Self-Organizing Map for the Prize-Collecting Traveling Salesman Problem

Abstract

In this paper, we propose novel adaptation rules for the selforganizing map to solve the prize-collecting traveling salesman problem (PC-TSP). The goal of the PC-TSP is to find a cost-efficient tour to collect prizes by visiting a subset of a given set of locations. In contrast with the classical traveling salesman problem, where all given locations must be visited, locations in the PC-TSP may be skipped at the cost of some additional penalty. Using the self-organizing map, locations for the final solution may be selected during network adaptation, and locations where visitation would be more expensive than their penalty can be avoided. We have applied the proposed self-organizing map learning procedure to autonomous data collection problems, where the proposed approach provides results competitive with an existing combinatorial solver.

Developing an Energy Effective Autonomous USV for Undertaking Missions at the Highlands of Peru

“…In practical missions, such as the water quality monitoring mission considered in this paper, due to the spatial distribution of the mission points, the measurements retrieved from one point could also be included in the information provided by other nearby points [9] making it not obligatory for the USV to transit through all points to complete the mission. Therefore, in such a case, differing from the conventional multi-task allocation problem, where the complete visiting of all mission points is compulsory, the problem to address the energy-efficient autonomous navigation should consider: 1) selecting the appropriate mission points according to mission requirements; 2) finding a mission execution sequence to complete the selected mission points; 3) visiting the mission points while avoiding obstacles en route; 4) re-planning the execution sequence by considering the energy constraints.…”

“…In such a case, the neurons are expelled away from obstacles during updating process to ensure the safety. Moreover, a new adaptive strategy was designed by [9], called the prize-collecting traveling salesman problem, with additional penalties given to certain mission points, which locations will be skipped during the travel.…”