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There are many optimization problems in the different disciplines of science that must be solved using the appropriate method. Population-based optimization algorithms are one of the most efficient ways to solve various optimization problems. Population-based optimization algorithms are able to provide appropriate solutions to optimization problems based on a random search of the problem-solving space without the need for gradient and derivative information. In this paper, a new optimization algorithm called the Group Mean-Based Optimizer (GMBO) is presented; it can be applied to solve optimization problems in various fields of science. The main idea in designing the GMBO is to use more effectively the information of different members of the algorithm population based on two selected groups, with the titles of the good group and the bad group. Two new composite members are obtained by averaging each of these groups, which are used to update the population members. The various stages of the GMBO are described and mathematically modeled with the aim of being used to solve optimization problems. The performance of the GMBO in providing a suitable quasi-optimal solution on a set of 23 standard objective functions of different types of unimodal, high-dimensional multimodal, and fixed-dimensional multimodal is evaluated. In addition, the optimization results obtained from the proposed GMBO were compared with eight other widely used optimization algorithms, including the Marine Predators Algorithm (MPA), the Tunicate Swarm Algorithm (TSA), the Whale Optimization Algorithm (WOA), the Grey Wolf Optimizer (GWO), Teaching–Learning-Based Optimization (TLBO), the Gravitational Search Algorithm (GSA), Particle Swarm Optimization (PSO), and the Genetic Algorithm (GA). The optimization results indicated the acceptable performance of the proposed GMBO, and, based on the analysis and comparison of the results, it was determined that the GMBO is superior and much more competitive than the other eight algorithms. [ABSTRACT FROM AUTHOR]