A discrete enzyme action optimizer for traveling salesman problems with a smart tourism routing application: a case...

Efficient route planning is a critical component of smart tourism and destination management, particularly in regions where touristic attractions are geographically dispersed. This study proposes a discrete adaptation of the enzyme action optimizer (EAO), named discrete enzyme action optimizer (D-EAO), to address permutation-based combinatorial optimization problems, with a specific focus on the traveling salesman problem (TSP). The proposed approach integrates random-key encoding to transform continuous solutions into valid permutations, multiple neighborhood operators to enhance search diversity, and a selective 2-opt local search mechanism to improve solution quality. Through this hybrid structure, D-EAO achieves a balanced exploration-exploitation behavior in discrete search spaces. The performance of D-EAO is first evaluated on several well-known benchmark TSP instances with varying problem sizes and is comparatively analyzed against recent discrete metaheuristic algorithms, including discrete Kirchhoff's law algorithm (D-KLA), discrete Tianji's horse racing optimization (D-THRO), and discrete hiking optimization algorithm (D-HOA). Experimental results demonstrate that D-EAO consistently achieves superior or competitive performance in terms of best, average, and standard deviation metrics. Statistical significance analyses using the Wilcoxon signed-rank test confirm that the observed performance improvements are statistically significant across most medium- and large-scale instances. In addition to benchmark evaluations, the proposed algorithm is applied to a real-world tourism-oriented TSP scenario involving 46 tourist points in Bitlis, Türkiye. The results show that D-EAO generates shorter, more stable, and geographically coherent tourism routes compared to competing methods. These findings highlight the effectiveness and scalability of the proposed approach and demonstrate its potential as a decision-support tool for smart tourism planning and sustainable destination management.