Several heuristic optimization algorithms have been applied to solve engineering problems. Most of these algorithms are based on populations that evolve according to different rules and parameters to reach the optimal value of a function cost through an iterative process. Different parallel strategies have been proposed to accelerate these algorithms. In this work, we combined coarse-grained strategies, based on multi-populations, with fine-grained strategies, based on a diffusion grid, to efficiently use a large number of processes, thus drastically decreasing the computing time. The Chaotic Jaya optimization algorithm has been considered in this work due to its good optimization and computational behaviors in solving both the constrained optimization engineering problems (seven problems) and the unconstrained benchmark functions (a set of 18 functions). The experimental results show that the proposed parallel algorithms outperform the state-of-the-art algorithms in terms of optimization behavior, according to the quality of the obtained solutions, and efficiently exploit shared memory parallel platforms.