The New Mushroom–Weed Hybrid Reproduction Optimization Algorithm and Its Application to Tourist Route Optimization

Nature-inspired metaheuristic algorithms are commonly applied to complex combinatorial optimization problems where exact methods are computationally impractical. Tourist route optimization is a representative multi-objective problem characterized by realistic constraints such as travel time, cost, opening hours, and transportation modes. Although Mushroom Reproduction Optimization (MRO) is computationally efficient, it often suffers from premature convergence in complex search spaces. This paper proposes a novel hybrid algorithm, Mushroom–Weed Hybrid Reproduction Optimization (MWHRO), which integrates the colony-based local search of MRO with the fitness-proportional reproduction and competitive elimination mechanisms of Invasive Weed Optimization (IWO). Hybridization enhances population diversity and global exploration while preserving fast convergence. The proposed algorithm is evaluated on a realistic tourist route optimization problem using real-world data from Zagreb, Croatia, across multiple transportation modes and objective-weight scenarios. Performance is compared against Ant Colony Optimization (ACO), IWO, and standard MRO under equal evaluation budgets. Experimental results demonstrate that MWHRO consistently achieves high-quality solutions with significantly lower execution times, particularly in constrained and multimodal scenarios. Statistical analysis confirms the robustness and practical suitability of the proposed approach for real-world route optimization.