Canonical and real-world network datasets for comparison experiments.

(RAR)</p

A parallel adaptive quantum genetic algorithm for the controllability of arbitrary networks - Fig 9

<p>Fitness and penalty curves as a function of iterating generation for (a) ER with ⟨k⟩ = 4.0, (b) SF with ⟨k⟩ = 4.0 and γ = 2.1, and (c) SW with ⟨k⟩ = 4.0. The red dotted line with a square is the best fitness corresponding to D_best at the current generation, the blue dashed line with a circle is the mean fitness of all control schemes at each generation, and the black line with a triangle is the penalty term corresponding to D_best at each generation.</p

N_cm as a function of H.

(a) Ncm as a function of H for ER and SF networks with fixed γ and variable ⟨k⟩. (b) Ncm as a function of H for ER, SF, and SW networks with variable γ and fixed ⟨k⟩. The networks are directed with N = P = 500.</p

Characteristics of the addressed networks.

<p>Red stars represent the node in-degree denoted by ⟨k_in⟩ and the green diamonds represent the node out-degree denoted by ⟨k_out⟩. (a) Random regular networks with homogeneous degree distribution of ⟨k_in⟩ = ⟨k_out⟩ = 4. (b) ER random networks with Poisson degree distribution; the degree heterogeneities rely on the average degree denoted by ⟨k⟩. (c) SF networks with power-law degree distribution, which results in large degree heterogeneities. (d) SW networks with long-tail degree distribution, which decreases much slower than the SF distribution.</p

Chromosome encoding in quantum genetic algorithm.

Chromosome encoding in quantum genetic algorithm.</p

Performance comparison of PAQGA, MMT, and MM on several large real-directed, -weighted and–unweighted networks in terms of N_cm and computational time.

<p>For data sources, see Supplementary information <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0193827#pone.0193827.s001" target="_blank">S1 Dataset</a>.</p

Performance comparison of PAQGA and parallel GA on different networks using eight MATLAB® workers in terms of n_cm, the minimum iterating generations, and computational time.

<p>For data sources, see Supplementary information <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0193827#pone.0193827.s001" target="_blank">S1 Dataset</a>.</p

Flow chart of the PAQGA.

<p>Flow chart of the PAQGA.</p

Performance comparison of PAQGA, GA, and EO on different networks in terms of <i>n</i>_<i>cm</i>, the minimum iterating generations, and computational time.

<p>Power-law index of SF networks in these experiments was γ = 2.1. ‘/’ indicates that the corresponding results were not available for the computational time limit. For data sources, see Supplementary information <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0193827#pone.0193827.s001" target="_blank">S1 Dataset</a>.</p

Impact of and C on N_cm of SW networks.

<p>(a) N_cm as a function of with fixed C. When C = 1, the network is fully connected and can be steered to any state with only one controller. (b) N_cm as a function of C with fixed ⟨k⟩. Networks are directed with N = P = 500.</p