Multi-strategy fusion improved Northern Goshawk optimizer is used for engineering problems and UAV path planning.

Addressing the imbalance between exploration and exploitation, slow convergence, local optima Traps, and low convergence precision in the Northern Goshawk Optimizer (NGO): Introducing a Multi-Strategy Integrated Northern Goshawk Optimizer (MINGO). In response to challenges faced by the Northern Goshawk Optimizer (NGO), including issues like the imbalance between exploration and exploitation, slow convergence, susceptibility to local optima, and low convergence precision, this paper introduces an enhanced variant known as the Multi-Strategy Integrated Northern Goshawk Optimizer (MINGO). The algorithm tackles the balance between exploration and exploitation by improving exploration strategies and development approaches. It incorporates Levy flight strategies to preserve population diversity and enhance convergence precision. Additionally, to avoid getting trapped in local optima, the algorithm introduces Cauchy mutation strategies, improving its capability to escape local optima during the search process. Finally, individuals with poor fitness are eliminated using the crossover strategy of the Differential Evolution algorithm to enhance the overall population quality. To assess the performance of MINGO, this paper conducts an analysis from four perspectives: population diversity, balance between exploration and exploitation, convergence behavior, and various strategy variants. Furthermore, MINGO undergoes testing on the CEC-2017 and CEC-2022 benchmark problems. The test results, along with the Wilcoxon rank-sum test results, demonstrate that MINGO outperforms NGO and other advanced optimization algorithms in terms of overall performance. Finally, the applicability and superiority of MINGO are further validated on six real-world engineering problems and a 3D Trajectory planning for UAVs.