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The Impact and Implications of Optimization

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Business Optimization Using Mathematical Programming

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 307))

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Abstract

In this chapter many issues are touched upon which are part of more general operational research concerns, particularly when these are amplified by using mathematical programming. It includes a discussion of the possibilities of parallel optimization.

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Notes

  1. 1.

    The term inefficient is a relative term and should give nobody a bad conscience. Before the light bulb was invented a candle produced sufficient light for Homer to write the Iliad and Copernicus to prove Earth was not the center of the universe.

  2. 2.

    See page 547 for further details on this issue.

  3. 3.

    See Gamrath et al. (2020,[207]).

References

  1. Alba, E.: Parallel Metaheuristics: A New Class of Algorithms. Wiley-Interscience, New York, NY (2005)

    Book  Google Scholar 

  2. Alba, E., Luque, G.: Measuring the performance of parallel metaheuristics. In: Alba, E. (ed.) Parallel Metaheuristics: A New Class of Algorithms. Wiley Series on Parallel and Distributed Computing, chap. 2, pp. 43–62. Wiley, New York (2005)

    Chapter  Google Scholar 

  3. Alba, E., Talbi, E.G., Luque, G., Melab, N.: Metaheuristics and parallelism. In: E. Alba (ed.) Parallel Metaheuristics: A New Class of Algorithms. Wiley Series on Parallel and Distributed Computing, chap. 4, pp. 79–104. Wiley, New York (2005)

    Chapter  Google Scholar 

  4. Alba, E., Luque, G., Nesmachnow, S.: Parallel metaheuristics: recent advances and new trends. Int. Trans. Oper. Res. 20(1), 1–48 (2013)

    Article  Google Scholar 

  5. Ashford, R.W., Connard, P., Daniel, R.C.: Experiments in solving mixed integer programming problems on a small array of transputers. J. Oper. Res. Soc. 43, 519–531 (1992)

    Article  Google Scholar 

  6. Baravykaité, M., Žilinskas, J.: Implementation of parallel optimization algorithms using generalized branch and bound template. In: Bogle, I.D.L., Žilinskas, J. (eds.) Computer Aided Methods in Optimal Design and Operations, chap. 3, pp. 21–28. World Scientific Publishing Co. Pte. Ltd., Singapore (2006)

    Chapter  Google Scholar 

  7. Bergstra, J., Bengio, Y.: Random search for hyper-parameter optimization. J. Mach. Learn. Res. 13, 281–305 (2012)

    Google Scholar 

  8. Bergstra, J., Bardenet, R., Bengio, Y., Kégl, B.: Algorithms for hyper-parameter optimization. In: Proceedings of the 24th International Conference on Neural Information Processing Systems, NIPS’11, pp. 2546–2554. Curran Associates Inc., New York (2011)

    Google Scholar 

  9. Berthold, T., Farmer, J., Heinz, S., Perregaard, M.: Parallelization of the FICO Xpress-optimizer. Optim. Methods Softw. 33(3), 518–529 (2018)

    Article  Google Scholar 

  10. Censor, Y., Zenios, S.: Parallel Optimization: Theory, Algorithms, and Applications. Oxford University Press, Oxford (1997)

    Google Scholar 

  11. Colombani, Y., Heipcke, S.: Multiple Models and Parallel Solving with Mosel. Tech. rep., FICO Xpress Optimization, Birmingham (2004). http://www.fico.com/fico-xpress-optimization/docs/latest/mosel/mosel_parallel/dhtml

    Google Scholar 

  12. Coutinho, D., de Souza, S.X., Aloise, D.: A scalable shared-memory parallel simplex for large-scale linear programming (2018). CoRR abs/1804.04737

    Google Scholar 

  13. Crainic, T.G.: Parallel metaheuristics and cooperative search. In: Gendreau, M., Potvin, J.Y. (eds.) Handbook of Metaheuristics, pp. 419–451. Springer, New york (2019)

    Google Scholar 

  14. de Silva, A., Abramson, D.: A parallel interior point method and its application to facility location problems. Comput. Optim. Appl. 9, 249–273 (1998)

    Article  Google Scholar 

  15. Figueira, J., Liefooghe, A., Talbi, E.G., Wierzbicki, A.: A parallel multiple reference point approach for multi-objective optimization. Eur. J. Oper. Res. 205(2), 390–400 (2010)

    Article  Google Scholar 

  16. Gamrath, G., Anderson, D., Bestuzheva, K., Chen, W.K., Eifler, L., Gasse, M., Gemander, P., Gleixner, A., Gottwald, L., Halbig, K., Hendel, G., Hojny, C., Koch, T., Bodic, P.L., Maher, S.J., Matter, F., Miltenberger, M., Mühmer, E., Müller, B., Pfetsch, M., Schlösser, F., Serrano, F., Shinano, Y., Tawfik, C., Vigerske, S., Wegscheider, F., Weninger, D., Witzig, J.: The SCIP Optimization Suite 7.0. Tech. Rep. 20-10, ZIB, Takustr. 7, 14195 Berlin (2020)

    Google Scholar 

  17. Geist, A., Beguelin, A., Dongarra, J., Jiang, W., Manchek, R., Sunderam, V.: PVM: Parallel Virtual Machines - A User’s Guide and Tutorial for Networked Parallel Computing. The MIT Press, Cambridge, MA (1994)

    Book  Google Scholar 

  18. Gendreau, M., Potvin, J.Y.: Handbook of Metaheuristics, 2nd edn. Springer Publishing Company, Incorporated, New York (2010)

    Book  Google Scholar 

  19. Ghildyal, V., Sahinidis, N.V.: Solving Global Optimization Problems with BARON. In: Migdalas, A., Pardalos, P., Värbrand, P. (eds.) From Local to Global Optimization, pp. 205–230. Kluwer Academic Publishers, Dordrecht (2001)

    Chapter  Google Scholar 

  20. Gleixner, A., Bastubbe, M., Eifler, L., Gally, T., Gamrath, G., Gottwald, R.L., Hendel, G., Hojny, C., Koch, T., Lübbecke, M.E., Maher, S.J., Miltenberger, M., Müller, B., Pfetsch, M.E., Puchert, C., Rehfeldt, D., Schlösser, F., Schubert, C., Serrano, F., Shinano, Y., Viernickel, J.M., Walter, M., Wegscheider, F., Witt, J.T., Witzig, J.: The SCIP Optimization Suite 6.0. Technical report, Optimization Online (2018). http://www.optimization-online.org/DB_HTML/2018/07/6692.html

  21. Gurobi Optimization, L.: Gurobi Optimizer Reference Manual (2019). http://www.gurobi.com

  22. Heipcke, S.: Xpress-Mosel: multi-solver, multi-problem, multi-model, multi-node modeling and problem solving. In: Kallrath, J. (ed.) Algebraic modeling systems: Modeling and solving real world optimization problems, pp. 77–110. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  23. Herlihy, M., Shavit, N.: The Art of Multiprocessor Programming, Revised Reprint, 1st edn. Morgan Kaufmann Publishers Inc., San Francisco, CA (2012)

    Google Scholar 

  24. Huangfu, Q., Hall, J.A.J.: Parallelizing the dual revised simplex method. Math. Program. Comput. 10(1), 119–142 (2018)

    Article  Google Scholar 

  25. IBM: IBM ILOG CPLEX Optimization Studio (2017) CPLEX Users Manual (2017). http://www.ibm.com

  26. Jozefowiez, N., Semet, F., Talbi, E.G.: Parallel and hybrid models for multi-objective optimization: application to the vehicle routing problem. In: Guervós, J.J.M., Adamidis, P., Beyer, H.G., Schwefel, H.P., Fernández-Villacañas, J.L. (eds.) Parallel Problem Solving from Nature — PPSN VII, pp. 271–280. Springer, Berlin, Heidelberg (2002)

    Chapter  Google Scholar 

  27. Kallrath, J., Blackburn, R., Näumann, J.: Grid-enhanced polylithic modeling and solution approaches for hard optimization problems. In: Bock, H.G., Jäger, W., Kostina, E., Phu, H.X. (eds.) Modeling, Simulation and Optimization of Complex Processes HPSC 2018 – Proceedings of the 7th International Conference on High Performance Scientific Computing, Hanoi, March 19–23, 2018, pp. 1–15. Springer Nature, Cham (2020)

    Google Scholar 

  28. Lančinskas, A., Ortigosa, P.M., Žilinskas, J.: Parallel optimization algorithm for competitive facility location. Math. Modell. Anal. 20(5), 619–640 (2015)

    Article  Google Scholar 

  29. Laundy, R.S.: Implementation of parallel Branch-and-Bound algorithms in Xpress-MP. In: Ciriani, T.A., Gliozzi, S., Johnson, E.L., Tadei, R. (eds.) Operational Research in Industry. MacMillan, London (1999)

    Google Scholar 

  30. Misener, R., Floudas, C.: ANTIGONE: algorithms for coNTinuous/Integer Global Optimization of Nonlinear Equations. J. Glob. Optim. 59, 503–526 (2014)

    Article  Google Scholar 

  31. Munguia, L.M., Oxberry, G., Rajan, D., Shinano, Y.: Parallel PIPS-SBB: multi-level parallelism for stochastic mixed-integer programs. Comput. Optim. Appl. (2019). Epub ahead of print

    Google Scholar 

  32. Pardalos, P.M., Pitsoulis, L.S., Mavridou, T.D., Resende, M.G.C.: Parallel search for combinatorial optimization: genetic algorithms, simulated annealing, tabu search and GRASP. In: Parallel Algorithms for Irregularly Structured Problems, Second International Workshop, IRREGULAR ’95, Lyon, September 4–6, 1995, Proceedings, pp. 317–331 (1995)

    Google Scholar 

  33. Ralphs, T., Shinano, Y., Berthold, T., Koch, T.: Parallel solvers for mixed integer linear optimization. In: Hamadi, Y., Sais, L. (eds.) Handbook of Parallel Constraint Reasoning, pp. 283 – 336. Springer, Cham (2018)

    Chapter  Google Scholar 

  34. Schrage, L.: LindoSystems: LindoAPI (2004)

    Google Scholar 

  35. Shinano, Y.: The ubiquity generator framework: 7 years of progress in parallelizing branch-and-bound. In: Operations Research Proceedings 2017, pp. 143–149 (2018)

    Google Scholar 

  36. Shinano, Y., Fujie, T., Kounoike, Y.: Effectiveness of parallelizing the ILOG-CPLEX mixed integer optimizer in the PUBB2 framework. In: Kosch, H., Böszörményi, L., Hellwagner, H. (eds.) Euro-Par 2003 Parallel Processing. Euro-Par 2003. Lecture Notes in Computer Science, vol. 2790, pp. 770–779 (2003)

    Article  Google Scholar 

  37. Shinano, Y., Achterberg, T., Fujie, T.: A dynamic load balancing mechanism for new ParaLEX. In: 2008 14th IEEE International Conference on Parallel and Distributed Systems, pp. 455–462 (2008)

    Google Scholar 

  38. Shinano, Y., Achterberg, T., Berthold, T., Heinz, S., Koch, T.: ParaSCIP: a parallel extension of SCIP. In: Competence in High Performance Computing 2010 - Proceedings of an International Conference on Competence in High Performance Computing, Schloss Schwetzingen, June 2010, pp. 135–148 (2010)

    Google Scholar 

  39. Shinano, Y., Achterberg, T., Berthold, T., Heinz, S., Koch, T., Winkler, M.: Solving open MIP instances with ParaSCIP on supercomputers using up to 80,000 cores. In: 2016 IEEE International Parallel and Distributed Processing Symposium (IPDPS), pp. 770–779 (2016)

    Google Scholar 

  40. Shinano, Y., Berthold, T., Heinz, S.: A first implementation of ParaXpress: combining internal and external parallelization to solve MIPs on supercomputers. In: International Congress on Mathematical Software, pp. 308–316. Springer, New York (2016)

    Google Scholar 

  41. Shinano, Y., Berthold, T., Heinz, S.: ParaXpress: an experimental extension of the FICO Xpress-optimizer to solve hard MIPs on supercomputers. Optim. Methods Softw. 33(3), 530–539 (2018)

    Article  Google Scholar 

  42. Shinano, Y., Heinz, S., Vigerske, S., Winkler, M.: FiberSCIP - a shared memory parallelization of SCIP. INFORMS J. Comput. 30(1), 11–30 (2018)

    Article  Google Scholar 

  43. Shinano, Y., Rehfeldt, D., Gally, T.: An easy way to build parallel state-of-the-art combinatorial optimization problem solvers: a computational study on solving Steiner tree problems and mixed integer semidefinite programs by using ug[SCIP-*,*]-libraries. In: Proceedings of the 9th IEEE Workshop Parallel/Distributed Combinatorics and Optimization, pp. 530–541 (2019)

    Google Scholar 

  44. Shinano, Y., Achterberg, T., Berthold, T., Heinz, S., Koch, T., Winkler, M.: Solving Previously Unsolved MIP Instances with ParaSCIP on Supercomputers by using up to 80,000 Cores. Tech. Rep. 20-16, ZIB, Berlin (2020)

    Google Scholar 

  45. Subramanian, R., Scheff(Jr.), R.P., Quinlan, J.D., Wiper, D.S., Marsten, R.E.: Coldstart: fleet assignment at delta air lines. Interfaces 24(1), 104–120 (1994)

    Google Scholar 

  46. Trelles, O., Rodriguez, A.: Bioinformatics and parallel metaheuristics. In: Alba, E. (ed.) Parallel Metaheuristics: A New Class of Algorithms. Wiley Series on Parallel and Distributed Computing, chap. 21, pp. 517–549. Wiley, Hoboken (2005)

    Chapter  Google Scholar 

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Kallrath, J. (2021). The Impact and Implications of Optimization. In: Business Optimization Using Mathematical Programming. International Series in Operations Research & Management Science, vol 307. Springer, Cham. https://doi.org/10.1007/978-3-030-73237-0_16

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