Jigsaw puzzle reassembly remains a highly challenging task, particularly when piece boundaries are irregularly eroded to simulate damage to cultural artifacts. On the GAP benchmark, existing methods achieve a perfect assembly accuracy of only 0.3% on
5×5 puzzles, whereas humans can solve jigsaw puzzles with remarkably high accuracy. Humans typically approach puzzle solving by identifying potentially adjacent pieces, evaluating the current assembly, and iteratively performing complex operations such as adding pieces, replacing incorrectly placed pieces, and moving entire connected groups of pieces. However, existing methods face a fundamental limitation: approaches that leverage global visual information typically predict piece arrangements directly, making it difficult to explicitly perform such complex iterative operations, while search based methods can rearrange pieces but primarily rely on pairwise boundary compatibility, lacking global visual information to evaluate and guide the search process. To bridge this gap, we propose GlobalPuzzle, a jigsaw puzzle reassembly framework that integrates global canvas level evaluation, action guidance, and genetic search. By incorporating global visual information into the evaluation and optimization of candidate assemblies, GlobalPuzzle aims to resolve ambiguous adjacency relationships that are difficult to determine from irregularly eroded piece boundaries alone, enabling flexible, globally informed reconstruction.