Intensification and diversification with elite tabu search solutions for the linear ordering problem

Abstract

-In this paper, we develop a new heuristic procedure for the linear ordering problem (LOP). This NP-hard problem has a significant number of applications in practice. The LOP, for example, is equivalent to the so-called triangulation problem for input-output tables in economics. In this paper we concentrate on matrices that arise in the context of this real-world application. The proposed algorithm is based on the tabu search methodology and incorporates strategies for search intensification and diversification. For search intensification, we experiment with path relinking, a strategy proposed several years ago in connection with tabu search, which has been rarely used in actual implementations. Extensive computational experiments with input-output tables show that the proposed procedure outperforms the best heuristics reported in the literature. Furthermore, the experiments also show the merit of achieving a balance between intensification and diversification in the search. Laguna, et al. / 2

Designing a Hybrid Genetic Algorithm for the Linear Ordering Problem

“…On the other hand, usually t 2 T 1 since in each "round", FirstFit has up to n 2 INSERT moves, while BestFit makes 1 best INSERT move. This may explain the results in [1] that BestFit even takes more real CPU time than FirstFit.…”

“…It contains 49 instances of real-world input-output tables from sectors in the European and United States Economies. The data together with optimal solutions can be obtained from www.iwr.uni-heidelberg.de/groups/comopt/software/LOLIB/ Nearly all papers on LOP use LOLIB as test instances: in [1], the results of Chanas-Kobylanski algorithm(CK) and Tabu Search with path relinking(TS-LOP) are reported. [2] shows computational results of two Scatter Search versions(SS, SS10).…”

“…However, all of these exact algorithms are extremely time-consuming. On the other hand, heuristic algorithms seem to be more practical in solving large instances of this problem [1,2,3,4,5]. The heuristic proposed by Chanas and Kobylanski [5] can usually provide acceptable solutions both in terms of time and quality.…”

“…The heuristic proposed by Chanas and Kobylanski [5] can usually provide acceptable solutions both in terms of time and quality. Laguna et al [1] applied Tabu Search technique with path relinking strategy on this problem successfully, while Campos et al [2] used Scatter Search to solve this problem. These two approaches are often regarded as the best at this moment.…”

“…The purpose of this paper includes: (1) to develop an effective heuristic for LOP and (2) to illustrate a general procedure of designing a hybrid genetic algorithm. Genetic algorithms(GA) have shown to be competitive technique for solving general combinatorial optimization problems.…”