Several optimization-based population search methods have been proposed; they use various operators that permit exploring the search space. These methods typically suffer from local search (LS) problems and are unbalanced between exploration and exploitation. Consequently, recent researchers sought to modify the algorithms to avoid search problems using local search techniques to intensify the exploitation when is necessary. This paper proposes a novel single-based local search optimization algorithm called the non-monopolize search (NO). The NO is a single-solution metaphor-free algorithm, and its operators are designed based to explore and exploit along the iterative process. The NO works only with a candidate solution, and the operators modify the dimension to move the current solution along the search space. The NO is an effective LS method that combines the benefits of exploration with exploitation. Different from other LS, the NO can escape from suboptimal solutions thanks to the randomness incorporated into its operators. This is the main advantage of the NO. Experiments are conducted on standard benchmark functions to validate the performance of the proposed non-monopolize search optimization technique. The results are compared with other well-known methods, and the proposed NO got better results. Moreover, the proposed NO can be considered a powerful alternative to improve the optimization algorithms’ performance and help avoid local search problems. Source codes of NO are publicly available at https://www.mathworks.com/matlabcentral/fileexchange/156154-the-non-monopolize-search-no.