Multi-objective red-billed blue magpie optimizer: A novel algorithm for multi-objective UAV path planning

Numerical optimization, UAV path planning, and engineering design challenges form key foundations in advancing artificial intelligence. This paper presents an extension of the single-objective Red-billed Blue Magpie Optimizer (RBMO) into a multi-objective framework, called the Multi-objective Red-billed Blue Magpie Optimizer (MORBMO), developed specifically to solve complex multi-objective UAV path planning problems. Drawing inspiration from the hunting behaviors and food storage strategies of Red-billed Blue Magpies, MORBMO improves both exploration and exploitation through group search mechanisms and team-based tactics. MORBMO builds on RBMO by adding a multi-objective repository system that uses non-dominated sorting to organize solutions into Pareto fronts and a crowding distance method to maintain solution diversity across the Pareto front. The algorithm also includes a food storage approach to keep high-quality solutions from earlier iterations, modifying RBMO's original single-objective methods for multi-objective optimization. These features let MORBMO effectively manage trade-offs between competing objectives while preserving a varied set of solutions. We tested MORBMO thoroughly against standard multi-objective benchmark problems (ZDT, DTLZ, WFG, UF, and CF) and compared it with existing algorithms using four measures: Generational Distance (GD), Spacing, Inverted Generational Distance (IGD), and Hypervolume (HV). Results show MORBMO performs well in achieving balance between solution quality, diversity, and spread, providing useful approaches for difficult multi-objective problems. We applied MORBMO to three UAV path planning challenges: minimizing (1) fuel and threat costs, (2) path length, height cost, and smoothness, and (3) path length, threat cost, height cost, and smoothness together. In each test, MORBMO produced effective, safe, and smooth flight paths that performed better than other methods. These outcomes demonstrate MORBMO's value as an enhanced version of RBMO for multi-objective UAV path planning tasks. The source code of MORBMO is available at https://github.com/oykc1234/MORBMO.