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Global Optimization: Software, Test Problems, and Applications

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Handbook of Global Optimization

Part of the book series: Nonconvex Optimization and Its Applications ((NOIA,volume 62))

Abstract

This chapter provides a concise review of the most prominent global optimization (GO) strategies currently available. This is followed by a discussion of GO software, test problems and several important types of applications, with additional pointers. The exposition is concentrated around topics related to continuous GO, although in certain aspects it is also pertinent to analogous issues in combinatorial optimization.

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References

  • Argonne National Laboratories (1993). MINPACK-2 Test Problem Collection. See also the accompanying notes titled `Large-scale optimization: Model problems’, by B.M. Averick and J.J. More. http://www-c.mcs.anl.gov/home/more/tprobs/html.

    Google Scholar 

  • Atkinson, A., Bogacka, B., and Zhigljaysky, A.A., editors (2001). Optimum Design 2000. Kluwer Academic Publishers, Dordrecht/Boston/London.

    MATH  Google Scholar 

  • Beck, M.B. (1985). Water Quality Management: A Review of the Development and Application of Mathematical Models. Springer-Verlag, Berlin/Heidelberg/New York.

    Google Scholar 

  • Beck, M.B., editor (1987). Systems Analysis in Water Quality Management. Pergamon Press, Oxford.

    Google Scholar 

  • Benson, H.P. (1995). Concave minimization: theory, applications, and algorithms. In Horst, R. and Pardalos, P.M., editors, Handbook of Global Optimization, pages 43–148. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Google Scholar 

  • Benson, H.P. and Sun, E. (2000). LGO–Versatile tool for global optimization. OR/MS Today, 27 (5): 52–55.

    Google Scholar 

  • Boender, C.G.E. and Romeijn, H.E. (1995). Stochastic methods. In Horst, R. and Pardalos, P.M., editors, Handbook of Global Optimization, pages 829–869. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Google Scholar 

  • Bomze, I.M., Csendes, T., Horst, R., and Pardalos, P.M., editors (1997). Developments in Global Optimization. Kluwer Academic Publishers, Dordrecht/Boston/London.

    MATH  Google Scholar 

  • Bracken, J. and McCormick, G.P. (1968). Selected Applications of Nonlinear Programming. John Wiley and Sons, New York.

    MATH  Google Scholar 

  • Brooke, A., Kendrick, D., and Meeraus, A. (1988). GAMS: A User’s Guide. The Scientific Press, Redwood City, California. Revised versions are available from the GAMS Corporation.

    Google Scholar 

  • Casti, J.L. (1990). Searching for Certainty. Morrow and Co., New York.

    Google Scholar 

  • Colville, A.R. (1968). A comparative study of nonlinear programming codes. Technical Report No. 320–2949, IBM Scientific Center, New York.

    Google Scholar 

  • Conway, J.H. and Sloane, N.J.A. (1988). Sphere Packings, Lattices and Groups. Springer-Verlag, Berlin/Heidelberg/New York, 2nd edition.

    Book  MATH  Google Scholar 

  • Corliss, G.F. and Kearfott, R.B. (1999). Rigorous global search: Industrial applications. In Csendes, T., editor, Developments in Reliable Computing, pages 1–16. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Chapter  Google Scholar 

  • De Leone, R., Murli, A., Pardalos, P.M., and Toraldo, G., editors (1998). High Performance Software for Nonlinear Optimization. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Google Scholar 

  • Dean, P.M. (1995). Molecular Similarity in Drug Design. Chapman and Hall, London.

    Book  Google Scholar 

  • Dembo, R.S. (1974). A set of geometric programming test problems and their solutions. Working paper, Department of Management Science, University of Waterloo, Waterloo, Ontario, Canada.

    Google Scholar 

  • Diener, I. (1995). Trajectory methods in global optimization. In Horst, R. and Pardalos, P.M., editors, Handbook of Global Optimization, pages 649–668. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Google Scholar 

  • Dill, K.A., Phillips, A.T., and Rosen, J.B. (1997). Molecular structure prediction by global optimization. In Bomze, I.M., Csendes, T., Horst, R., and Pardalos, P.M., editors, Developments in Global Optimization, pages 217–234. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Chapter  Google Scholar 

  • Dixon, L.C.W. and Szegb, G.P., editors (1975, 1978 ). Towards Global Optimisation, Volumes 1–2. North-Holland, Amsterdam, The Netherlands.

    Google Scholar 

  • Dorfman, R., Jacoby, H.D., and Thomas, H.A., editors (1974). Models for Managing Regional Water Quality. Harvard University Press, Cambridge, Massachusetts.

    Google Scholar 

  • Eason, E.D. and Fenton, R.G. (1974). A comparison of numerical optimization methods for engineering design. ASME J. Eng. Ind. Ser. B, 96 (1): 196–200.

    Article  Google Scholar 

  • Edgar, T.F., Himmelblau, D.M., and Lasdon, L.S. (2001). Optimization of Chemical Processes. McGraw-Hill, Boston, Massachusetts, 2nd edition.

    Google Scholar 

  • Eigen, M. and Winkler, R. (1975). Das Spiel. Piper and Co., München, Germany.

    Google Scholar 

  • Floudas, C.A. (1999). Deterministic Global Optimization: Theory, Algorithms and Applications. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Google Scholar 

  • Floudas, C.A. and Pardalos, P.M. (1990). A Collection of Test Problems for Constrained Global Optimization Algorithms, volume 455 of Lecture Notes in Computer Science. Springer-Verlag, Berlin/Heidelberg/New York.

    Google Scholar 

  • Floudas, C.A. and Pardalos, P.M., editors (2000). Optimization in Computational Chemistry and Molecular Biology - Local and Global Approaches. Kluwer Academic Publishers, Dordrecht/Boston/London.

    MATH  Google Scholar 

  • Floudas, C.A., Pardalos, P.M., Adjiman, C., Esposito, W.R., Gumus, Z.H., Harding, S.T., Klepeis, J.L., Meyer, C.A., and Schweiger, C.A. (1999). Handbook of Test Problems in Local and Global Optimization. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Book  MATH  Google Scholar 

  • Forster, W. (1995). Homotopy methods. In Horst, R. and Pardalos, P.M., editors, Handbook of Global Optimization, pages 669–750. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Google Scholar 

  • Fourer, R. (2001). Nonlinear programming frequently asked questions. Optimization Technology Center of Northwestern University and Argonne National Laboratory. http: //www-unix.mcs. anl. gov/otc/ Guide/faq/nonlinear-programming-faq.html.

    Google Scholar 

  • Fourer, R., Gay, D.M., and Kernighan, B.W. (1993). AMPL - A Modeling Language for Mathematical Programming. The Scientific Press, Redwood City, California. Reprinted by Boyd and Fraser, Danvers, Massachusetts, 1996.

    Google Scholar 

  • Frontline Systems (2001). Premium Solver Platform - Field-Installable Solver Engines. User Guide. Frontline Systems, Inc., Incline Village, Nevada.

    Google Scholar 

  • Glover, F. and Laguna, M. (1997). Tabu Search. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Book  MATH  Google Scholar 

  • Greengard, L. (1988). The Rapid Evaluation of Potential Fields in Particle Systems. The MIT Press, Cambridge, Massachusetts.

    Google Scholar 

  • Grossmann, I.E., editor (1996). Global Optimization in Engineering Design. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Google Scholar 

  • Haith, D.A. (1982). Environmental Systems Optimization. Wiley, New York.

    Google Scholar 

  • Hansen, E.R. (1992). Global Optimization Using Interval Analysis. Marcel Dekker, New York.

    Google Scholar 

  • Hartke, B. (1999). Global cluster geometry optimization by a phenotype algorithm with niches: Location of elusive minima, and low-order scaling with cluster size. Journal of Computational Chemistry, 20(16):1752–1759.

    Google Scholar 

  • Hendrix, E.M.T. (1998). Global Optimization at Work. PhD thesis, Agricultural University Wageningen, Wageningen, The Netherlands.

    Google Scholar 

  • Hichert, J., Hoffman, A., and Phú, H.X. (1997). Convergence speed of an integral method for computing the essential supremum. In Bomze, I.M., Csendes, T., Horst, R., and Pardalos, P.M., editors, Developments in Global Optimization,pages 153-170. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Google Scholar 

  • Hock, W. and Schittkowski, K. (1981). Test Examples for Nonlinear Programming Codes,volume 187 of Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, Berlin/Heidelberg/New York.

    Google Scholar 

  • Horst, R. and Pardalos, P.M., editors (1995). Handbook of Global Optimization. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Google Scholar 

  • Horst, R. and Tuy, H. (1996). Global Optimization - Deterministic Ap- proaches. Springer, Berlin/Heidelberg/New York, 3rd edition.

    Google Scholar 

  • Jacob, C. (2001). Illustrating Evolutionary Computation with Mathematica. Morgan Kaufmann Publishers, San Francisco, California.

    Google Scholar 

  • Jansson, C. and Knüppel, 0. (1992). A global minimization method: The multi-dimensional case. Bericht 92.1,FiuK, TUHH, Hamburg-Harburg, Germany. Journal of Global Optimization. Kluwer Academic Publishers, Dordrecht/Boston/London. Published since 1991.

    Google Scholar 

  • Kearfott, R.B. (1996). Rigorous Global Search: Continuous Problems. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Google Scholar 

  • Khompatraporn, C., Zabinsky, Z.B., and Pintér, J.D. (2001). Comparative assessment of algorithms and software for global optimization. Submitted for publication.

    Google Scholar 

  • Laguna, M. and Gonzalez-Velarde, J.-L., editors (2000). Computing Tools for Modeling, Optimization and Simulation. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Google Scholar 

  • Lahey Computer Systems (1999). Fortran 90 User’s Guide. Lahey Computer Systems, Inc., Incline Village, Nevada.

    Google Scholar 

  • Levy, A.V. and Gomez, S. (1985). The tunneling method applied for the global minimization of functions. In Boggs, P.T., editor, Numerical Optimization, pages 213–244. SIAM, Philadelphia, Pennsylvania. LINDO Systems (1996). Solver Suite. LINDO Systems, Inc., Chicago, Illinois.

    Google Scholar 

  • Loucks, D.P., Stedinger, J.R., and Haith, D.A. (1981). Water Resources Systems Planning and Analysis. Prentice-Hall, Englewood Cliffs, New Jersey.

    Google Scholar 

  • Mandelbrot, B.B. (1983). The Fractal Geometry of Nature. Freeman and Co., New York.

    Google Scholar 

  • Mathar, R. and Zilinskas, A. (1994). A class of test functions for global optimization. Journal of Global Optimization, 5: 195–199.

    Article  MathSciNet  MATH  Google Scholar 

  • Maximal Software (1998). MPL Modeling System. Maximal Software, Inc., Arlington, Virginia.

    Google Scholar 

  • Michalewicz, Z. (1996). Genetic Algorithms + Data Structures = Evolution Programs. Springer, Berlin/Heidelberg/New York, 3rd edition.

    Book  MATH  Google Scholar 

  • Migdalas, A., Pardalos, P.M., and Värbrand, P., editors (1997). Multilevel Optimization: Algorithms and Applications. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Google Scholar 

  • Mistakidis, E.S. and Stavroulakis, G.E. (1997). Nonconvex Optimization. Algorithms, Heuristics and Engineering Applications of the F.E.M. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Google Scholar 

  • Mittelmann, H.D. and Spellucci, P. (2001). Decision tree for optimization software. http://plato.la.asu.edu/guide.html.

    Google Scholar 

  • Mockus, J., Eddy, W., Mockus, A., Mockus, L., and Reklaitis, G. (1996). Bayesian Heuristic Approach to Discrete and Global Optimization. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Google Scholar 

  • Moré, J.J., Garbow, B.S., and Hillström, K.E. (1981). Testing unconstrained optimization software. ACM Transactions on Mathematical Software, 7: 17–41.

    Article  MATH  Google Scholar 

  • Moré, J.J. and Wright, S.J. (1993). Optimization Software Guide, volume 14 of Frontiers in Applied Mathematics Series. SIAM, Philadelphia, Pennsylvania.

    Google Scholar 

  • Moré, J.J. and Wu, Z. (1997). Global continuation for distance geometry problems. SIAM Journal on Optimization, 7: 814–836.

    Article  MathSciNet  MATH  Google Scholar 

  • Murray, J.D. (1989). Mathematical Biology. Springer-Verlag, Berlin/Heidelberg/New York.

    Book  MATH  Google Scholar 

  • Neumaier, A. (1990). Interval Methods for Systems of Equations. Cambridge University Press, Cambridge.

    MATH  Google Scholar 

  • Neumaier, A. (1997). Molecular modeling of proteins and mathematical prediction of protein structure. SIAM Review, 39: 407–460.

    Article  MathSciNet  MATH  Google Scholar 

  • Neumaier, A. (1999). Molecular modeling of proteins. http://solon.cma.univie.ac.at/“neum/protein.html.

    Google Scholar 

  • Neumaier, A. (2001). Global optimization. http://www.mat.univie.ac.at/Tneum/glopt.html. Nonconvex Optimization and its Applications. Kluwer Academic Publishers, Dordrecht/Boston/London. Bbook series, published since 1995.http://www.wkap.nl/series.htm/NOIA.

    Google Scholar 

  • Orlob, G.T., editor (1983). Mathematical Modeling of Water Quality: Streams, Lakes and Reservoirs. Wiley, New York.

    Google Scholar 

  • Osman, I.H. and Kelly, J.P., editors (1996). Meta-Heuristics: Theory and Applications. Kluwer Academic Publishers, Dordrecht/Boston/London.

    MATH  Google Scholar 

  • Pain, R.H., editor (1994). Mechanisms of Protein Folding. Oxford University Press, Oxford.

    Google Scholar 

  • Papalambros, P.M. and Wilde, D.J. (2000). Principles of Optimal Design - Modeling and Computation. Cambridge University Press, Cambridge, 2nd edition.

    Book  MATH  Google Scholar 

  • Pardalos, P.M. (1995). An open global optimization problem on the unit sphere. Journal of Global Optimization, 6: 213.

    Article  MathSciNet  MATH  Google Scholar 

  • Pardalos, P.M., Shalloway, D., and Xue, G. (1996). Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding, volume 23 of DIMACS Series. American Mathematical Society, Providence, Rhode Island.

    Google Scholar 

  • Pintér, J.D. (1996a). Global Optimization in Action (Continuous and Lipschitz Optimization: Algorithms, Implementations and Applications). Kluwer Academic Publishers, Dordrecht/Boston/London.

    MATH  Google Scholar 

  • Pintér, J.D. (1996b). Continuous global optimization software: A brief review. Optima, 52:1–8. Web version is available at: http://plato.la.asu.edu/gom.html.

    Google Scholar 

  • Pintér, J.D. (1999). Continuous global optimization: An introduction to models, solution approaches, tests and applications. Interactive Transactions in Operations Research and Management Science, 2 (2). http://catt.bus.okstate.edu/itorms/pinter/.

  • Pintér, J.D. (2000a). Globally optimized spherical point arrangements: Model variants and illustrative results. To appear in Annals of Operations Research.

    Google Scholar 

  • Pintér, J.D. (2000b). LGO - A Model Development System for Continuous Global Optimization. User’s Guide. Pintér Consulting Services, Inc., Halifax, Nova Scotia, Canada. For summary descriptions, see http://is. dal.ca/-jdpinter/lgoide.htm; http://www.solver.com/xlslgoeng.htm.

    Google Scholar 

  • Pintér, J.D. (2001a). Computational Global Optimization in Nonlinear Systems - An Interactive Tutorial. Lionheart Publishing, Inc., Atlanta, Georgia. This work is also available electronically, at http://www.lionhrtpub.com/books/globaloptimization.html.

    Google Scholar 

  • Pintér, J.D., editor (2001b). Global Optimization: Selected Case Studies. Kluwer Academic Publishers, Dordrecht/Boston/London. To appear.

    Google Scholar 

  • Prékopa, A. (1995). Stochastic Programming. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Book  Google Scholar 

  • Ratschek, H. and Rokne, J. (1988). New Computer Methods for Global Optimization. Ellis Horwood, Chichester.

    MATH  Google Scholar 

  • Ratschek, H. and Rokne, J. (1993). Experiments using interval analysis for solving a circuit design problem. Journal of Global Optimization, 3: 501–518.

    Article  MathSciNet  MATH  Google Scholar 

  • Reklaitis, G.V., Ravindran, A., and Ragsdell, K.M. (1983). Engineering Optimization Methods and Applications. John Wiley and Sons, New York.

    Google Scholar 

  • Saff, E.B. and Kuijlaars, A.B.J. (1997). Distributing many points on a sphere. The Mathematical Intelligencer, 19 (1): 5–11.

    Article  MathSciNet  MATH  Google Scholar 

  • Sandgren, E. and Ragsdell, K.M. (1980). The utility of nonlinear programming algorithms: A comparative study–parts 1 and 2. ASME Journal of Mechanical Design, 102 (3): 540–551.

    Article  Google Scholar 

  • Sandia National Laboratories (1997). A Survey of Global Optimization Methods. Prepared by Gray, P., Hart, W.E., Painton, L., Phillips, C., Trahan, M., and Wagner, J. http://www.cs.sandia.gov/opt/survey/main.html.

    Google Scholar 

  • Schittkowski, K. (1980). Nonlinear Programming Codes: Information, Tests, Performance, volume 183 of Lecture Notes in Economics and Mathematical Systems. Springer-Verlag, Berlin/Heidelberg/New York.

    Google Scholar 

  • Schoen, F. (1993). A wide class of test functions for global optimization. Journal of Global Optimization, 3: 133–138.

    Article  MathSciNet  MATH  Google Scholar 

  • Schroeder, M. (1991). Fractals, Chaos, Power Laws. Freeman and Co., New York.

    MATH  Google Scholar 

  • Sethi, S.P. and Thompson, G.L. (2000). Optimal Control Theory. Applications to Management Science and Economics. Kluwer Academic Publishers, Dordrecht/Boston/London, 2nd edition.

    MATH  Google Scholar 

  • Somlyódy, L. and van Straten, G., editors (1983). Modeling and Managing Shallow Lake Eutrophication. Springer-Verlag, Berlin/Heidelberg/New York.

    Google Scholar 

  • Stewart, I. (1995). Nature’s Numbers. Basic Books. Harper and Collins, New York.

    Google Scholar 

  • Strongin, R.G. and Sergeyev, Ya.D. (2000). Global Optimization with Non-Convex Constraints: Sequential and Parallel Algorithms. Kluwer Academic Publishers, Dordrecht/Boston/London.

    MATH  Google Scholar 

  • Voss, S., Martello, S., Osman, LH., and Roucairol, C., editors (1999). Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization. Kluwer Academic Publishers, Dordrecht/Boston/London.

    MATH  Google Scholar 

  • Wales, D.J. and Scheraga, H.A. (1999). Global optimization of clusters, crystals, and biomolecules. Science, 285: 1368–1372.

    Article  Google Scholar 

  • Wolfram, S. (1996). The Mathematica Book. Wolfram Media and Cambridge University Press, 3rd edition.

    Google Scholar 

  • Zheng, Q. and Zhuang, D. (1995). Integral global minimization: algorithms, implementations and numerical tests. Journal of Global Optimization, 7: 421–454.

    Article  MathSciNet  MATH  Google Scholar 

  • Zhigljaysky, A.A. (1991). Theory of Global Random Search. Kluwer Academic Publishers, Dordrecht/Boston/London.

    Book  Google Scholar 

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Authors and Affiliations

  1. Pintér Consulting Services Inc. and Dalhousie University, 129 Glenforest Drive, Halifax, Nova Scotia, Canada, B3M 1J2

    János D. Pintér

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  1. János D. Pintér
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  1. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, USA

    Panos M. Pardalos  & H. Edwin Romeijn  & 

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Pintér, J.D. (2002). Global Optimization: Software, Test Problems, and Applications. In: Pardalos, P.M., Romeijn, H.E. (eds) Handbook of Global Optimization. Nonconvex Optimization and Its Applications, vol 62. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-5362-2_15

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  • DOI: https://doi.org/10.1007/978-1-4757-5362-2_15

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