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Differential evolution (DE) algorithms compose an efficient type of evolutionary algorithm (EA) for the global optimization domain. Although it is well known that the population structure has a major influence on the behavior of EAs, there are few works studying its effect in DE algorithms. In this paper, we propose and analyze several DE variants using different panmictic and decentralized population schemes. As it happens for other EAs, we demonstrate that the population scheme has a marked influence on the behavior of DE algorithms too. Additionally, a new operator for generating the mutant vector is proposed and compared versus a classical one on all the proposed population models. After that, a new heterogeneous decentralized DE algorithm combining the two studied operators in the best performing studied population structure has been designed and evaluated. In total, 13 new DE algorithms are presented and evaluated in this paper. Summarizing our results, all the studied algorithms are highly competitive compared to the state-of-the-art DE algorithms taken from the literature for most considered problems, and the best ones implement a decentralized population. With respect to the population structure, the proposed decentralized versions clearly provide a better performance compared to the panmictic ones. The new mutation operator demonstrates a faster convergence on most of the studied problems versus a classical operator taken from the DE literature. Finally, the new heterogeneous decentralized DE is shown to improve the previously obtained results, and outperform the compared state-of-the-art DEs.