A New Constructive Heuristic Driven by Machine Learning for the Traveling Salesman Problem

Recent systems applying Machine Learning (ML) to solve the Traveling Salesman Problem (TSP) exhibit issues when they try scale up real case scenarios with several hundred vertices. The use of Candidate Lists (CLs) has been brought cope issues. A CL is defined as a subset all edges linked given vertex such that it contains mainly are believed be found in optimal tour. initialization procedure identifies for each TSP aids solver by restricting search space during solution creation. It results reduction computational burden well, which highly recommended solving large TSPs. So far, ML was engaged create CLs and values on elements these expressing preferences at insertion. Although promising, do not restrict what learns does solutions, bringing them some generalization Therefore, motivated exploratory statistical studies behavior multiple this work, we rethink usage purposely employing system just task avoids well-known weaknesses, training presence frequent outliers detection under-represented events. confirm inclusion most likely optimal. edge considered employed an input neural network, charge distinguishing from not. proposed approach enables reasonable unveils efficient balance between optimization techniques. Our ML-Constructive heuristic trained small instances. Then, able produce solutions—without losing quality—for problems well. We compare our method against classic constructive heuristics, showing new performs well TSPLIB instances 1748 cities. exhibits expensive constant computation time due training, proved complexity worst-case scenario—for construction after training—is O(n2logn2), n being number vertices instance.