IEEE Computational Intelligence Magazine - May 2022 - 26

0.2
0.4
0.6
0.8
1
2
4
SAS 6
8
10
-4
(a)
-2
logP
DEL Front 1
DEL Front 2
DEL Front 3
DEL Front 4
DEL Front 5
qEHVI Front 1
qEHVI Front 2
qEHVI Front 3
qEHVI Front 4
qEHVI Front 5
b = 00104 "
qParEGO Front 1
qParEGO Front 2
qParEGO Front 3
qParEGO Front 4
qParEGO Front 5
2
4
0.2
0.4
0.6
0.8
1
2
4
SAS 6
8
10
-4
(b)
-2
logP
2
4
FIGURE 6 Pareto fronts of DEL and MO-BO (. .). In the legend, the solution set from the last iteration of qParEGO or qEHVI is written
as Front 1. (a) ZINC. (b) PCBA.
TABLE IV Hypervolumes of individual DEL, qParEGO, or qEHVI Pareto fronts and non-dominated sorting of combination of DEL,
qParEGO, and qEHVI Pareto fronts. Reference point [0, −10, −8.2521] was used in calculation of all hypervolumes in this paper.
PARETO FRONT SIZE (HYPERVOLUME)
FOR COMPARISON
DATA
ZINC
ZINC
PCBA
PCBA
DEL HYPERPARAMETER
b 01 04 " =
b = 00104 "
b 01 04 " =
b = 00104 "
..
..
..
..
DEL
243 (91.79)
200 (91.55)
228 (93.85)
183 (92.92)
qParEGO
46 (78.92)
46 (80.89)
46 (75.50)
46 (75.72)
qEHVI
45 (78.65)
40 (79.21)
36 (73.70)
43 (74.73)
DEL
243 (100%)
200 (100%)
228 (100%)
183 (100%)
IN NEW PARETO FRONT
qParEGO
0 (0%)
0 (0%)
0 (0%)
1 (2.17%)
qEHVI
0 (0%)
1 (2.5%)
0 (0%)
2 (4.65%)
TABLE V Numbers of top novel molecules satisfying
{QED $ 0.88 & SAS # 3 & logP # 1} obtained by optimization
methods starting from same population of 20K molecules
(ZINC) and latent space.
MODEL
SO-DEL(. )001
GB
b =
MO-PSO
COUNT
25
4
4
MODEL
MO-DEL(. )001
GB(DME)
b =
MO-PSO(DME)
COUNT
115
39
28
F. Comparison with Single-Objective DEL (SO-DEL)
The advantages of weighted sum of individual objectives to a
scalar are simplicity and efficiency. However, it is well-known
that the scalarization method faces difficulties in selecting combination
weights, and fails for non-convex problems [54]. SODEL
linearly combines all three objectives into a single one
with equal weights where all the properties (sign of QED
26 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | MAY 2022
should be flipped before normalization) in the data are normalized
to have mean 0 and standard deviation 1. Our results
reported in Table V and Figure 7 corroborate that MO-DEL
performs better than SO-DEL.
G. Comparison with Gradient-Based Methods
Two gradient-based methods were realized: (1) GB: updates z
using gradient (with respect to z) of the sum of the predicted
values of the three properties from the property predictor in
the latent space of VAE, and (2) GB(DME): updates z in the
latent space of VAE and updates the latent space (i.e., datamodel
co-evolution similar to DEL). From Table V and Figure
7, it can be seen that GB(DME) outperforms GB
(implying the advantage of data-model co-evolution), but performs
worse than SO-DEL (implying the betterment of evolutionary
methods over gradient-based methods in nonconvex
problems).
QED
QED
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