When sharing fails

Sharing, introduced by D.E. Goldberg and J. Richardson (1987), is probably one of the most investigated ideas for multimodal optimization. Empirical tests have indicated that sharing is capable of maintaining multiple peaks located simultaneously, a feature that allows a final human selection among the found solutions. The author presents a theoretical argument regarding the performance of sharing. The argument is supported with a series of tests on variants of a simple problem, which is one of Goldberg and Richardson's original test functions where a constant is added. The results from these tests indicated that sharing is very sensitive to the range of fitness values. Finally, three extensions of sharing are proposed and discussed.