This paper examines various approaches to evaluating points in expensive multiobjective optimization. Existing approaches, such as Expected Improvement and Lower Confidence Bound, often struggle with convergence to local optima and poor exploration-exploitation balance. To address these limitations, we propose a method called Entropy-Informed Stochastic Improvement, which uses entropy-based uncertainty estimation to determine the next evaluation point based on the indicator value. The proposed method has been implemented in an Expensive Multi/Many-Objective Evolutionary Algorithm. Experiments on benchmark problems with three objective functions demonstrated that the use of proposed criteria, which is based on maximizing information gain, significantly improves convergence to the Pareto front in most problems by more accurately accounting for the uncertainty of surrogate models.