In this section, the set of 868 LON samplings (for each LON algorithm, totalling 1,736) for QAPLIB is used. Recall that these are associated with 124 QAPLIB instances, each having seven LONs produced per algorithm (differentiated by sampling parameter configuration). Table 5 shows the algorithmic performance prediction model summaries, indicating the strength of the models in terms of $R2$ and MSE. Tables 6 and 7 record predictor rankings for the random forest models for Markov-Chain LON Samples and Snowball LON Samples, respectively. Rows 1 and 5 of Table 5 (linear regression to predict ILS response) show that neither Markov-Chain nor Snowball LON features build a good model. The $R2$ values are just too weak. However, when we look at the equivalent random forest models (rows 3 and 7) we have strong models with around 64% (Markov-Chain) and 80% (Snowball) of variance explained, and very small relative MSE values. This could reflect the capability of regression trees to capture nonlinearity and complex interactions between predictors. The same trend is seen in the tabu search prediction models in Table 5. Linear models (rows 2 and 6) are weak, with small $R2$ and comparably larger MSE. The random forest results (rows 4 and 8) are strong, with 90% or over variance explained by features of LONs produced by both LON construction algorithms.

Table 5:
Linear and random forest regression model summary statistics for full QAPLIB LON set. $R2$ and MSE are given.
LON MethodRegressionResponse Variable$R2$MSE
Markov-Chain Linear ILS 0.043 0.002
Markov-Chain Linear TS 0.180 0.081
Markov-Chain RandomForest ILS 0.645 0.000
Markov-Chain RandomForest TS 0.925 0.008
Snowball Linear ILS 0.057 0.003
Snowball Linear TS 0.252 0.029
Snowball RandomForest ILS 0.804 0.000
Snowball RandomForest TS 0.922 0.003
LON MethodRegressionResponse Variable$R2$MSE
Markov-Chain Linear ILS 0.043 0.002
Markov-Chain Linear TS 0.180 0.081
Markov-Chain RandomForest ILS 0.645 0.000
Markov-Chain RandomForest TS 0.925 0.008
Snowball Linear ILS 0.057 0.003
Snowball Linear TS 0.252 0.029
Snowball RandomForest ILS 0.804 0.000
Snowball RandomForest TS 0.922 0.003
Table 6:
Predictor rankings for main QAPLIB RF models—Markov-Chain LON samples. Fitness features in italics.
Predicting ILSPredicting TS
mean fitness mean fitness
funnel-floor fitness funnel-floor fitness
number optima edges
incoming global diameter
edges number optima
diameter out-degree
out-degree incoming global
Predicting ILSPredicting TS
mean fitness mean fitness
funnel-floor fitness funnel-floor fitness
number optima edges
incoming global diameter
edges number optima
diameter out-degree
out-degree incoming global
Table 7:
Predictor rankings for main QAPLIB RF models using Snowball LONs.
Predicting ILSPredicting TS
mean fitness mean fitness
maximum HC paths fitness correlation
fitness correlation maximum HC paths
mean HC length weight disparity
weight disparity maximum HC length
maximum HC length mean HC length
weight loops weight loops
Predicting ILSPredicting TS
mean fitness mean fitness
maximum HC paths fitness correlation
fitness correlation maximum HC paths
mean HC length weight disparity
weight disparity maximum HC length
maximum HC length mean HC length
weight loops weight loops

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