The features selection could constitute an optimization problem because the features constitute qualitative variables. To solve this kind of ` problems you can use the Integration of Variables method. I am attaching 2 works helped by wich you can acquire a vision of the method and the ways it application to optimize problems with qualitative independent variables.
For me, the answer is yes. I've ever tried to optimize the prediction result in economy of a country determined by many variables. When i use feature selection for that variables, the accuracy of the prediction is increased.
Be wise in feature selection too, some rules maybe appear that every cases can be different.
By definition it says that, feature selection is the process of reducing the inputs for processing and analysis, or of finding the most meaningful inputs. So, feature selection is ultimately an optimization problem and its objective is to find meaningful information. Therefore, the definition of meaningful information can be varied depending on application. For example, we have a two classification problem and each class has 100 features. Now, our one objective is to find the features that ensures the minimum distance within-class and maximum distance between-class.
An interested reader may review following articles--
Chapter A Hybrid Feature Selection Scheme Based on Local Compactness...
Conference Paper Feature selection techniques for increasing reliability of f...
Article A Hybrid Feature Selection Scheme for Reducing Diagnostic Pe...