Horseshoe Crab Optimization: A Novel Nature-inspired Metaheuristic based on Spawning and Satellite Male Aggregation Behaviours

A novel population-based metaheuristic algorithm, termed Horseshoe Crab Optimization (HCO), inspired by the reproductive behaviour of horseshoe crabs (Limulidae) in tidal ecosystems, is introduced in this paper.HCO models two key biological mechanisms: spawning aggregation and satellite male behaviour.Spawning aggregation, occurring during high-tide periods, drives the population toward favourable regions for egg-laying and serves as an effective global exploration mechanism, while satellite male behaviour, in which males position themselves around high-quality females and adjust their locations precisely, is modelled as a targeted local exploitation process.This mechanism facilitates focused search in regions containing high-quality solutions and, through the incorporation of stochastic components, prevents premature convergence to local optima.The mathematical formulation of HCO incorporates tidal-phase modulation, adaptive convergence factors, and stochastic intensities, enabling dynamic transitions between exploration and exploitation phases.Each member of the population represents a candidate solution, and updates are governed by movement rules inspired by reproductive behaviour along with a fitness-based acceptance criterion, ensuring both solution diversity and convergence stability.HCO is evaluated on 23 benchmark functions, including unimodal, high-dimensional multimodal, and fixed-dimensional multimodal problems, and its performance compared with nine state-of-the-art metaheuristic algorithms.The results demonstrate that HCO achieves first-rank performance in 20 out of 23 functions, exhibiting superior convergence speed, solution accuracy, and robustness, thereby establishing it as a reliable and versatile framework for addressing complex, high-dimensional optimization problems.