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A gradient-based optimizer (GBO) is a recently inspired meta-heuristic technique centered on Newton's gradient-based approach. In this paper, an advanced developed version of the GBO is merged with a crossover operator (GBOC) to enhance the diversity of the created solutions. The merged crossover operator causes the solutions in the next generation to be more random. The proposed GBOC maintains the original Gradient Search Rule (GSR) and Local Escaping Operator (LEO). The GSR directs the search to potential areas and aids in its convergence to the optimal answer, while the LEO aids the searching process in avoiding local optima. The proposed GBOC technique is employed to optimally place and size the distribution static VAR compensator (D-SVC), one of the distribution flexible AC transmission devices (D-FACTS). It is developed to maximize the yearly energy savings via power losses concerning simultaneously different levels of the peak, average, and light loadings. Its relevance is tested on three distribution systems of IEEE 33, 69, and 118 nodes. Based on the proposed GBOC, the outputs of the D-SVCs are optimally varying with the loading level. Furthermore, their installed ratings are handled as an additional constraint relating to two compensation levels of 50% and 75% of the total reactive power load to reflect a financial installation limit. The simulation applications of the proposed GBOC declare great economic savings in yearly energy losses for the three distribution systems with increasing compensation levels and iterations compared to the initial case. In addition, the effectiveness of the proposed GBOC is demonstrated compared to several techniques, such as the original GBO, the salp swarm algorithm, the dwarf mongoose algorithm, differential evolution, and honey badger optimization. [ABSTRACT FROM AUTHOR]

• An economic environmental operation in hybrid AC-MTDC power systems is introduced. • An Improved Artificial Hummingbird Optimizer (IAHO) is developed to minimize fuel costs, environmental pollution, and losses in AC-MTDC systems. • The proposed IAHO includes a variety of territorial foraging tactics and a linear control process that improve both local and universal searching capabilities. • The simulation findings declare high economic, environmental, and technical benefits via the proposed IAHO with significant outperformance over several reported algorithms. Innovative technologies of multi-terminal high voltage direct current (HVDC), often known as "MTDC," represent additional features for better active and reactive power control when hybridized with traditional AC power systems. In this sequence, optimal operation in hybrid AC and MTDC power systems becomes highly economically and environmentally necessary. This paper presents an Improved Artificial Hummingbird Optimizer (IAHO) technique for reducing total generation fuel costs, environmental pollution, and whole power losses in AC-MTDC power systems. The proposed IAHO includes a variety of territorial foraging tactics (TFTs) and a Linear Control Process (LCP) which improve both local and universal searching capabilities. The proposed IAHO and AHO are performed on modified IEEE 57-bus and 30-bus hybrid AC and multi-terminal HVDC power systems. The simulation findings declare high economic, environmental, and technical benefits based on the proposed IAHO. A significant reduction in fuel costs, emissions, and losses with 22%, 59.51%, and 71.83% compared to the initial case for the IEEE 57-bus hybrid AC-MTDC power system. Also, the IEEE 30-bus hybrid AC-MTDC power system significantly reduced fuel costs, emissions, and losses by 17.01%, 16.04%, and 28.49% compared to the initial case. Moreover, the significant outperformance of the proposed IAHO is demonstrated over several reported algorithms. [ABSTRACT FROM AUTHOR]