A benchmark library and a comparison of heuristic methods for the linear ordering problem

The linear ordering problem consists of finding an acyclic tournament in a complete weighted digraph of maximum weight. It is one of the classical NP‐hard combinatorial optimization problems. This paper surveys a collection of heuristics and metaheuristic algorithms for finding near‐optimal solutions and reports about extensive computational experiments with them. We also present the new benchmark library LOLIB which includes all instances previously used for this problem as well as new ones.