LOLIB is a library of sample instances for the linear ordering problem. LOLIB includes data as well as optimum solution values. The Linear Ordering Problem is the following question. A set of n objects is given which have to be ordered in a linear sequence. For every pair i and j of objects there are coefficients c_{ij} (c_{ji}) expressing the preference for having i before j (j before i) in this sequence. The task is to find a linear sequence such that the sum of the coefficients that are compatible with this ordering is maximized. A popular application of the Linear Ordering Problem occurs in economics as the so-called Triangulation Problem for Input-Output Matrices. Our data comes from this application.

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  1. Doignon, Jean-Paul; Rexhep, Selim: Primary facets of order polytopes (2016)
  2. Terán-Villanueva, J.David; Fraire Huacuja, Héctor Joaquín; Carpio Valadez, Juan Martín; Pazos Rangel, Rodolfo; Puga Soberanes, Héctor José; Martínez Flores, José A.: A heterogeneous cellular processing algorithm for minimizing the power consumption in wireless communications systems (2015)
  3. Fernández, Elena; Puerto, Justo; Rodríguez-Chía, Antonio M.: On discrete optimization with ordering (2013)
  4. Anjos, Miguel F.; Liers, Frauke: Global approaches for facility layout and VLSI floorplanning (2012)
  5. Caspard, Nathalie; Leclerc, Bruno; Monjardet, Bernard: Finite ordered sets. Concepts, results and uses (2012)
  6. Chistyakov, Vyacheslav V.; Goldengorin, Boris I.; Pardalos, Panos M.: Extremal values of global tolerances in combinatorial optimization with an additive objective function (2012)
  7. Gutin, Gregory; Yeo, Anders: Constraint satisfaction problems parameterized above or below tight bounds: a survey (2012)
  8. Martí, Rafael; Reinelt, Gerhard; Duarte, Abraham: A benchmark library and a comparison of heuristic methods for the linear ordering problem (2012)
  9. Palagi, Laura; Piccialli, Veronica; Rendl, Franz; Rinaldi, Giovanni; Wiegele, Angelika: Computational approaches to MAX-cut (2012)
  10. Pedings, Kathryn E.; Langville, Amy N.; Yamamoto, Yoshitsugu: A minimum violations ranking method (2012)
  11. Chaovalitwongse, W.Art; Oliveira, Carlos A.S.; Chiarini, Bruno; Pardalos, Panos M.; Resende, Mauricio G.C.: Revised GRASP with path-relinking for the linear ordering problem (2011)
  12. Duarte, Abraham; Laguna, Manuel; Martí, Rafael: Tabu search for the linear ordering problem with cumulative costs (2011)
  13. Sukegawa, Noriyoshi; Yamamoto, Yoshitsugu; Zhang, Liyuan: Lagrangian relaxation and pegging test for linear ordering problems (2011)
  14. Wimer, Shmuel; Moiseev, Konstantin; Kolodny, Avinoam: On VLSI interconnect optimization and linear ordering problem (2011)
  15. Buchheim, Christoph; Wiegele, Angelika; Zheng, Lanbo: Exact algorithms for the quadratic linear ordering problem (2010)
  16. Charon, Irène; Hudry, Olivier: An updated survey on the linear ordering problem for weighted or unweighted tournaments (2010)
  17. Cook, William: Fifty-plus years of combinatorial integer programming (2010)
  18. Oswald, M.; Reinelt, G.; Seitz, H.: Applying mod-$k$-cuts for solving linear ordering problems (2009)
  19. Anjos, Miguel F.; Vannelli, Anthony: Computing globally optimal solutions for single-row layout problems using semidefinite programming and cutting planes (2008)
  20. Bertacco, Livio; Brunetta, Lorenzo; Fischetti, Matteo: The linear ordering problem with cumulative costs (2008)

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