DOC

A New Quantum Clone Evolutionary Algorithm for Multi-objective Optimization

By James Moore,2014-08-13 16:37
11 views 0
A New Quantum Clone Evolutionary Algorithm for Multi-objective Optimization

    数量经济理论与方法?一,?计量经济学等,

    A New Quantum Clone Evolutionary Algorithm

    for Multi-objective Optimization

     Zhoufangzhao, Quzhentao, Zhouzheng

     (The Research Center of Economics, Harbin University of Commerce, Harbin 150028, P.R. China)

    Email:fangzhaozhou@yahoo.com.cn

    Abstract: Most of the quantum inspired evolution algorithms(QEA) is improved and used for the optimization of continuous functions with multi-peak now, However, they are easy to be trapped into the 1ocal deceptive peakIn this papera new improved quantum evolution algorithm is proposed to overcome the shortcoming of traditional QEA. The new improved QEA combines the main mechanisms of clone (QCEA). Every individual of each chromosome will make its own dynamic clone to build its new sub-swarm; then every new chromosome will be mutation in its low bit; at last, the QCEA will update the whole swarm by using random strategy. The algorithm not only has the global searching capacitybut also

    improves the local searching capacity of algorithm by using quantum probabilistic searchExperiments are

    implemented and compared with other QEAs. The result indicates that the new algorithm in this paper can search and get the global optimum solution in a shorter time.

Keywords: Quantum Clone Evolution Algorithm, Clone, Mutation

作者简介(

    周方召?1978—,(男!在读博士研究生!哈尔滨商业大学经济研究中心讲师。

    联系方式(fangzhaozhou@yahoo.com.cn

    曲振涛?1957—,(男!博士、教授、博士生导师!哈尔滨商业大学经济研究中心教授!

     正?1975—,(男!在读博士研究生!哈尔滨商业大学经济研究中心副教授。

    A New Quantum Clone Evolutionary Algorithm

    for Multi-objective Optimization

     Zhoufangzhao, Quzhentao, Zhouzheng

     (The Research Center of Economics, Harbin University of Commerce, Harbin 150028, P.R. China)

    Email:fangzhaozhou@yahoo.com.cn

    Abstract: Most of the quantum inspired evolution algorithms(QEA) is improved and used for the optimization of continuous functions with multi-peak now, However, they are easy to be trapped into the 1ocal deceptive peakIn this papera new improved quantum evolution algorithm is proposed to overcome

    the shortcoming of traditional QEA. The new improved QEA combines the main mechanisms of clone (QCEA). Every individual of each chromosome will make its own dynamic clone to build its new sub-swarm; then every new chromosome will be mutation in its low bit; at last, the QCEA will update the whole swarm by using random strategy. The algorithm not only has the global searching capacitybut also

    improves the local searching capacity of algorithm by using quantum probabilistic searchExperiments are

    implemented and compared with other QEAs. The result indicates that the new algorithm in this paper can search and get the global optimum solution in a shorter time.

Keywords: Quantum Clone Evolution Algorithm, Clone, Mutation

    I INTRODUCTION [1]Quantum Evolutionary Algorithm is a new probability optimization method based on quantum

    calculation theory. QEA has triumphantly applied to the optimization of continuous and low dimensionality

    [25]functions of multi-peak. However, when QEA is used to deal with the complex functions, it will

    [6]definitely become slow converging speed and prematurity. In He’s paper, he proposed an improved QEA,

    firstly he divided domain into a lot of parts, then he get the best solution in each small part. His result indicates that his algorithm will overcome the prematurity, but this algorithm inevitably increases the

    [7]complexity at the same time. In Xie’s paper, he attempts to make a new hybrid quantum evolution

    algorithm, and the result indicates that the new hybrid QEA is better than QEA in both quality of final result and the convergence rate. This algorithm has obvious advantage when it is used for the optimization of continuous and low dimensionality functions with one-peak, however, when it is not fit for the high and low

    [8]dimensionality functions with multi-peak. Li is the pioneer to import the mechanisms of clone to QEA,

    he design a new quantum inspired evolution algorithm which can be used for solving the prematurity effectively in a shorter time, however, the fact of Li’s algorithm is just combine the theory of quantum with the mechanisms of clone simply, and the result of clone is to copy each chromosome to keep the diversity of the solution space of functions, so when the chromosome is replaced with quantum gate, the probability of the diversity of the solution space of functions will be increased. This is a good change as a new QEA, but we should find two problems, firstly, the result of clone is just increase the probability to get the best individual of chromosome, it will not help to improve the algorithm’s search space; secondly, when Li begin to delete the chromosome simply in order to keep the scale of the swarm after replacing chromosome with quantum gate, it will enhance the probability of degradation of the solution space.

    In this paper, the mechanisms of clone will be imported into QEA, and apply it to the optimization of continuous and low and high dimensionality functions of multi-peak, it is testified that this new algorithm improves from two points: search capability and computing time.

    II. OVERVIEW OF QEA

    QEA relies on a basic concept which is quantum bit or qubit. A qubit can take value 0, 1 or a superposition of the two at the same time. Its state can be defined by:

     (1) 0;(1

    Where and represent the classical bit values 0 and 1 respectively; and, are complex 10(

    2numbers that specify the probability amplitudes of the corresponding states. gives the probability that

    2the qubit will be found in the 0 state and gives the probability that the qubit will be found in the 1 (

    state. Normalization of the state to unity guarantees

    22 (2) ,(;=1

    The state of a qubit can be changed by the operation with a quantum gate. Inspired by the