Learning-to-rank is an applied domain of supervised machine learning. As feature selection has been found to be effective for improving the accuracy of learning models in general, it is intriguing to investigate this process for learning-to-rank domain. In this study, we investigate the use of a popular meta-heuristic approach called simulated annealing for this task. Under the general framework of simulated annealing, we explore various neighborhood selection strategies and temperature cooling schemes. We further introduce a new hyper-parameter called the progress parameter that can effectively be used to traverse the search space. Our algorithms are evaluated on five publicly benchmark datasets of learning-to-rank. For a better validation, we also compare the simulated annealing-based feature selection algorithm with another effective meta-heuristic algorithm, namely local beam search. Extensive experimental results show the efficacy of our proposed models.