Is the not-sampled issue in tournament selection critical?

The standard tournament selection samples individuals with replacement. The sampling-with-replacement strategy has its advantages but also has issues. One of the commonly recognised issues is that it is possible to have some individuals not sampled at all during the selection phase. The not-sampled issue aggravates the loss of program diversity. However, it is not clear how the issue affects Genetic Programming (GP) search. This paper investigates the importance of the issue. The theoretical and experimental results show that the issue can be solved and the loss of diversity contributed by not-sampled individuals can be minimised. However, doing so does not appears to significantly improve a GP system. Our conclusion is that the not-sampled issue does not seriously affect the selection performance in the standard tournament selection.