inconsistent / ambiguous values for silhouette_score for identical configuration of TimeSeriesKMeans

Describe the bug
When clustering with TimeSeriesKMeans, silhouette_score yields different results even though the configuration (except for the random state obviously) is identical.

Problem is, sometimes the silhouette score for n=2 is higher than the score for n=3 and sometimes the other way around. So it is not possible to use the silhouette score for determination of optimal amount of clusters.

Is this expected behavior?

To Reproduce

from tslearn.datasets import UCR_UEA_datasets
from tslearn.clustering import TimeSeriesKMeans, silhouette_score

X_train, y_train, X_test, y_test = ds.load_dataset("CBF")

Repeat the same clustering process (n=2 clusters) for 10 times and print silhouette score:

for i in range(2,11):
    km = TimeSeriesKMeans(n_clusters=2, metric="dtw", max_iter=500, random_state=i*2)
    km.fit(X_train)
    print(silhouette_score(X_train,
                           km.predict(X_train),
                           metric="dtw"))

Results in

0.1379816483983626
0.12501642312525266 # lowest
0.19600175472468492
0.21242253672651584 # highest
0.16945987450892622
0.1696772853353848
0.1924580995443414
0.17290448200720934
0.14888132304396023

Repeat the above procedure with n=3 clusters and print silhouette score:

for i in range(2,11):
    km = TimeSeriesKMeans(n_clusters=3, metric="dtw", max_iter=500, random_state=i*2)
    km.fit(X_train)
    print(silhouette_score(X_train,
                           km.predict(X_train),
                           metric="dtw"))

Results in

0.20512134769791557
0.23869052731302476 # highest
0.1988968698176969
0.210215409064512
0.21938781768333507
0.20512134769791557
0.23869052731302476 # highest
0.17423182636957274
0.10851683338892922 # lowest

So depending on the result, either n=2 or n=3 would be selected, but it is not unambiguous

Expected behavior
I would have expected a a more or less consistent silhouette score (maybe around +- 0.02). At least that the levels stay the same.

Environment (please complete the following information):

• OS: Windows 10 Enterprices
• tslearn version 0.4.1

Additional context
I detected the problem in a different data set which I did not share here. There, the differences were even higher (n=2) sometimes returned 0.17 (lowest) and 0.52 (highest)

Start by running the provided CBF reproduction with TimeSeriesKMeans and silhouette_score, comparing repeated runs for two and three clusters. Trace the behavior of these two entry points to determine whether the variation is expected or indicates a bug, then make the result consistent or clarify the documented behavior.