Metaheuristics are an important branch of optimization algorithms that attract lots of research and application efforts. In this paper, the research of predicting solution value for Nested Partitions (NP) is proposed, which is a newly developed metaheuristic algorithm for solving large-scale optimization problems. The lower bound embedded prediction procedures are developed to predict the future performance of NP based on the solution values obtained at early iterations. The prediction procedures are used in an enhanced NP algorithm to select a proper algorithm setting for NP at early stage, which saves a lot of computational resource for large-scale problems. The computational tests show the accuracy and effectiveness of the proposed algorithm. These prediction procedures can be also applied to some other metaheuristics.