Geometric Generalisation of Surrogate Model-Based Optimisation to Combinatorial and Program Spaces
Table 1
Results for SMBO, an evolutionary algorithm (EA), a (1 + 1) evolutionary algorithm ((1 + 1) EA), and random search (RS) on the NK-landscape benchmark for all combinations of = 2, 3, 4, 5 and = 10, 15, 20, 25.
(optimum)
SMBO
EA
(1 + 1) EA
RS
Best
Average
Best
Average
Best
Average
Best
Average
n = 10
2 (0.704)
0.704
0.702
0.704
0.686
0.698
0.675
0.704
0.649
3 (0.794)
0.794
0.775
0.794
0.724
0.745
0.705
0.794
0.724
4 (0.787)
0.787
0.755
0.787
0.725
0.787
0.714
0.787
0.727
5 (0.810)
0.810
0.762
0.727
0.706
0.810
0.729
0.810
0.718
n = 15
2 (0.743)
0.743
0.742
0.714
0.693
0.681
0.628
0.714
0.674
3 (0.738)
0.738
0.718
0.706
0.678
0.706
0.622
0.717
0.677
4 (0.747)
0.747
0.721
0.711
0.685
0.705
0.646
0.710
0.680
5 (0.760)
0.758
0.737
0.749
0.711
0.728
0.672
0.757
0.700
n = 20
2 (0.729)
0.729
0.726
0.718
0.689
0.668
0.613
0.711
0.673
3 (0.777)
0.777
0.767
0.761
0.718
0.639
0.606
0.777
0.706
4 (0.775)
0.775
0.747
0.731
0.708
0.676
0.640
0.707
0.684
5 (0.766)
0.761
0.744
0.745
0.710
0.709
0.637
0.721
0.684
n = 25
2 (0.753)
0.753
0.747
0.727
0.698
0.679
0.590
0.701
0.673
3 (0.798)
0.798
0.781
0.742
0.727
0.666
0.607
0.749
0.698
4 (0.775)
0.762
0.743
0.750
0.714
0.639
0.595
0.695
0.679
5 (0.774)
0.756
0.736
0.751
0.713
0.705
0.622
0.722
0.676
The best (maximum) and average values of the best solution found by each algorithm are given for 50 runs. Bold numbers are the highest maxima and italic numbers are the second highest maxima.
