Tiếp tục quá trình này, chúng ta có thể viết ra một biểu thức cho tất cả các cách có thể hình thành Pj dân số từ một tập hợp các n lựa chọn và tái tổ hợp các bước: Xác suất mà dân số Pj được sản xuất từ dân số Pi là sản phẩm của hai biểu thức (tạo thành một | Chapter 4 Theoretical Foundations of Genetic Algorithms used in the work of Tanese 1989 gives an individual with fitness one standard deviation above the mean expected offspring. If ExpVal i t was less than 0 Tanese arbitrarily reset it to so that individuals with very low fitness had some small chance of reproducing. At the beginning of a run when the standard deviation of fitnesses is typically high the fitter individuals will not be many standard deviations above the mean and so they will not be allocated the lion s share of offspring. Likewise later in the run when the population is typically more converged and the standard deviation is typically lower the fitter individuals will stand out more allowing evolution to continue. Elitism Elitism first introduced by Kenneth De Jong 1975 is an addition to many selection methods that forces the GA to retain some number of the best individuals at each generation. Such individuals can be lost if they are not selected to reproduce or if they are destroyed by crossover or mutation. Many researchers have found that elitism significantly improves the GA s performance. Boltzmann Selection Sigma scaling keeps the selection pressure more constant over a run. But often different amounts of selection pressure are needed at different times in a run for example early on it might be good to be liberal allowing less fit individuals to reproduce at close to the rate of fitter individuals and having selection occur slowly while maintaining a lot of variation in the population. Later it might be good to have selection be stronger in order to strongly emphasize highly fit individuals assuming that the early diversity with slow selection has allowed the population to find the right part of the search space. One approach to this is Boltzmann selection an approach similar to simulated annealing in which a continuously varying temperature controls the rate of selection according to a preset schedule. The temperature starts out high
