Artificial jellyfish search algorithm (JS) is a recently proposed optimization algorithm inspired by the search behavior of jellyfish in the ocean. There are two different search behaviors in JS: the motion of the jellyfish due to ocean currents (global search) and the motion of the jellyfish within the swarm (local search). In this study, two modifications, one in the local and the other in the global search formula, were made to strengthen the search capability of the standard algorithm. By means of the modification made in the global search, the search direction was directed toward the best and elite set individuals and higher quality solutions were found. A more detailed search around the individuals and the longer preservation of diversity in the population were ensured by another modification to the local search. In addition, it was studied to find the most ideal value for the time control mechanism that provides the transition between local and global search. The new modified algorithm (MJS), obtained as a result of all these modifications, was tested on a total of eighty minimization problems, including standard benchmark functions, Congress of Evolutionary Computation 2013 (CEC2013) test function, and Congress of Evolutionary Computation 2017 (CEC2017) test functions. The results of these tests for different dimensions were compared to the standard JS algorithm and the algorithms selected from the literature. Also, the results were interpreted by means of statistical tests. These comparisons and statistical tests showed that the proposed MJS algorithm produced acceptable, successful, and competitive results.