Understanding instance complexity in the linear ordering problem

Abstract

The Linear Ordering Problem is a combinatorial optimization problem which has been frequently addressed in the literature due to its numerous applications in diverse fields. In spite of its popularity, little is known about its complexity. In this paper we analyze the linear ordering problem trying to identify features or characteristics of the instances that can provide useful insights into the difficulty of solving them. Particularly, we introduce two different metrics, insert ratio and ubiquity ratio, that measure the difficulty of solving the LOP with local search type algorithms with the insert neighborhood system. Conducted experiments demonstrate that the proposed metrics clearly correlate with the complexity of solving the LOP with a multistart local search algorithm. © 2013 Springer-Verlag.