the search space. In the operator, first, the Q-bits of each individual in the population are updated based on the personal best measurement of that individual and the best measurement of current generation. Then, a restriction is applied to each Q-bit to prevent the premature convergence of its values. The results of experiments on the 0-1 knapsack and NK-landscapes problems show that NQEA performs better than a classical genetic algorithm, CGA, and two quantum-inspired evolutionary algorithms, QEA and vQEA, in terms of convergence speed and accuracy.
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In this paper, quantum rotate gate is improved, which is the main operation in the population update of the traditional quantum evolutionary algorithm. A new rotation angle is defined, preventing the algorithm from easily falling into local optimum state in the middle and late term. Based on the characteristics of TSP, a modified quantum rotate gate is proposed in this paper to adaptively adjust the rotation angle, according to the evolution generations and the adapt to degree of the value to adaptive dynamic adjustment of the rotation angle, resulting a better global search capability. At the same time, in order to prevent the extramalisation of the probability amplitudes α and β falling into local optimal algorithm, this paper adopted the Hε gate on the probability amplitude of the rotation to make the corrective manipulation. The comparative experimental results showed that the algorithm's stability and accuracy have been greatly improved in solving the TSP problem, compared with the conventional quantum evolutionary algorithm.