This paper presents a study on the use of fitness inheritance as a surrogate model to assist a genetic algorithm (GA) in solving optimization problems with a limited computational budget.We compared the impact to the evolutionary search introducing three surrogate models: (i) averaged inheritance, (ii) weighted inheritance and (iii) parental inheritance. Numerical experiments are performed in order to assess the applicability and the performance of the proposed approach. The results show that when using a fixed reduced budget of expensive simulations, the surrogate-assisted genetic algorithm allows for improving the final solutions when compared to the standard GA. We find that the averaged and parental inheritance are more effective when compared to weighted inheritance, and they are recommended for expensive of optimization problems using GA-based search.