Open-text responses provide researchers and educators with rich, nuanced insights that multiple-choice questions cannot capture. When reliably assessed, such responses have the potential to enhance teaching and learning. However, scaling and consistently capturing these nuances remain significant challenges, limiting the widespread use of open-text questions in educational research and assessments. In this paper, we introduce and evaluate "GradeOpt," a unified multi-agent automatic short-answer grading (ASAG) framework that leverages large language models (LLMs) as graders for short-answer responses. More importantly, "GradeOpt" incorporates two additional LLM-based agents--the "reflector" and the "refiner"--into the multi-agent system. This enables "GradeOpt" to automatically optimize the original grading guidelines by performing self-reflection on its errors. To assess "GradeOpt"'s effectiveness, we conducted experiments on two representative ASAG datasets, which include items designed to capture key aspects of teachers' pedagogical knowledge and students' learning progress. Our results demonstrate that "GradeOpt" consistently outperforms representative baselines in both grading accuracy and alignment with human evaluators across different knowledge domains. Finally, comprehensive ablation studies validate the contributions of "GradeOpt"'s individual components, confirming their impact on overall performance. [For the complete proceedings, see ED675583.]