A good paraphrase is semantically similar to the original sentence but it must be also well formed, and syntactically different to ensure diversity. To deal with this tradeoff, we propose to cast the paraphrase generation task as a multi-objectives search problem on the lattice of text transformations. We use BERT and GPT2 to measure respectively the semantic distance and the correctness of the candidates. We study two search algorithms: Monte-Carlo Tree Search For Paraphrase Generation (MCPG) and Pareto Tree Search (PTS) that we use to explore the huge sets of candidates generated by applying the PPDB-2.0 edition rules. We evaluate this approach on 5 datasets and show that it performs reasonably well and that it outperforms a state-of-the-art edition-based text generation method.