2,352
Views
2
CrossRef citations to date
0
Altmetric
Original Articles

A splitting algorithm for simulation-based optimization problems with categorical variables

ORCID Icon, ORCID Icon, ORCID Icon, ORCID Icon & ORCID Icon
Pages 815-831 | Received 30 May 2017, Accepted 09 Jun 2018, Published online: 30 Jul 2018

References

  • Abhishek, K., S. Leyffer, and J. T. Linderoth. 2010. “Modeling without Categorical Variables: A Mixed-Integer Nonlinear Program for the Optimization of Thermal Insulation Systems.” Optimization and Engineering 11 (2): 185–212. doi: 10.1007/s11081-010-9109-z
  • Alexandrov, N. M., and M. Y. Hussaini, eds. 1997. Multidisciplinary Design Optimization: State of the Art. Philadelphia, PA: SIAM.
  • Atiqullah, M. M., and S. S. Rao. 2000. “Simulated Annealing and Parallel Processing: An Implementation for Constrained Global Design Optimization.” Engineering Optimization 32 (5): 659–685. doi: 10.1080/03052150008941317
  • Audet, C., and J. E. Dennis Jr. 2004. “A Pattern Search Filter Method for Nonlinear Programming without Derivatives.” SIAM Journal on Optimization 14 (4): 980–1010. doi: 10.1137/S105262340138983X
  • Audet, C., and J. E. Dennis Jr. 2006. “Mesh Adaptive Direct Search Algorithms for Constrained Optimization.” SIAM Journal on Optimization 17 (1): 188–217. doi: 10.1137/040603371
  • Audet, C., S. Le Digabel, and C. Tribes. 2009. NOMAD User Guide. Tech. Rep. G-2009-37. Montréal, QC, Canada: Les cahiers du GERAD.
  • Box, G. E. P. 1957. “Evolutionary Operation: A Method for Increasing Industrial Productivity.” Journal of the Royal Statistical Society. Series C (Applied Statistics) 6 (2): 81–101.
  • Boyd, S., and L. Vandenberghe. 2004. Convex Optimization. Cambridge, UK: Cambridge University Press.
  • Carlson, S. E. 1996. “Genetic Algorithm Attributes for Component Selection.” Research in Engineering Design 8 (1): 33–51. doi: 10.1007/BF01616555
  • Coleman, T. F., B. S. Garbow, and J. J. Moré. 1985. “Software for Estimating Sparse Hessian Matrices.” ACM Transactions on Mathematical Software 11 (4): 363–377. doi: 10.1145/6187.6190
  • Coleman, T. F., and Y. Zhang. 2015. Optimization Toolbox User's Guide, Revised for Version 7.3 (Release 2015b). Natick, MA: The MathWorks, Inc.
  • Dhingra, A. K., and S. S. Rao. 1992. “A Neural Network Based Approach to Mechanical Design Optimization.” Engineering Optimization 20 (3): 187–203. doi: 10.1080/03052159208941280
  • Dolan, E. D., and J. J. Moré. 2002. “Benchmarking Optimization Software with Performance Profiles.” Mathematical Programming 91 (2): 201–213. doi: 10.1007/s101070100263
  • Floudas, Christodoulos A. 1995. Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications. 1st ed. OUP Series on Topics in Chemical Engineering. Don Mills, ON, Canada: Oxford University Press.
  • Fuchs, M., D. Girimonte, D. Izzo, and A. Neumaier. 2008. “Robust and Automated Space System Design.” In Robust Intelligent Systems, edited by A. Schuster, 251–272. New York: Springer Science & Businees Media.
  • Fuchs, M., and A. Neumaier. 2010a. “A Splitting Technique for Discrete Search Based on Convex Relaxation.” Journal of Uncertain Systems 4 (1): 14–21.
  • Fuchs, M., and A. Neumaier. 2010b. “Discrete Search in Design Optimization.” In Complex Systems Design & Management, edited by M. Aiguier, F. Bretaudeau, and D. Krob, 113–122. Berlin-Heidelberg: Springer.
  • Graham, R. L., and P. Hell. 1985. “On the History of the Minimum Spanning Tree Problem.” Annals of the History of Computing 7 (1): 43–57. doi: 10.1109/MAHC.1985.10011
  • Horst, R., and H. Tuy. 1996. Global Optimization: Deterministic Approaches. New York: Springer.
  • Huyer, W., and A. Neumaier. 1999. “Global Optimization by Multilevel Coordinate Search.” Journal of Global Optimization 14 (4): 331–355. doi: 10.1023/A:1008382309369
  • Jones, D. R., C. D. Perttunen, and B. E. Stuckman. 1993. “Lipschitzian Optimization without the Lipschitz Constant.” Journal of Optimization Theory and Applications 79 (1): 157–181. doi: 10.1007/BF00941892
  • Leyffer, S. 1993. “Deterministic Methods for Mixed Integer Nonlinear Programming.” PhD diss., University of Dundee, UK.
  • Lindroth, P. 2012. “TyreOpt—Fuel Consumption Reduction by Tyre Drag Optimisation.” [In Swedish]. Project number: P34882-1. Swedish Energy Agency, Stockholm. Accessed 14 April 2017. http://www.energimyndigheten.se/forskning-och-innovation/projektdatabas/.
  • Locatelli, M., and F. Schoen. 2013. Global Optimization: Theory, Algorithms, and Applications. Philadelphia, PA: SIAM.
  • Moré, J. J., and S. M. Wild. 2009. “Benchmarking Derivative-Free Optimization Algorithms.” SIAM Journal on Optimization 20 (1): 172–191. doi: 10.1137/080724083
  • Nedělková, Z., P. Lindroth, and B. Jacobson. 2017. “Modelling of Optimal Tyres Selection for a Certain Truck and Transport Application.” International Journal of Vehicle Systems Modelling and Testing 12 (3–4): 284–303. doi: 10.1504/IJVSMT.2017.089998
  • Nedělková, Z., P. Lindroth, M. Patriksson, and A.-B. Strömberg. 2018. “Efficient Solution of Many Instances of a Simulation-Based Optimization Problem Utilizing a Partition of the Decision Space.” Annals of Operations Research 265 (1): 93–118. doi:10.1007/s10479-017-2721-y.
  • Nedělková, Z., P. Lindroth, A.-B. Strömberg, and M. Patriksson. 2016. “Integration of Expert Knowledge into Radial Basis Function Surrogate Models.” Optimization and Engineering 17 (3): 577–603. doi: 10.1007/s11081-015-9297-7
  • Nemhauser, G. L., and L. A. Wolsey. 1999. Integer and Combinatorial Optimization. 1st ed. Vol. 55 of the Wiley Series Discrete Mathematics and Optimization. Hoboken, NJ: Wiley.
  • Neumaier, A., M. Fuchs, E. Dolejsi, T. Csendes, J. Dombi, B. Bánhelyi, Z. Gera, and D. Girimonte. 2007. Application of Clouds for Modeling Uncertainties in Robust Space System Design, Final Report. Tech. Rep. ACT Ariadna Research ACT-RPT-05-5201, European Space Agency. http://www.esa.int/gsp/ACT/doc/ARI/ARI%20Study%20Report/ACT-RPT-INF-ARI-055201-Clouds.pdf.
  • Nowak, I., and S. Vigerske. 2008. “LaGO: A (Heuristic) Branch and Cut Algorithm for Nonconvex MINLPs.” Central European Journal of Operations Research 16 (2): 127–138. doi: 10.1007/s10100-007-0051-x
  • Parker, R. G., and R. L. Rardin. 2014. Discrete Optimization. 2nd ed. Elsevier Series on Computer Science and Scientific Computing. Cambridge, MA: Elsevier.
  • Ryoo, J., and P. Hajela. 2004. “Decomposition-Based Design Optimization Method Using Genetic Co-Evolution.” Engineering Optimization 36 (3): 361–378. doi: 10.1080/03052150410001657587
  • Šabartová, Z. 2015. “Mathematical Modelling for Optimization of Truck Tyres Selection.” Lic. thesis, Chalmers University of Technology and Department of Mathematical Sciences, University of Gothenburg.
  • Šabartová, Z., A.-B. Strömberg, M. Patriksson, and P. Lindroth. 2014. “An Optimization Model for Truck Tyres Selection.” In Engineering Optimization IV. Proceedings of the International Conference on Engineering Optimization (ENGOPT 2014), edited by H. C. Rodrigues, José Herskovits, C. M. Mota Soares, J. M. Guedes, Aurelio L. Araújo, J. O. Folgado, F. Moleiro, and J. F. A. Madeira, 561–566. Leiden, The Netherlands: CRC Press/Balkema.
  • Sóbester, A., A. I. J. Forrester, D. J. J. Toal, E. Tresidder, and S. Tucker. 2014. “Enginering Design Applications of Surrogate-Assisted Optimization Techniques.” Optimization and Engineering 15 (1): 243–265. doi: 10.1007/s11081-012-9199-x
  • Tawarmalani, M., and N. V. Sahinidis. 2004. “Global Optimization of Mixed-Integer Nonlinear Programs: A Theoretical and Computational Study.” Mathematical Programming 99 (3): 563–591. doi: 10.1007/s10107-003-0467-6
  • Thanedar, P. B., and G. N. Vanderplaats. 1995. “Survey of Discrete Variable Optimization for Structural Design.” Journal of Structural Engineering 121 (2): 301–306. doi: 10.1061/(ASCE)0733-9445(1995)121:2(301)
  • The MathWorks. 2015. MATLABȍ Release 2015b. Natick, MA: The MathWorks, Inc.
  • Timoshenko, Stephen, and James M. Gere. 1972. Mechanics of Materials. Boston, MA: Van Nostrand Reinhold.
  • Toh, K. C., M. J. Todd, and R. H. Tutuncu. 1999. “SDPT3—A MATLAB Software Package for Semidefinite Programming.” Optimization Methods and Software 11 (1-4): 545–581. doi:10.1080/10556789908805762.
  • Wolkowicz, H., R. Saigal, and L. Vandenberghe. 2012. Handbook of Semidefinite Programming: Theory, Algorithms, and Applications. Springer International Series on Operations Research & Management Science. New York: Springer Science & Business Media.
  • Zhao, Z., J. C. Meza, and M. Van Hove. 2006. “Using Pattern Search Methods for Surface Structure Determination of Nanomaterials.” Journal of Physics: Condensed Matter 18 (39): 86–93.
  • Žilinskas, J. 2008. “Branch and Bound with Simplicial Partitions for Global Optimization.” Mathematical Modelling and Analysis 13 (1): 145–159. doi: 10.3846/1392-6292.2008.13.145-159