Abstract A new fitness evaluation criterion for Genetic Algorithms (GAs) is introduced where the fitness value of an individual is determined by considering its own fitness as well as that of its ancestors. The guidelines for selecting the weighting coefficients, both heuristically and automatically, which quantify the importance to be given on the fitness of the individual and its ancestors, are provided. The Schema theorem for the proposed concept is derived. The effectiveness of this new method has been demonstrated on the problems of optimizing complex functions. Results are found to be superior to those of the conventional genetic algorithms, both in terms of goodness of solution and the lower bound of the number of instances of good schemata.