D-NSGA-II: Dynamic Multi-Objective Optimization Using Modified NSGA-IIΒΆ
The algorithm is implemented based on [3]. D-NSGA-II modifies the commonly-used NSGA-II procedure in tracking a new Pareto-optimal front as soon as there is a change in the problem. The introduction of a few random solutions or a few mutated solutions provides some diversity and gives the algorithm a chance to escape from a local optimum over time.
[1]:
from pymoo.algorithms.moo.dnsga2 import DNSGA2
from pymoo.core.callback import CallbackCollection, Callback
from pymoo.optimize import minimize
from pymoo.problems.dyn import TimeSimulation
from pymoo.problems.dynamic.df import DF1
import matplotlib.pyplot as plt
problem = DF1(taut=2, n_var=2)
algorithm = DNSGA2()
simulation = TimeSimulation()
class ObjectiveSpaceAnimation(Callback):
def _update(self, algorithm):
if algorithm.n_gen % 20 == 0:
F = algorithm.opt.get("F")
pf = algorithm.problem.pareto_front()
plt.clf()
plt.scatter(F[:, 0], F[:, 1])
if pf is not None:
plt.plot(pf[:, 0], pf[:, 1], color="black", alpha=0.7)
plt.show()
res = minimize(problem,
algorithm,
termination=('n_gen', 100),
callback=CallbackCollection(ObjectiveSpaceAnimation(), simulation),
seed=1,
verbose=True)
==========================================================================
n_gen | n_eval | n_nds | igd | gd | hv
==========================================================================
1 | 100 | 22 | 0.0406157738 | 0.0232449442 | 0.3857609533
2 | 410 | 45 | 0.0263321324 | 0.0207824613 | 0.3960674761
3 | 620 | 62 | 0.0237748654 | 0.0203548008 | 0.4009007302
4 | 930 | 58 | 0.0346067981 | 0.0300876898 | 0.3840870050
5 | 1140 | 88 | 0.0334836462 | 0.0299320209 | 0.3876566424
6 | 1450 | 57 | 0.0512547245 | 0.0528774022 | 0.3601083284
7 | 1660 | 84 | 0.0455702841 | 0.0492041654 | 0.3698029876
8 | 1970 | 50 | 0.0614278344 | 0.0623640078 | 0.3426451356
9 | 2180 | 68 | 0.0586873395 | 0.0617217600 | 0.3483687313
10 | 2490 | 56 | 0.0707280473 | 0.0772451610 | 0.3287838862
11 | 2700 | 65 | 0.0646647058 | 0.0706581281 | 0.3389049648
12 | 3010 | 48 | 0.0710240693 | 0.0723691723 | 0.3245673141
13 | 3220 | 71 | 0.0686131431 | 0.0692033978 | 0.3330436708
14 | 3530 | 61 | 0.0745450091 | 0.0712756130 | 0.3225411355
15 | 3740 | 85 | 0.0721097194 | 0.0696076243 | 0.3303550918
16 | 4050 | 82 | 0.0770226806 | 0.0791481651 | 0.3212008750
17 | 4260 | 100 | 0.0759551977 | 0.0796877644 | 0.3255725897
18 | 4570 | 79 | 0.0780567829 | 0.0792255693 | 0.3208460392
19 | 4780 | 100 | 0.0767752831 | 0.0754245937 | 0.3245871718
20 | 5090 | 93 | 0.0775395030 | 0.0776330687 | 0.3217840824
21 | 5300 | 100 | 0.0767647032 | 0.0768481217 | 0.3248824392
22 | 5610 | 100 | 0.0760216170 | 0.0739669803 | 0.3248936770
23 | 5820 | 100 | 0.0756579236 | 0.0764579632 | 0.3270964567
24 | 6130 | 100 | 0.0737687767 | 0.0720297744 | 0.3302190362
25 | 6340 | 100 | 0.0736659479 | 0.0730912075 | 0.3308874574
26 | 6650 | 100 | 0.0731545166 | 0.0815881159 | 0.3288540356
27 | 6860 | 100 | 0.0721427149 | 0.0808767001 | 0.3320348130
28 | 7170 | 67 | 0.0720931585 | 0.0807877928 | 0.3270910962
29 | 7380 | 92 | 0.0690956617 | 0.0739976698 | 0.3334097599
30 | 7690 | 56 | 0.0677577441 | 0.0813987101 | 0.3314955544
31 | 7900 | 72 | 0.0629420409 | 0.0637868311 | 0.3420432010
32 | 8210 | 58 | 0.0618027037 | 0.0629233945 | 0.3403101424
33 | 8420 | 65 | 0.0564889245 | 0.0573917268 | 0.3498165110
34 | 8730 | 42 | 0.0515244146 | 0.0543256472 | 0.3577657931
35 | 8940 | 63 | 0.0462319883 | 0.0495466344 | 0.3676830644
36 | 9250 | 46 | 0.0388020367 | 0.0377727687 | 0.3775898467
37 | 9460 | 68 | 0.0338576523 | 0.0332735237 | 0.3873106640
38 | 9770 | 58 | 0.0288631302 | 0.0271924094 | 0.3938744581
39 | 9980 | 79 | 0.0246669832 | 0.0251419387 | 0.4015148240
40 | 10290 | 45 | 0.0263042610 | 0.0308257967 | 0.4010065433
41 | 10500 | 59 | 0.0182289056 | 0.0210831155 | 0.4122532620
42 | 10810 | 100 | 0.0149463954 | 0.0142699748 | 0.4560504763
43 | 11020 | 100 | 0.0148756650 | 0.0148667573 | 0.4580237827
44 | 11330 | 73 | 0.0282744310 | 0.0271196375 | 0.4730048711
45 | 11540 | 96 | 0.0299741502 | 0.0285630072 | 0.4785132845
46 | 11850 | 57 | 0.0442173278 | 0.0419419656 | 0.4963499517
47 | 12060 | 72 | 0.0484249272 | 0.0485190702 | 0.5041148452
48 | 12370 | 63 | 0.0623579558 | 0.0659356784 | 0.5254220568
49 | 12580 | 76 | 0.0675836208 | 0.0628508117 | 0.5346652419
50 | 12890 | 58 | 0.0862753402 | 0.0816461854 | 0.5579247912
51 | 13100 | 83 | 0.0902126704 | 0.0871270043 | 0.5667420648
52 | 13410 | 67 | 0.1052707332 | 0.0994010742 | 0.5909723459
53 | 13620 | 99 | 0.1075585802 | 0.1019567776 | 0.5959646038
54 | 13930 | 86 | 0.1203967122 | 0.1181201594 | 0.6155533874
55 | 14140 | 100 | 0.1232812380 | 0.1252262959 | 0.6213457202
56 | 14450 | 88 | 0.1333269434 | 0.1358633262 | 0.6374913733
57 | 14660 | 100 | 0.1350379099 | 0.1358659370 | 0.6402714617
58 | 14970 | 92 | 0.1411733326 | 0.1517724007 | 0.6495374473
59 | 15180 | 100 | 0.1438606029 | 0.1479847764 | 0.6533479913
60 | 15490 | 98 | 0.1462196018 | 0.1598204955 | 0.6567650077
61 | 15700 | 100 | 0.1478347821 | 0.1579384036 | 0.6584202651
62 | 16010 | 100 | 0.1460618809 | 0.1543043303 | 0.6551322642
63 | 16220 | 100 | 0.1461939278 | 0.1585676058 | 0.6552147488
64 | 16530 | 100 | 0.1400418007 | 0.1454001131 | 0.6437867692
65 | 16740 | 100 | 0.1400851819 | 0.1420272960 | 0.6442184088
66 | 17050 | 100 | 0.1259024551 | 0.1289662197 | 0.6229861641
67 | 17260 | 100 | 0.1262934239 | 0.1288227002 | 0.6239578263
68 | 17570 | 97 | 0.1044057675 | 0.1065120638 | 0.5924824716
69 | 17780 | 100 | 0.1071659543 | 0.1119953635 | 0.5966936868
70 | 18090 | 74 | 0.0837471664 | 0.0874156951 | 0.5611377539
71 | 18300 | 100 | 0.0856398376 | 0.0897192729 | 0.5661534032
72 | 18610 | 62 | 0.0624133301 | 0.0618096331 | 0.5277147639
73 | 18820 | 80 | 0.0662584736 | 0.0687729684 | 0.5329110043
74 | 19130 | 60 | 0.0487452657 | 0.0630417924 | 0.5003246007
75 | 19340 | 88 | 0.0481605727 | 0.0593538161 | 0.5077002330
76 | 19650 | 54 | 0.0270897006 | 0.0321536868 | 0.4651321439
77 | 19860 | 74 | 0.0282078117 | 0.0340163609 | 0.4743821213
78 | 20170 | 42 | 0.0196510050 | 0.0149372843 | 0.4356000388
79 | 20380 | 62 | 0.0150939295 | 0.0122741334 | 0.4460344548
80 | 20690 | 41 | 0.0193800204 | 0.0119109358 | 0.4132807114
81 | 20900 | 61 | 0.0137014765 | 0.0097048739 | 0.4224286253
82 | 21210 | 91 | 0.0202126466 | 0.0192038970 | 0.4088260759
83 | 21420 | 100 | 0.0187103851 | 0.0187444030 | 0.4121792354
84 | 21730 | 60 | 0.0404702340 | 0.0454094217 | 0.3757471126
85 | 21940 | 71 | 0.0354560658 | 0.0358390005 | 0.3834515498
86 | 22250 | 51 | 0.0529138094 | 0.0533157448 | 0.3545642949
87 | 22460 | 60 | 0.0497058101 | 0.0494229431 | 0.3619749759
88 | 22770 | 54 | 0.0593052089 | 0.0589529084 | 0.3451109034
89 | 22980 | 81 | 0.0567458089 | 0.0552530226 | 0.3504790478
90 | 23290 | 60 | 0.0645442407 | 0.0672821037 | 0.3384956450
91 | 23500 | 81 | 0.0616334824 | 0.0619673684 | 0.3450492851
92 | 23810 | 50 | 0.0697778769 | 0.0766854153 | 0.3301403594
93 | 24020 | 79 | 0.0670055508 | 0.0695406200 | 0.3360101771
94 | 24330 | 69 | 0.0759941881 | 0.0759065545 | 0.3212419929
95 | 24540 | 84 | 0.0730221588 | 0.0782523446 | 0.3284115028
96 | 24850 | 62 | 0.0794457311 | 0.0855982456 | 0.3172744673
97 | 25060 | 88 | 0.0767291898 | 0.0837423684 | 0.3221836726
98 | 25370 | 78 | 0.0799834732 | 0.0868988771 | 0.3164850150
99 | 25580 | 100 | 0.0777148831 | 0.0824918900 | 0.3223695802
100 | 25890 | 74 | 0.0784573875 | 0.0796731981 | 0.3200140153
