Ing. Jindřiška Deckerová

In this paper, we propose a solution to the non-Euclidean variant of the Traveling Salesman Problem with Neighborhoods on a Sphere (TSPNS). The introduced problem formulation is motivated by practical scenarios of employing unmanned aerial vehicles in the Reflectance Transformation Imaging (RTI). In the RTI, a vehicle is requested to visit a set of sites at a constant distance from the object of interest and cast light from different directions to model the object from the images captured from another fixed location. Even though the problem can be formulated as an instance of the regular traveling salesman problem, we report a significant reduction of the solution cost by exploiting a non-zero tolerance on the light direction and defining the sites as regions on a sphere. The continuous neighborhoods of the TSPNS can be sampled into discrete sets, and the problem can be transformed into the generalized traveling salesman problem. However, finding high-quality solutions requires dense sampling, which increases the computational requirements. Therefore, we propose a practical heuristic solution based on the unsupervised learning of the Growing Self-Organizing Array (GSOA) that quickly finds an initial solution with the competitive quality to the sampling-based method. Furthermore, we propose a fast post-processing optimization to improve the initial solutions of both solvers. Based on the reported results, the proposed GSOA-based solver provides solutions of a similar quality to the transformation approach while it is about two orders of magnitude less computationally demanding.

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.

In this letter, we address the multi-goal path planning problem to determine a cost-efficient path to visit a set of three-dimensional regions. The problem is a variant of the traveling salesman problem with neighborhoods (TSPN) where an individual neighborhood consists of multiple regions, and the problem is to determine a shortest multi-goal path to visit at least one region of each neighborhood. Because each neighborhood may consist of several regions, it forms a neighborhood set, and the problem is called the generalized TSPN (GTSPN) in the literature. We propose two heuristic algorithms to provide a feasible solution of the GTSPN quickly. The first algorithm is based on a decoupled approach using a solution of the generalized TSP that is further improved by a quick post-processing procedure. Besides, we propose to employ the existing unsupervised learning technique called the growing self-organizing array to quickly find a feasible solution of the GTSPN that can be further improved by more demanding optimization. The reported results on existing benchmarks for the GTSPN indicate that both proposed heuristics provide better or competitive solutions than the state-of-the-art reference algorithm, but they are up to two orders of magnitude faster.

In this paper, we report on our early results on deploying unsupervised learning technique for solving a multi-goal path planning problem to determine a shortest path to visit a given set of 3D regions. The addressed problem is motivated by data collection missions in which a robotic vehicle is requested to visit a set of locations to perform particular measurements. Instead of precise visitation of the specified locations, it is allowed to take the measurements at the respective distance from the locations, and thus save the travel cost by exploiting non-zero sensing radius of the vehicle. In particular, the problem is formulated as a 3D variant of the Close-Enough Traveling Salesman Problem (CETSP), and the proposed approach is based on the recently introduced technique called the Growing Self-Organizing Array (GSOA). The GSOA is a neural network for routing problems that is accompanied with unsupervised learning procedure to determine a solution of the TSP-like problems in a finite number of learning epochs. Based on the reported results, the proposed GSOA-based approach provides competitive or better results than existing combinatorial heuristics based on the so-called Steiner zones, while the computational requirements are significantly lower.