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In this paper, we present a new hybrid swarm optimization and differential evolution algorithm for solving constrained and engineering optimization problems. The proposed algorithm is called hybrid particle swarm optimization and differential evolution with population size reduction (HPSODEPSR). The powerful performance of any metaheuristics algorithm is measured by its capability to balance between the exploration and exploitation process. In the beginning of the search, the algorithm needs to explore the search space with a large number of solutions in the population then during the search the need of the exploration process is reduces while the need of the exposition process increases. From this point, we propose a population size reduction mechanism (PSRM), in PSRM, the proposed algorithm starts with a large number of solutions in the population and during the search the number of these solutions decreases after applying the greedy selection operator in order to remove the worst solutions from the population. Also, we propose a new automatic termination criterion which is called a progress vector V. V is a (1×n) zero vector, where n equal to the number of population partitions and contains of a number of subsets equal to the number of population reduction steps (partitions), when the population reduced, the corresponding subset value in V converted to one. The algorithm terminates the search when all subsets values in the progress vector become ones. Moreover, we test the proposed algorithm on eleven benchmark functions and five engineering optimization problems.We compare our proposed algorithm against seven algorithms in order to investigate the general performance of it. The numerical experiments show that the proposed algorithm is a promising algorithm and can reach to the optimal or near optimal solution faster than the other comparative algorithms.

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