MOPS – Mathematical optimization system. This paper discusses a software system for solving large scale linear and mixed-integer optimization models. The system in its present form is the result of several years of research and development. The first functional version of MOPS was completed 1987 for the IBM 6150 (a predecessor of the RS/6000) under AIX. A benchmark model from the Petroleum industry with 5563 rows and 6181 columns was solved with MOPS in 5 hours. The newest version solves this model in 6.51 minutes on a MS-DOS PC with i80486 processor (25 Mhz). This paper discusses only LP optimization. The MIP optimizer in MOPS is a prototype version which will undergo major changes in the future. We describe algorithmic aspects, implementation issues and numerical results on Netlib and other real-life LP models. Sophisticated LP optimizers — although simple from a mathematical point of view — are algorithmically very complex. The discussion is therefore limited to a few fundamental issues that we feel are important.

References in zbMATH (referenced in 20 articles , 1 standard article )

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  1. Wesselmann, Franz; Koberstein, Achim; Suhl, Uwe H.: Pivot-and-reduce cuts: an approach for improving Gomory mixed-integer cuts (2011)
  2. Wiese, Jörg; Suhl, Leena; Kliewer, Natalia: Mathematical models and solution methods for optimal container terminal yard layouts (2010)
  3. Wesselmann, Franz; Koberstein, Achim; Suhl, Uwe H.: Strengthening Gomory mixed-integer cuts (2009)
  4. Kliewer, Natalia; Gintner, Vitali; Suhl, Leena: Line change considerations within a time-space network based multi-depot bus scheduling model (2008)
  5. Koberstein, Achim: Progress in the dual simplex algorithm for solving large scale LP problems: Techniques for a fast and stable implementation (2008)
  6. Koberstein, Achim; Suhl, Uwe H.: Progress in the dual simplex method for large scale LP problems: Practical dual phase 1 algorithms (2007)
  7. Christophel, Philipp M.; Suhl, Leena; Suhl, Uwe H.: Finding feasible solutions to hard mixed-integer programming problems using hybrid heuristics (2006)
  8. Guo, Yufeng; Mellouli, Taïeb; Suhl, Leena; Thiel, Markus P.: A partially integrated airline crew scheduling approach with time-dependent crew capacities and multiple home bases (2006)
  9. Kliewer, Natalia; Mellouli, Taïeb; Suhl, Leena: A time-space network based exact optimization model for multi-depot bus scheduling (2006)
  10. Mellouli, Taïeb: A network flow approach to crew scheduling based on an analogy to an aircraft/train maintenance routing problem (2001)
  11. Jünger, Michael; Thienel, Stefan: The ABACUS system for branch-and-cut-and-price algorithms in integer programming and combinatorial optimization (2000)
  12. Meyr, H.: Simultaneous lotsizing and scheduling by combining local search with dual reoptimization (2000)
  13. Fletcher, R.: Block triangular orderings and factors for sparse matrices in LP (1998)
  14. Fletcher, Roger: A new degeneracy method and steepest-edge-based conditioning for LP (1998)
  15. Mathies, S.; Mevert, P.: A hybrid algorithm for solving network flow problems with side constraints. (1998)
  16. Ye, Yinyu: Interior point algorithms. Theory and analysis (1997)
  17. Andersen, Erling D.; Gondzio, Jacek; Mészáros, Csaba; Xu, Xiaojie: Implementation of interior-point methods for large scale linear programs (1996)
  18. Suhl, Uwe H.: MOPS -- Mathematical optimization system (1994)
  19. Suhl, Uwe H.; Szymanski, Ralf: Supernode processing of mixed-integer models (1994)
  20. Suhl, Leena M.; Suhl, Uwe H.: A fast LU update for linear programming (1993)