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Automated library migration reduces refactoring costs but challenges traditional evolutionary algorithms, which often suffer from premature convergence and poor recall in sparse, complex API mapping spaces. To address this, we propose QIMIG, a multi-objective optimization framework integrating quantum-inspired encoding with quality-aware and greedy heuristic filtering. QIMIG utilizes a probabilistic Q-bit representation to maintain population diversity and avoid local optima. Simultaneously, its heuristic components leverage historical usage context to filter semantic noise and guide the search toward valid mappings. Evaluated on 9 real-world migration rules derived from 57,447 open-source projects, QIMIG statistically significantly outperforms state-of-the-art baselines such as UNSGA-III. The framework achieves a global mean F1-score of 0.92, exceeding the best-performing baseline by an absolute margin of 0.05, and demonstrates strong stability in resolving complex mapping structures.
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