Meta-bird mating optimizer for combinatorial optimization problems

Combinatorial optimization problems, such as the Traveling Salesman Problem (TSP) and the Berth Allocation Problem (BAP), are challenging problems due to their complex search spaces. These challenges require an effective optimization with an efficient balance between exploration (searching through new areas of the solution space) and exploitation (refining existing solutions). The Bird Mating Optimizer (BMO) algorithm has shown improved exploitation capabilities when hybridized with local search algorithms (LS). However, this hybridization introduces additional components that need precise tuning to achieve an optimal balance between BMO exploration and LS exploitation, allowing the algorithm to perform well across different optimization problems. These components are the appropriate LS type, defining the best LS neighborhood structure, and setting optimal BMO parameters. Tuning these components manually is challenging because there is no proof on which values would consistently enhance the performance of the hybrid algorithm across all instances and throughout various search stages. Consequently, effective tuning must consider both the problem type and the current search status. To address this challenge, a new meta-bird mating optimizer (Meta-BMO) employs two levels of BMO: an upper level (BMO-optimizer) and a lower level (BMO-solver). The BMO-optimizer dynamically adjusts the components and configurations of the BMO-solver based on the search status. The BMO-solver, which is a hybrid of BMO and LS, works on solving the original optimization problem using configurations generated by the BMO-optimizer. The performance of the proposed Meta-BMO algorithm was evaluated using two combinatorial optimization problems: the Traveling Salesman Problem and the Berth Allocation Problem. The results demonstrate that the Meta-BMO algorithm outperforms the hybrid BMO with LS on both problems. Additionally, the Meta-BMO achieved competitive results compared to state-of-the-art algorithms, matching the best-known solutions for most instances.