Abstract

In this paper, we report on the Hopfield Neural Network (HNN) for the Orienteering Problem (OP) that is generalized to solve instances of the Close Enough Orienteering Problem (CEOP). In the orienteering problems, we are searching for a limited budget tour to maximize collected rewards by visiting selected target locations. In the CEOP, it is allowed to collect the reward remotely within a non-zero communication range. Thus we can save travel costs by collecting rewards at suitable visiting locations of the disk-shaped neighborhoods of target locations. The proposed approach combines the HNN for the OP with the Second-Order Cone Programming (SOCP) that is employed to determine locally optimal locations of visits to the disk-shaped neighborhoods of the target locations. Regarding the reported evaluation results using standard benchmarks, the proposed SOCP-based approach provides solutions with the improved solution quality compared to the previous HNN-based method with discrete samples of the possible locations of visits.