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The Distributed Deterministic Spiral Algorithm (DDSA) has shown great foraging efficiency in robot swarms. However, when the number of robots in the swarm increases, scalability becomes a significant bottleneck due to increased collisions among robots, making it challenging to deploy them in the search space (e.g., 20 robots). To address this issue, we propose an adaptive Multiple-Distributed Bidirectional Spiral Algorithm (MDBSA) that enhances scalability. Our proposed algorithm partitions the squared search arena into multiple identical squared regions and assigns robots to regions dynamically based on the number of regions. In each region, a bidirectional spiral search path is planned, and when a robot completes its search, it is assigned to either an unassigned region or a region with one robot. The two robots will then travel along the path from the starting and ending points of the spiral path. We evaluated the performance of robot swarms using the MDBSA algorithm in the ARGoS robot simulator. Our experimental results show that the proposed MDBSA algorithm outperforms DDSA. When robots deliver collected resources to regions instead of the center, it reduces collisions and significantly improves the scalability of the robot swarm. Our findings suggest that a multiple-distributed search strategy is an efficient solution for foraging robot swarms.