In the fields of engineering and data sciences, the optimization problems arise on regular basis. With the progress in the field of scientific computing and research, the optimization is not a problem for small data sets and lower dimensional problems. The problem arise, when the data is large, stochastic in nature, and/or multidimensional. The basic optimization tools fail for such problems due to the complexity. The genetic algorithms, based on the natural selection hypothesis, play an imperative role to deal with such complex problems. Genetic algorithms are used in the literature to optimize numerous problems. In the field of computational biology, these algorithms have provided cost effective solutions to find optimal values for large data sets. The genetic algorithms have been used for image reconstruction. These algorithms are based on sub-algorithms to improve the accuracy and precision. We will discuss the advanced genetic algorithms and their applications in detail. Genetic algorithm, in hybrid form have attracted interest of researchers from almost all fields, including computer science, applied mathematics, engineering and computational biology. These tools help to analyze the systems in a swift manner. This important feature is discussed with the aid of examples. The time series forecasting and the Bayesian inference, in combination with the genetic algorithms, can prove to be powerful artificial intelligence tools. We will discuss this important aspect in detail with the aid of some examples. © 2021, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.