This study proposes Enhanced Beaver Behavior Optimizer (EBBO) to overcome the original BBO algorithm’s limitations in handling complex optimization problems. EBBO integrates a three-phase cooperative framework, incorporating adaptive mutation, dynamic opposition-based learning, and an risk-aware decision strategy inspired by simulated annealing. Comprehensive evaluations on the CEC 2017 and CEC 2020 benchmark suites demonstrate that EBBO significantly outperforms nine widely used algorithms (e.g., BBO, FATA, DE) in convergence accuracy, stability, and robustness, especially for high-dimensional and multimodal functions. EBBO achieves average objective value reductions of 15–50% and standard deviation reductions of 30–70% compared to the original BBO, with Wilcoxon rank-sum tests confirming statistical significance across most functions. When applied to three classical engineering design problems—step-cone pulley, pressure vessel, three-bar truss optimization, and 3D UAV path planning—EBBO consistently achieved the best or near-optimal solutions while satisfying all nonlinear constraints. The results confirm that EBBO effectively balances exploration and exploitation, offering a reliable and efficient approach for solving complex constrained optimization challenges in both benchmark and real-world engineering contexts.

The Kangaroo Escape Optimizer (KEO) is a recently proposed biomimetic metaheuristic inspired by the adaptive escape strategies of kangaroos in predator–prey interactions. Although effective, KEO-like algorithms based on many populations may suffer from premature convergence and loss of population diversity when addressing complex, multimodal, and constrained optimization problems. This paper proposes an Enhanced Kangaroo Escape Optimizer (EKEO) that integrates Differential Evolution Mutation (DEM) and Quasi-Oppositional Learning (QOL) to address fundamental limitations in exploration–exploitation balance. From a biomimetic perspective, DEM mimics the refined high-frequency muscular adjustments of a kangaroo during close-range evasion, enabling local refinement around promising solutions, while QOL emulates the animal’s sudden directional changes and scanning behavior to preserve population diversity and escape local optima. Their principled integration yields a robust optimization framework that consistently outperforms state-of-the-art and classical metaheuristics across benchmark functions and real-world engineering problems. The findings suggest a generalizable design principle for biomimetic hybrid metaheuristics, demonstrating that coupling directed exploitation with diversity-preserving exploration leads to reliable high-performance optimization. The performance of EKEO is rigorously evaluated in two phases. First, its optimization accuracy and convergence speed are benchmarked against 11 state-of-the-art and classical metaheuristics on 23 classical benchmark functions and the CEC 2019 test suite. Second, its practical applicability and constraint-handling effectiveness are validated on four real-world engineering design problems: step-cone pulley, gear system, tubular column, and pressure vessel design. The experimental results are supported by comprehensive statistical analyses (including Wilcoxon rank-sum tests) and convergence curves, showing that EKEO consistently outperforms its competitors in solution quality, convergence speed, and robustness. These findings establish EKEO as a competitive, reliable, and versatile biomimetic optimization tool suitable for solving complex continuous and constrained engineering optimization problems.

This paper proposes an Enhanced Projection-Iterative-Methods-based Optimizer (EPIMO) to overcome the limitations of its predecessor, the Projection-Iterative-Methods-based Optimizer (PIMO), including deterministic parameter decay, insufficient diversity maintenance, and static exploration–exploitation balance. The enhancements incorporate three core strategies: (1) an adaptive decay strategy that introduces stochastic perturbations into the step-size evolution; (2) a mirror opposition-based learning strategy to actively inject structured population diversity; and (3) an adaptive adjustment mechanism for the Lévy flight parameter $\beta$ to enable phase-sensitive optimization behavior. The effectiveness of EPIMO is validated through a multi-stage experimental framework. Systematic evaluations on the CEC 2017 and CEC 2022 benchmark suites, alongside four classical engineering optimization problems (Himmelblau function, step-cone pulley design, hydrostatic thrust bearing design, and three-bar truss design), demonstrate its comprehensive superiority. The Wilcoxon rank-sum test confirms statistically significant performance improvements over its predecessor (PIMO) and a range of state-of-the-art and classical algorithms. EPIMO exhibits exceptional performance in convergence accuracy, stability, robustness, and constraint-handling capability, establishing it as a highly reliable and efficient metaheuristic optimizer. This research contributes a systematic, adaptive enhancement framework for projection-based metaheuristics, which can be generalized to improve other swarm intelligence systems when facing complex, constrained, and high-dimensional engineering optimization tasks.

Low-altitude UAV (Unmanned Aerial Vehicle) path planning in urban areas must balance energy efficiency, safety, terrain clearance, climb constraints, and restricted-airspace avoidance. To address this problem, this study formulates urban low-altitude UAV path planning as a constrained bi-objective optimization model that simultaneously minimizes flight energy consumption and cumulative threat exposure. An enhanced multi-objective Grey Wolf Optimizer, denoted as IMOGWO, is developed to solve the proposed energy–threat-aware path-planning model. To improve search performance in fragmented urban feasible spaces, two path-oriented candidate-generation mechanisms are incorporated. The first is an elite-guided Gaussian multiplicative perturbation, which refines waypoint offsets around high-quality feasible paths. The second is a center-constrained quasi-opposite candidate generation, which explores complementary bypass corridors by sampling between the classical opposite point and the search-space center, thereby reducing the risk of generating extreme infeasible solutions. Experiments are conducted on two representative urban low-altitude scenarios: Map 1 with 100 buildings and one no-fly zone and Map 2 with 150 buildings. An additional Map 2 configuration with dense buildings and three no-fly zones is also evaluated as Scenario 3 together with a non-GWO NSGA-II baseline. The proposed IMOGWO achieves the highest hypervolume (HV) values in both original scenarios. In the additional Scenario 3, the 30-run mean HV of IMOGWO is also higher than those of the four baselines, including NSGA-II. Compared with MOPSO, MOGWO, and MOGGO, IMOGWO improves HV by 19.05%, 2.36%, and 3.46% in Map 1 and by 26.51%, 12.17%, and 4.22% in Map 2, respectively. The results demonstrate that the proposed method improves Pareto-set quality and provides more practical energy–threat trade-off paths for UAV operations in constrained urban low-altitude airspace.