Ranking the set of search results according to their relevance to a user query is an important task in an Information Retrieval (IR) systems such as a Web Search Engine. Learning the optimal ranking function for this task is a challenging problem because one must consider complex non-linear interactions between numerous factors such as the novelty, authority, contextual similarity, etc. of thousands of documents that contain the user query. We model this task as a non-linear ranking problem, for which we propose Rank-PMBGP, an efficient algorithm to learn an optimal non-linear ranking function using Probabilistic Model Building Genetic Programming. We evaluate the proposed method using the LETOR dataset, a standard benchmark dataset for training and evaluating ranking functions for IR. In our experiments, the proposed method obtains a Mean Average Precision (MAP) score of 0.291, thereby significantly outperforming a non-linear baseline approach that uses Genetic Programming.