Abstract
The aging of the Portuguese population is a multifaceted challenge that requires a coordinated and comprehensive response from society. In this context, social service institutions play a fundamental role in providing aid and support to the elderly, ensuring that they can enjoy a dignified and fulfilling life even in the face of the challenges of aging. This research proposes a Balanced Multiple Traveling Salesman Problem based on the Ant Colony Optimization algorithm (ACO-BmTSP) to solve a distribution of meals problem in the municipality of Mogadouro, Portugal. The Multiple Traveling Salesman Problem (mTSP) is an NP-complete problem where m salesmen perform a shortest tour between different cities, visiting each only once. The primary purpose is to minimize the sum of all distance traveled by all salesmen keeping the tours balanced. This paper shows the results of computing obtained for three, four, and five agents with this new approach and their comparison with other approaches like the standard Particle Swarm Optimization and Ant Colony Optimization algorithms. As can be seen, the ACO-BmTSP, in addition to obtaining much more equitable paths, also achieves better results in lower total costs. In conclusion, some benchmark problems were used to evaluate the efficiency of ACO-BmTSP, and the results clearly indicate that this algorithm represents a strong alternative to be considered when the problem size involves fewer than one hundred locations. © 2025 Elsevier B.V., All rights reserved.