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Optimization seeks to find inputs for an objective function that result in a maximum or minimum. Optimization methods are divided into exact and approximate (algorithms). Several optimization algorithms imitate natural phenomena, laws of physics, and behavior of living organisms. Optimization based on algorithms is the challenge that underlies machine learning, from logistic regression to training neural networks for artificial intelligence. In this paper, a new algorithm called two-stage optimization (TSO) is proposed. The TSO algorithm updates population members in two steps at each iteration. For this purpose, a group of good population members is selected and then two members of this group are randomly used to update the position of each of them. This update is based on the first selected good member at the first stage, and on the second selected good member at the second stage. We describe the stages of the TSO algorithm and model them mathematically. Performance of the TSO algorithm is evaluated for twenty-three standard objective functions. In order to compare the optimization results of the TSO algorithm, eight other competing algorithms are considered, including genetic, gravitational search, grey wolf, marine predators, particle swarm, teaching-learning-based, tunicate swarm, and whale approaches. The numerical results show that the new algorithm is superior and more competitive in solving optimization problems when compared with other algorithms. [ABSTRACT FROM AUTHOR]