A Variable Neighborhood Search Approach for the S-labeling Problem

The S-labeling problem is a graph layout problem that assigns numeric labels to the vertices of a graph. It aims to minimize the sum of the minimum numeric label assigned to each pair of adjacent vertices. In this preliminary work, we propose the use of the Variable Neighborhood Search (VNS) framework to test different Shake procedures and Local Search methods for the problem. We compare our VNS variants with the state-of-the-art Population-based Iterated Greedy algorithm on a set of benchmark instances. The results show that our VNS methods can obtain competitive solutions with a low deviation, but they are not able to improve the best-known values. We discuss the strengths and weaknesses of our proposal and suggest some future research directions. This work lays the groundwork for future research into the S-Labeling problem using Variable Neighborhood Search.