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The log\u2010sigmoid function is used to construct the fitness function. The implementation of ANN on SPDDE problems is formulated for different solvers and trained with different weights. The optimization solvers such as the genetic algorithm (GA), sequential quadratic programming (SQP), and pattern search (PS) are hybridized with the active set technique (AST) and the interior\u2010point technique (IPT) and is used to check the accuracy and rapid convergence of the numerical results of the SPDDE model. The numerical outcomes demonstrate that the system is easy to handle and efficient to solve with boundary conditions. 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