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• The first deterministic non-redundant parallel DIRECT-type algorithms for generally constrained global optimization are introduced. • The introduced load balancing scheme for the master-worker parallel implementation can be easily adapted for other DIRECT-type algorithms. • Dynamic data structures are included in the sequential DIRECT-GLce algorithm, resulting in one of the most efficient DIRECT-type methods. • The created dataset of generally constrained global optimization problems and developed source codes of the algorithms are freely available. In this paper, two different acceleration techniques for a deterministic DIRECT (DIviding RECTangles)-type global optimization algorithm, DIRECT-GLce, are considered. We adopt dynamic data structures for better memory usage in MATLAB implementation. We also study shared and distributed parallel implementations of the original DIRECT-GLce algorithm, and a distributed parallel version for the aggressive counterpart. The efficiency of DIRECT-type parallel versions is evaluated solving box- and generally constrained global optimizations problems with varying complexity, including a practical NASA speed reducer design problem. Numerical results show a good efficiency, especially for the distributed parallel version of the original DIRECT-GLce on a multi-core PC. [ABSTRACT FROM AUTHOR]