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This paper introduces an innovative extension of the DIRECT algorithm specifically designed to solve global optimization problems that involve Lipschitz continuous functions subject to linear constraints. Our approach builds upon recent advancements in DIRECT-type algorithms, incorporating novel techniques for partitioning and selecting potential optimal hyper-rectangles. A key contribution lies in applying a new mapping technique to eliminate the infeasible region efficiently. This allows calculations to be performed only within the feasible region defined by linear constraints. We perform extensive tests using a diverse set of benchmark problems to evaluate the effectiveness and performance of the proposed algorithm compared to existing DIRECT solvers. Statistical analyses using Friedman and Wilcoxon tests demonstrate the superiority of a new algorithm in solving such problems. [ABSTRACT FROM AUTHOR]

Applied optimization problems often include constraints. Although the well-known derivative-free global-search DIRECT algorithm performs well solving box-constrained global optimization problems, it does not naturally address constraints. In this article, we develop a new algorithm DIRECT-GLce for general constrained global optimization problems incorporating two-step selection procedure and penalty function approach in our recent DIRECT-GL algorithm. The proposed algorithm effectively explores hyper-rectangles with infeasible centers which are close to boundaries of feasibility and may cover feasible regions. An extensive experimental investigation revealed the potential of the proposed approach compared with other existing DIRECT-type algorithms for constrained global optimization problems, including important engineering problems. [ABSTRACT FROM AUTHOR]

• 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]