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:

LON Method . | Regression . | Response 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 Method . | Regression . | Response 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:

Predicting ILS . | Predicting 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 ILS . | Predicting 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:

Predicting ILS . | Predicting 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 ILS . | Predicting 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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