Solving real-life engineering problems can be time-consuming and difficult because problems may have multiple conflicting objectives, functions involved highly nonlinear and containing multiple local minima, and function values are often produced via a time-consuming simulation process. Problems of this type can be solved using global multiobjective optimization methods, preferably with interactive approaches, which allow the designer (or decision maker in general) to learn about the behaviour of the problem during the solution process. In an interactive approach the designer specifies preferences and Pareto optimal solution(s) following these preferences are generated, typically by forming a scalarizing function and solving it. In simulation based optimization this may take time. Thus, the designer may have to wait for a long before (s)he can continue the solution process. Although some efficient global optimization algorithms exist, it is of outmost importance to be able to reduce the computational burden. In our study, we show that substantial savings in calculation time can be achieved using a decreased number of function evaluations at the beginning of the interactive solution process, without compromising the quality of the final solution too much. Furthermore, at each iteration we use simple heuristics to judge sufficient amount for computation. As the designer has gained more understanding about the problem, (s)he may approach the final solution with an ever increasing accuracy and number of objective function evaluations. We show results using several different budget schemes for calculation, and identify levels where a sufficient quality for final solutions is retained.