This paper "re-introduces" the genetics into the population based incremental learning algorithm (PBIL). PBIL was proposed in 1994 by Baluja; one major goal of the PBIL was to "remove the genetics from the GA". Nevertheless, this paper shows that one can improve the performance of PBIL significantly with different forms of crossover. This is achieved by re-introducing usual forms of crossover working on individuals and by introducing crossover among "probability vectors" which effectively results in a form of migration inspired by the well known Island Model GA (also called coarse-grained GA). An analysis of the behavior of PBIL on a genetic drift model is performed and furthermore the paper explains the destructive effect of using an elite in combination with PBIL. Significant performance improvements are shown on four well-known function optimization problems (with and without constraints). Further, comparisons are made between our novel methods C-PBIL and IM-PBIL, and the standard PBIL, a continuous-valued PBIL called "PBIL/sub C/", and finally an evolutionary strategy (ES). Altogether we show that our "re-introduction of genetics" improves the performance of PBIL in all considered cases.
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