Domestic service robots offer a solution to the increasing demand for daily care and support. A human-in-the-loop approach that combines automation and operator intervention is considered to be a realistic approach to their use in society. Therefore, we focus on the task of retrieving target objects from open-vocabulary user instructions in a human-in-the-loop setting, which we define as the learning-to-rank physical objects (LTRPO) task. For example, given the instruction "Please go to the dining room which has a round table. Pick up the bottle on it," the model is required to output a ranked list of target objects that the operator/user can select. In this paper, we propose MultiRankIt, which is a novel approach for the LTRPO task. MultiRankIt introduces the Crossmodal Noun Phrase Encoder to model the relationship between phrases that contain referring expressions and the target bounding box, and the Crossmodal Region Feature Encoder to model the relationship between the target object and multiple images of its surrounding contextual environment. Additionally, we built a new dataset for the LTRPO task that consists of instructions with complex referring expressions accompanied by real indoor environmental images that feature various target objects. We validated our model on the dataset and it outperformed the baseline method in terms of the mean reciprocal rank and recall@k. Furthermore, we conducted physical experiments in a setting where a domestic service robot retrieved everyday objects in a standardized domestic environment, based on users' instruction in a human--in--the--loop setting. The experimental results demonstrate that the success rate for object retrieval achieved 80%. Our code is available at https://github.com/keio-smilab23/MultiRankIt.