Scientific progress depends on the continual generation of innovative re-search ideas. However, the rapid growth of scientific literature has greatly increased the cost of knowledge filtering, making it harder for researchers to identify novel directions. Although existing large language model (LLM)-based methods show promise in research idea generation, the ideas they produce are often repetitive and lack depth. To address this issue, this study proposes a multi-agent iterative planning search strategy inspired by com-binatorial innovation theory. The framework combines iterative knowledge search with an LLM-based multi-agent system to generate, evaluate, and re-fine research ideas through repeated interaction, with the goal of improving idea diversity and novelty. Experiments in the natural language processing domain show that the proposed method outperforms state-of-the-art base-lines in both diversity and novelty. Further comparison with ideas derived from top-tier machine learning conference papers indicates that the quality of the generated ideas falls between that of accepted and rejected papers. These results suggest that the proposed framework is a promising approach for supporting high-quality research idea generation. The source code and dataset used in this paper are publicly available on Github repository: https://github.com/ChenShuai00/MAGenIdeas. The demo is available at https://huggingface.co/spaces/cshuai20/MAGenIdeas.