Any disadvantages of elastic net over lasso? What are the disadvantages of using elastic net in comparison to lasso. 
I know that the elastic net is able to select groups of variables when they are highly correlated. 


*

*It doesn't have the problem of selecting more than $n$ predictors when $p \gg  n$. Whereas lasso saturates when $p \gg n$.

*When there are highly correlated predictors lasso tends to just pick one predictor out of the group. 

*When $n \gg p$ and the predictors are correlated, the prediction performance of lasso is smaller than that of ridge. 
All these disadvantages of lasso are overcome by the elasic net. 
What I don't understand is when should the lasso be then used? Is there any reason to use it when the elastic net performs better than lasso?
What are the disadvantages of using elastic net in some cases?
In which cases would the lasso be a better choice?
 A: One disadvantage is the computational cost. You need to cross-validate the relative weight of L1 vs. L2 penalty, $\alpha$, and that increases the computational cost by the number of values in the $\alpha$ grid.
Another disadvantage (but at the same time an advantage) is the flexibility of the estimator. With greater flexibility comes increased probability of overfitting. It may be that the optimal $\alpha$ for the population and for the given sample size is $0$, turning elastic net into lasso, but you happen to choose a different value due to chance (because that value delivers better performance when cross-validating in the particular sample).
A: A very late reply, but if you're interested in tuning the elastic net: my blog post explains why it is actually very hard to tune alpha and lambda together, which is a disadvantage.
Here's the argumentation in a nutshell.
First empirical. When one plots cross-validated likelihood (CVL) against alpha and lambda one will notice a ridge in the landscape along which the CVL is very flat and close to the maximum. CVL is strongly linked to marginal likelihood, which is another criterion to tune hyperparameters (= empirical Bayes). For marginal likelihood one can prove that for elastic net this is approximately a Gaussian likelihood with only one variance parameter v. An infinite number of alpha-lambda combinations can render v, implying non-identifiability.
