Designed optimization problems in different disciplines of science should be solved using appropriate techniques. Optimization algorithms are among the most effective and widely used methods in solving optimization problems that are able to provide suitable solutions for these problems. Innovation and scientific contribution of this article in designing a new optimizer called Random Selected Leader Based Optimizer (RSLBO) in order to be used in optimizing the objective functions of optimization problems and achieving the desired solutions. The main idea of the proposed RSLBO is to increase the search power using a random leader. In fact, instead of the algorithm population update relying on several specific members, such as the best member or the worst member, any ordinary member of the population can be a leader in guiding and updating the algorithm population. RSLBO is described, then mathematically modelled to be used in solving optimization problems. The main feature and advantage of the proposed RSLBO is that its implementation and relationships are very simple and understandable, and it also lacks control parameters. The performance of the proposed RSLBO is evaluated on a set of twenty-three standard functions. Also, in order to analyse the quality of the proposed RSLBO in providing appropriate solutions to optimization problems, the results obtained from the proposed algorithm are compared with eight well-known algorithms including Flow Direction Algorithm (FDA), Hide Object Game Optimizer (HOGO), Whale Optimization Algorithm (WOA), Grey Wolf Optimization (GWO), Teaching-Learning-Based Optimization (TLBO), Gravitational Search Algorithm (GSA), Particle Swarm Optimization (PSO), and Genetic Algorithm (GA). The results of optimization of objective functions indicate the high ability of the RSLBO to solve optimization problems and provide appropriate and acceptable solutions. Also, the analysis and comparison of the performance of the eight well-known optimization algorithms against the proposed RSLBO shows that the RSLBO has provided more appropriate solutions and is superior and much more competitive than the eight compared algorithms.