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The Team Orienteering Problem With Time Windows (TOPTW) is a transportation problem case that have a set of vertices with a score, service time, and the time windows, start and final at a depot location. A number of paths are constructed to maximize the total collected score by the vertices which is visited. Each vertice can be visited only once and the visit can only start during the  time window of vertices. This paper proposes a Particle Swarm Optimization algorithm for solving the TOPTW, by defining a specific particle for representing the solution of TOPTW within the PSO algorithm and two alternatives, called PSO_TOPTW1 and PSO_TOPTW2, for translating the particle position to form the routes of the path. The performance of the proposed PSO algorithm is evaluated through some benchmark data problem available in the literature. The computational results show that the proposed PSO is able to produce sufficiently good TOPTW solutions that are comparable with corresponding solutions from other existing methods for solving the TOPTW.

Applying Particle Swarm Optimization for Solving Team Orienteering Problem with Time Windows