A hybrid artificial algae and ant colony optimization algorithm for combinatorial problems

The Traveling Salesman Problem (TSP) is a classical Nondeterministic Polynomial time (NP)-hard optimization problem that continues to inspire new metaheuristic designs. This study proposes a hybrid algorithm, termed Artificial Algae and Ant Colony Optimization (AAACO), which integrates the global search capability of Ant Colony Optimization (ACO) with the adaptive local exploitation of the Artificial Algae Algorithm (AAA) and the diversity-preserving mechanisms of Genetic Algorithms (GA). The hybrid design begins with an ACO-based seeding phase that generates high-quality initial solutions, followed by AAA-driven refinement using permutation-based crossover operators—flip, swap, and slide—to explore local neighborhoods efficiently. The algorithm’s performance was validated on ten benchmark instances from Traveling Salesman Problem Library (TSPLIB) and a real-world case covering all 81 provinces of Türkiye. Experimental results demonstrate that AAACO consistently achieves near-optimal route lengths with substantially lower computational cost compared with state-of-the-art ACO, Particle Swarm Optimization (PSO), and Artificial Bee Colony (ABC) variants. Statistical analyses, including Wilcoxon signed-rank tests, confirm that these improvements are significant at the 95% confidence level. The proposed hybrid framework thus provides a robust and scalable approach for complex routing problems and can be readily adapted to other combinatorial and continuous optimization tasks.