Markov-Chain LON Sampling and Snowball LON Sampling produce LONs which capture different fitness landscape information. Features to do with edge and node density, as well as those relating to path lengths, are redundant as predictors when calculated on a Snowball LON: they are prescribed by the sampling algorithm parameters. A speculation is put forward now that the union of different features from LON types, for the same problem instances, might predict more accurately than using one LON type only. The three best-ranked predictors (according to Section 5.3) for each response variable (ILS or TS) and each LON method (Markov or Snowball) are bundled together into single models. The results are in Table 8. Rankings are in Table 9. Table 8 illuminates further that linear regression may not suit LON performance prediction models, with rows 1 and 2 showing weak $R2$ values. The lack of specificity suggests they miss nonlinear interactions between variables. This is in contrast to the random forest counterparts, rows 3 and 4, strikingly stronger than the linear models. They account for 97% (ILS) and 99% (TS) of search variance explained. The error rates (see MSE column) appear to be low. The $R2$ values surpass those seen when using features from one type of LON.

Table 8:
Model summary statistics when using features from both LON types.
RegressionResponse Variable$R2$MSE
Linear ILS 0.076 0.003
Linear TS 0.254 0.026
RandomForest ILS 0.972 0.000
RandomForest TS 0.991 0.000
RegressionResponse Variable$R2$MSE
Linear ILS 0.076 0.003
Linear TS 0.254 0.026
RandomForest ILS 0.972 0.000
RandomForest TS 0.991 0.000
Table 9:
Predictor rankings for RF models using both LON types.
Predicting ILSPredicting TS
mean fitness (Snowball LONs) mean fitness (Snowball LONs)
funnel-floor fitness funnel-floor fitness
mean fitness (Markov LONs) mean fitness (Markov LONs)
number optima maximum HC paths
maximum HC length fitness correlation
mean HC length edges
Predicting ILSPredicting TS
mean fitness (Snowball LONs) mean fitness (Snowball LONs)
funnel-floor fitness funnel-floor fitness
mean fitness (Markov LONs) mean fitness (Markov LONs)
number optima maximum HC paths
maximum HC length fitness correlation
mean HC length edges

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