Optimization of noisy fitness functions with univariate marginal distribution algorithm

Darwinian-type genetic algorithms stress the performance of an individual. If an individual has a high fitness, it also has a high probability to survive and to generate offspring. Since in optimization of noisy fitness functions, the fitness of a candidate obtained is not accurate. This characteristic induces its clumsiness for noisy optimization. Compared with Darwinian-type genetic algorithms, the novel computing model estimation of distribution algorithms (EDAs) pay attention to analyzing the selected subpopulations, which makes it more suitable to tackle noisy optimizations. This paper first briefly introduces univariate marginal distribution algorithm (UMDA), and then proves that for WOneMax problem with noise, under the probability limited condition, UMDA can converge to the global optimal point. But for the limited population size, noise doesn´t only delay the convergent time, but also aggravates genetic drift. Since univariate marginal distribution algorithm with smoothing filter (SUMDA) is a feasible technique to diminish genetic drift in UMDA, we adopt SUMDA to tackle noisy optimization. Numerical results show that this method is effective.