Improved Group Theory Optimization Algorithm Based on Dual Encoding for Traveling Salesman Problem

The Traveling Salesman Problem (TSP) is a classical combinatorial optimization problem whose complexity grows rapidly with problem size, making it difficult to solve efficiently using exact algorithms. This paper proposes an improved group theory optimization algorithm based on dual encoding (DE-GTOA). Built on Group Theory Optimization Algorithm (GTOA), DE-GTOA introduces two TSP-specific encoding schemes and a conversion mechanism to enhance performance and maintain feasibility. The 3 -opt local search is also integrated to refine solutions. Experiments on TSPLIB instances show that DE-GTOA delivers high solution quality, strong stability, and competitive robustness, demonstrating its effectiveness for solving TSP.