Estimation of distribution algorithms making use of both high quality and low quality individuals

Most estimation of distribution algorithms only make use of some high quality individuals and neglect other low quality individuals. However like high quality individuals, these neglected low quality individuals also contain some important information that may be useful for guiding the search of estimation of distribution algorithms. This paper proposes a novel kind of estimation of distribution algorithms, where both high quality and low quality individuals in the old population are employed for reproducing new candidate individuals at the next generation. In particular, both the density P^H (X) of high quality individuals and the density P^L (X) of low quality individuals are estimated; then the new population G is obtained with the following steps employed: 1) a new candidate individual x is reproduced through sampling from the density P^H (X); 2) to let P^H (X = x) and P^L (X = x) compare and the individual x will be stored into the new population G if and only if P^H (X = x) ≥ P^L (X = x); 3) the above steps repeat until M new individuals have been successfully generated where M is the population size. To demonstrate the usefulness of low quality individuals for estimation of distribution algorithms, estimation of distribution algorithms using both high quality and low quality individuals are tested on several benchmark problems and their results are compared with those obtained by estimation of distribution algorithms where only high quality individuals are used. The usefulness of low quality individuals for speeding up the search of estimation of distribution algorithms is confirmed by the experimental results.