An analysis of multi-sampled issue and no-replacement tournament selection

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 the same individual sampled multiple times in a tournament. Although the impact of this multi-sampled issue on genetic programming is not clear, some researchers believe that it may lower the probability of some good individuals being sampled or selected. One solution is to use an alternative tournament selection (no-replacement tournament selection), which samples individuals in a tournament without replacement. This paper analyses no-replacement tournament selection to investigate the impact of the scheme and the importance of the issue. Theoretical simulations show that when common tournament sizes and population sizes are used, no-replacement tournament selection does not make the selection behaviour significantly different from that in the standard one and that the multi-sampled issue seldom occurs. In general, the issue is not crucial to the selection behaviour of standard tournament selection.