Exploratory Landscape Analysis (ELA), also known as Fitness Landscape Analysis, is an umbrella term for sample-based methods that produce one or more features related to the characteristics of the cost function (Mersmann et al., 2011). For this work we employed 33 ELA features listed in Table 1, which have shown to be good predictors of algorithm performance (Bischl et al., 2012; Muñoz and Smith-Miles, 2017). To calculate each of them, we generate an input sample, $X$, of size $D\xd7103$ candidates using Latin hypercube design (LHD). We deem this sample size to be sufficient considering the evidence by Kerschke et al. (2016). The output sample, $Y$, is generated by evaluating $X$ on each instance from the COCO benchmark. By sharing $X$ across instances, we guarantee that the differences observed in the features are not due to sample size or sampling method. Moreover, sharing $X$ reduces the overall computational cost, as no new candidates must be taken from the space. All features were scaled to zero mean and unit standard deviation.

Table 1:

. | Correlations (Jones and Forrest, 1995) . | ||
---|---|---|---|

$FDC$ . | Fitness distance correlation . | . | . |

Average distances (Lunacek and Whitley, 2006) | |||

$DISP1%$ | Dispersion of points within 1% of $yt$ | ||

Surrogate models (Mersmann et al., 2011) | |||

$R\xafL2$ | Adjusted coefficient of determination of a linear model | $R\xafLI2$ | Adjusted coefficient of determination of a linear model including interactions |

$R\xafQ2$ | Adjusted coefficient of determination of a purely quadratic model | $R\xafQI2$ | Adjusted coefficient of determination of a quadratic model including interactions |

$\beta min$ | Minimum of the absolute value of the linear model coefficients | $\beta max$ | Maximum of the absolute value of the linear model coefficients |

$CN$ | Ratio between the minimum and the maximum absolute values of the quadratic term coefficients in the purely quadratic model | $EL10$ | Mean cross-validation accuracy (MCVA) of a Linear Discriminant (LDA) at 10% |

$EQ10$ | MCVA of a Quadratic Discriminant (QDA) at 10% | $ET10$ | MCVA of a Classification and Regression Tree (CART) at 10% |

$LQ10$ | The ratio between $EL10$ and $EQ10$ | $EL25$ | MCVA of a LDA at 25% |

$EQ25$ | MCVA of a QDA at 25% | $ET25$ | MCVA of a CART at 25% |

$LQ25$ | The ratio between $EL25$ and $EQ25$ | $EL50$ | MCVA of a LDA at 50% |

$EQ50$ | MCVA of a QDA at 50% | $ET50$ | MCVA of a CART at 50% |

$LQ50$ | The ratio between the $EL50$ and $EQ50$ | ||

Entropic Significance (Seo and Moon, 2007) | |||

$\xi D$ | Significance of $D$-th order | $\xi 1$ | Significance of first order |

$\sigma 1$ | Standard deviation of the significance of first order | $\xi 1$ | Significance of second order |

$\sigma 2$ | Standard deviation of the significance of second order | ||

$\gamma Y$ | Skewness of the cost distribution | $\kappa Y$ | Kurtosis of the cost distribution |

$HY$ | Entropy of the cost distribution | $PKS$ | Number of peaks of the cost distribution |

Fitness sequences (Muñoz, Kirley et al., 2015) | |||

$Hmax$ | Maximum information content | $\epsilon S$ | Settling sensitivity |

$M0$ | Initial partial information |

. | Correlations (Jones and Forrest, 1995) . | ||
---|---|---|---|

$FDC$ . | Fitness distance correlation . | . | . |

Average distances (Lunacek and Whitley, 2006) | |||

$DISP1%$ | Dispersion of points within 1% of $yt$ | ||

Surrogate models (Mersmann et al., 2011) | |||

$R\xafL2$ | Adjusted coefficient of determination of a linear model | $R\xafLI2$ | Adjusted coefficient of determination of a linear model including interactions |

$R\xafQ2$ | Adjusted coefficient of determination of a purely quadratic model | $R\xafQI2$ | Adjusted coefficient of determination of a quadratic model including interactions |

$\beta min$ | Minimum of the absolute value of the linear model coefficients | $\beta max$ | Maximum of the absolute value of the linear model coefficients |

$CN$ | Ratio between the minimum and the maximum absolute values of the quadratic term coefficients in the purely quadratic model | $EL10$ | Mean cross-validation accuracy (MCVA) of a Linear Discriminant (LDA) at 10% |

$EQ10$ | MCVA of a Quadratic Discriminant (QDA) at 10% | $ET10$ | MCVA of a Classification and Regression Tree (CART) at 10% |

$LQ10$ | The ratio between $EL10$ and $EQ10$ | $EL25$ | MCVA of a LDA at 25% |

$EQ25$ | MCVA of a QDA at 25% | $ET25$ | MCVA of a CART at 25% |

$LQ25$ | The ratio between $EL25$ and $EQ25$ | $EL50$ | MCVA of a LDA at 50% |

$EQ50$ | MCVA of a QDA at 50% | $ET50$ | MCVA of a CART at 50% |

$LQ50$ | The ratio between the $EL50$ and $EQ50$ | ||

Entropic Significance (Seo and Moon, 2007) | |||

$\xi D$ | Significance of $D$-th order | $\xi 1$ | Significance of first order |

$\sigma 1$ | Standard deviation of the significance of first order | $\xi 1$ | Significance of second order |

$\sigma 2$ | Standard deviation of the significance of second order | ||

$\gamma Y$ | Skewness of the cost distribution | $\kappa Y$ | Kurtosis of the cost distribution |

$HY$ | Entropy of the cost distribution | $PKS$ | Number of peaks of the cost distribution |

Fitness sequences (Muñoz, Kirley et al., 2015) | |||

$Hmax$ | Maximum information content | $\epsilon S$ | Settling sensitivity |

$M0$ | Initial partial information |

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