In this paper, we present a simultaneous exploration and object search framework for the application of autonomous trolley collection. For environment representation, a task-oriented environment partitioning algorithm is presented to extract diverse information for each sub-task. First, LiDAR data is classified as potential objects, walls, and obstacles after outlier removal. Segmented point clouds are then transformed into a hybrid map with the following functional components: object proposals to avoid missing trolleys during exploration; room layouts for semantic space segmentation; and polygonal obstacles containing geometry information for efficient motion planning. For exploration and simultaneous trolley collection, we propose an efficient exploration-based object search method. First, a traveling salesman problem with precedence constraints (TSP-PC) is formulated by grouping frontiers and object proposals. The next target is selected by prioritizing object search while avoiding excessive robot backtracking. Then, feasible trajectories with adequate obstacle clearance are generated by topological graph search. We validate the proposed framework through simulations and demonstrate the system with real-world autonomous trolley collection tasks.