The most recent research uses reinforcement learning (RL) to post-train Multi-modal Large Language Models (MLLMs) such that these models are able to iteratively call search engines to dynamically access external knowledge when handling complex Visual Question Answering (VQA) tasks. However, existing methods face two major limitations in effectiveness and efficiency: i) For effectiveness, the objective of these methods, which only considers the correctness of the generated final response, overlooks the quality of intermediate search results, thus leading to suboptimal search strategies. ii) For efficiency, existing methods often unnecessarily invoke search calls during reasoning, making the inference inefficient. To address these issues, we propose , a customized dual-objective reinforcement learning framework to improve the search strategies of MLLMs, enhancing their search quality yet minimizing search frequency. The key ideas include (1) a reward function that promotes correct reasoning trajectories with fewer search calls; and (2) dual optimization objectives that jointly optimize search quality and answer correctness. Extensive experiments on 3 real-world datasets demonstrate that DORA outperforms state-of-the-art methods, achieving up to 8.4% higher accuracy while reducing the number of search calls by 9.7%.