The Node Weight Dependent Traveling Salesperson Problem: Approximation Algorithms and Randomized Search Heuristics
This addresses optimization challenges in vehicle routing and evolutionary computation, such as the Traveling Thief Problem, by modeling weight-dependent costs, but it is incremental as it builds on known TSP variants.
The paper tackles the node weight dependent Traveling Salesperson Problem (TSP), where travel cost increases with visited node weights, by providing a 3.59-approximation algorithm for metric distances and bounded positive weights, and experimentally shows the impact of weights on node positions in tours using randomized search heuristics.
Several important optimization problems in the area of vehicle routing can be seen as a variant of the classical Traveling Salesperson Problem (TSP). In the area of evolutionary computation, the traveling thief problem (TTP) has gained increasing interest over the last 5 years. In this paper, we investigate the effect of weights on such problems, in the sense that the cost of traveling increases with respect to the weights of nodes already visited during a tour. This provides abstractions of important TSP variants such as the Traveling Thief Problem and time dependent TSP variants, and allows to study precisely the increase in difficulty caused by weight dependence. We provide a 3.59-approximation for this weight dependent version of TSP with metric distances and bounded positive weights. Furthermore, we conduct experimental investigations for simple randomized local search with classical mutation operators and two variants of the state-of-the-art evolutionary algorithm EAX adapted to the weighted TSP. Our results show the impact of the node weights on the position of the nodes in the resulting tour.