Unlike the conventional multi-modal optimization where a “bounded search area” is pre-determined, this paper addresses the multi-modal optimization for an “unbounded search space”. For this purpose, this paper proposes Novelty-based Multi-objectivization with Local and Rough Search based on dynamic area exploration (NM-LRS), which adds the novelty criterion in the given optimization criteria to roughly search the unbounded search space for obtaining the “potential area” where the optimal solution is most likely located and then searches the “potential area” to find the optimal solution by a local search. To investigate the effectiveness of the proposed method, NM-LRS is compared with the other optimization methods for the unbounded search space, and the following implications have been revealed: the proposed method has a higher solution-finding rate than all existing methods for functions with complex landscapes, and it also finds the optimal solution far from the initial search area, which confirms the effectiveness of a rough search.