This paper introduces an Improved Pigeon-Inspired Optimization (IPIO) algorithm to solve MTSPs with multiple complex constraints, addressing both single-depot (SDMTSP) and multi-depot (MDMTSP) scenarios. For the first time, the Pigeon-Inspired Optimization (PIO) algorithm is applied to the TSP and MTSP domains, with three novel operators specifically developed to address the unique challenges of these problems: the Probability Heuristic Initialization Operator, the Greedy Crossover Operator, and the Probability Crossover Operator. These operators significantly enhance the worldwide exploration ability of the algorithm and convergence rate while preventing path overlaps and redundancy. To confirm the efficiency of the IPIO algorithm, three widely recognized comparative algorithms—Improved Partheno Genetic Algorithm (IPGA), Particle Swarm Optimization (PSO), and Partheno Genetic Algorithm (PGA)—were implemented, with extensive comparative experiments conducted on multiple benchmark instances. The investigative results demonstrate that the IPIO algorithm is markedly outperformed by the other algorithms in solution quality for large-scale MTSPs while exhibiting exceptional computational efficiency. Furthermore, this paper explores the impact of the number of salespeople and cities on the outcome, emphasizing the importance of optimizing the number of salespeople to enhance algorithm performance. The proposed approach offers new perspectives and methods for addressing TSP and MTSP-related problems.