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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×103 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:
List of the Calculated Exploratory Landscape Analysis (ELA) Features.
Correlations (Jones and Forrest, 1995)
FDCFitness distance correlation
 Average distances (Lunacek and Whitley, 2006) 
DISP1% Dispersion of points within 1% of yt   
 Surrogate models (Mersmann et al., 2011) 
R¯L2 Adjusted coefficient of determination of a linear model R¯LI2 Adjusted coefficient of determination of a linear model including interactions 
R¯Q2 Adjusted coefficient of determination of a purely quadratic model R¯QI2 Adjusted coefficient of determination of a quadratic model including interactions 
βmin Minimum of the absolute value of the linear model coefficients βmax 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) 
ξD Significance of D-th order ξ1 Significance of first order 
σ1 Standard deviation of the significance of first order ξ1 Significance of second order 
σ2 Standard deviation of the significance of second order   
γY Skewness of the cost distribution κY 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 εS Settling sensitivity 
M0 Initial partial information   
Correlations (Jones and Forrest, 1995)
FDCFitness distance correlation
 Average distances (Lunacek and Whitley, 2006) 
DISP1% Dispersion of points within 1% of yt   
 Surrogate models (Mersmann et al., 2011) 
R¯L2 Adjusted coefficient of determination of a linear model R¯LI2 Adjusted coefficient of determination of a linear model including interactions 
R¯Q2 Adjusted coefficient of determination of a purely quadratic model R¯QI2 Adjusted coefficient of determination of a quadratic model including interactions 
βmin Minimum of the absolute value of the linear model coefficients βmax 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) 
ξD Significance of D-th order ξ1 Significance of first order 
σ1 Standard deviation of the significance of first order ξ1 Significance of second order 
σ2 Standard deviation of the significance of second order   
γY Skewness of the cost distribution κY 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 εS Settling sensitivity 
M0 Initial partial information   

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