Using Consecutive Swaps to Explore the Insertion Neighborhood in Tabu Search Solution of the Linear Ordering Problem

Abstract

In this paper the linear Ordering Problem (LOP) is approached. This problem consists in to find an ordering of rows and columns of a matrix weights, such that the sum of all the values above the main diagonal is minimized. We propose in this ongoing research, increases the efficiency of exploration method in the insertion neighborhood in the state of the art Tabu search solution. The approach is evaluated on the broad set of standard instances that include the most difficult XLOLIB instances, from which the optima values are unknown. The results for instances which optimum values are known (OI), show that the proposed method has obtained reductions in execution time ranging between 21% and 97%, while, for the most difficult instances included in the set with unknown optima (BI), the reduction reaching 98%.Wilcoxon test is used to prove that the proposed method ITS, obtains similar % average error for OI instances than the reference method RTS, and a significance reduction in the average time. Now we are working in developing additional diversification strategies that take advantage of the savings in time to explore new regions of the search space.