SCIENCE CHINA Information Sciences, Volume 63 , Issue 5 : 159201(2020) https://doi.org/10.1007/s11432-018-9618-2

Hybrid quantum particle swarm optimization algorithm and its application

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  • ReceivedMay 11, 2018
  • AcceptedSep 5, 2018
  • PublishedSep 10, 2019


There is no abstract available for this article.


This work was supported by National Natural Science Foundation of China (Grant Nos. 71571091, 71771112, 61473054).


Appendixes A–E.


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  • Figure 1

    (Color online) GSTs of Au($n$) $(n=12,\ldots,30)$ clusters achieved by HQPSO.


    Algorithm 1 HQPSO

    Require:The population size $M$, maximum iteration number $T$, search range $[X_{\rm~min},~X_{\rm~max}]$, step length factors $\lambda$ and parameter $L$;

    Output:Obtain the best solution $G$ and best fitness value Fg of the problem;

    $t=1$; initialize the population, calculate the fitness value of each particle, and record the personal best solution ${\rm~Pb}_{i}$ and its fitness ${\rm~Fb}_{i}$, the globe best solution $G$ and its fitness Fg;

    while $t<T$ do

    for $i$ to $M$

    if ${\rm~rand}<\psi$ ($\psi$ is calculated using Eq. (6)) then

    if ${\rm~rand}<0.5$ then

    Execute global search strategy using Eq. (2);


    Execute local search strategy using Eq. (3);

    end if


    Execute enhanced search strategy usingEq. (5);

    end if

    Calculate the fitness of each new particle; update ${\rm~Pb}_{i}$ and $~{\rm~Fb}_{i}$, $G$ and Fg by using greedy selection method;

    if fitness of ${\rm~Pb}_{i}$ has not updated in recent $L$ iterations then

    Execute hopping operation using Eq. (4);

    end if

    end for


    end while