Search Space Analysis of the Linear Ordering Problem

The Linear Ordering Problem (LOP) is an NP-hard combinatorial optimization problem that arises in a variety of applications and several algorithmic approaches to its solution have been proposed. However, few details are known about the search space characteristics of LOP instances. In this article we develop a detailed study of the LOP search space. The results indicate that, in general, LOP instances show high fitness-distance correlations and large autocorrelation length but also that there exist significant differences between real-life and randomly generated LOP instances. Because of the limited size of real-world instances, we propose new, randomly generated large real-life like LOP instances which appear to be much harder than other randomly generated instances. Additionally, we propose a rather straightforward Iterated Local Search algorithm, which shows better performance than several state-of-the-art heuristics.