A Variable Neighborhood Search for Solving the Linear Ordering Problem

A Systematic change of Neighborhood within a possibly randomized local search algorithm yields asimple and effective metaheuristic for combinatorial and global optimization. In this paper we presenta VariableNeighborhoodSearch implementation designed to find high quality solutionsfor the NP-hardLinear Ordering Problem, which has a significant number of application in practice, such triangulationof input-output matrices, archeological seriation, minimizing total weighted completion time in one-machine scheduling, and aggregation of individual preferences.We perform our implementation on theset of 49 instances in LOLIB, in order to compare our results with the Tabu Search of Laguna, et al.