Selective discrete particle swarm optimization for the team orienteering problem with time windows and partial scores

Abstract This paper introduces the Team Orienteering Problem with Time Windows and Partial Scores (TOPTW-PS), which is an extension of the Team Orienteering Problem with Time Windows (TOPTW). In the context of the TOPTW-PS, each node is associated with a set of scores with respect to a set of attributes. The objective of TOPTW-PS is to find a set of routes that maximizes the total score collected from a subset of attributes when visiting the nodes subject to the time budget and the time window at each visited node. We develop a mathematical model and propose a discrete version of the Particle Swarm Optimization (PSO), namely, the Selective-Discrete PSO (S-DPSO), to solve TOPTW-PS. The proposed S-DPSO uses four different movement schemes to move a particle from its current position. The best movement scheme is selected to determine the next position of the particle. To evaluate the performance of the proposed S-DPSO algorithm, we first test S-DPSO on two variants of Orienteering Problem, namely, Team Orienteering Problem (TOP) and TOPTW. Experimental results show that S-DPSO performs well in solving benchmark instances of TOP and TOPTW. In general, S-DPSO is comparable to the state-of-the-art algorithms for these problems. We also apply the S-DPSO to solve 168 newly generated TOPTW-PS instances and conclude that the proposed S-DPSO can produce high-quality TOPTW-PS solutions.