A sequential approach for unconstrained optimization via a partitioning technique

References

• E.P. Adorio, Mvf – multivariate test functions library in C for unconstrained global optimization, Tech. Rep., Department of Mathematics, 2005.
   Google Scholar
• T. Bäck, Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms, Oxford University Press, Oxford, 1996.
   Google Scholar
• T. Back, D.B. Fogel, and Z. Michalewicz(eds.), Handbook of Evolutionary Computation, 1st ed., IOP Publishing, Bristol, 1997.
   Google Scholar
• T. Buzan and B. Buzan, The Mind Map Book: How to Use Radiant Thinking to Maximize Your Brain's Untapped Potential, Plume, New York, 1993.
   Google Scholar
• L.S.D.M.P.J. Castro-Gutierrez, Dynamic lexicographic approach for heuristic multi-objective optimization, in Proceedings of the Workshop on Intelligent Metaheuristics for Logistic Planning (CAEPIA-TTIA 2009), Seville, Spain, 2009, pp. 153–163.
   Google Scholar
• J. Castro-Gutierrez, D. Landa-Silva, and J. Perez, Improved dynamic lexicographic ordering for multi-objective optimisation, in Parallel Problem Solving from Nature, PPSN XI, R. Schaefer, C. Cotta, J. Kolodziej, and G. Rudolph, eds., Lecture Notes in Computer Science, Vol. 6239, Springer, Berlin, 2010, pp. 31–40.
   Google Scholar
• K. Deb. Multi-Objective Optimization using Evolutionary Algorithms, Wiley-Interscience Series in Systems and Optimization. John Wiley & Sons, Chichester, 2001.
   Google Scholar
• J.E. DennisJr. and R.B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, Eaglewood Cliffs, NJ, 1983.
   Google Scholar
• M. Ehrgott, Multicriteria Optimization, 2nd ed., Springer, Berlin, 2005.
   Google Scholar
• M. Epitropakis, D. Tasoulis, N. Pavlidis, V. Plagianakos, and M. Vrahatis, Enhancing differential evolution utilizing proximity-based mutation operators, IEEE Trans. Evol. Comput. 15 (2011), pp. 99–119. doi: 10.1109/TEVC.2010.2083670
   Web of Science ®Google Scholar
• P.C. Fishburn, Lexicographic orders, utilities and decision rules: A survey, Manage. Sci. 20 (1974), pp. 1442–1471. doi: 10.1287/mnsc.20.11.1442
   Web of Science ®Google Scholar
• A.O. Griewank, Generalized descent for global optimization, J. Optim. Theory Appl. 34 (1981), pp. 11–39. doi: 10.1007/BF00933356
   Web of Science ®Google Scholar
• D. Himmelblau, Applied Nonlinear Programming, McGraw-Hill, New York, 1972.
   Google Scholar
• P.M. Pardalos, and H.E. Romeijn, Handbook of Global Optimization, Vol. 2, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2002.
   Google Scholar
• K.W. Jee, D.L. McShan, and B.A. Fraass, Lexicographic ordering: Intuitive multicriteria optimization for IMRT, Phys. Med. Biol. 52 (2007), pp. 1845. Available at http://stacks.iop.org/0031-9155/52/i=7/a=006.
   Google Scholar
• T. Long, M. Matuszak, M. Feng, B.A. Fraass, R.K. Ten Haken, and H.E. Romeijn, Sensitivity analysis for lexicographic ordering in radiation therapy treatment planning, Med. Phys. 39 (2012), pp. 3445–3455. doi: 10.1118/1.4720218
   PubMed Web of Science ®Google Scholar
• M.M. Mäkelä and Y. Nikulin, Properties of efficient solution sets under addition of objectives, Oper. Res. Lett. 36 (2008), pp. 718–721. doi: 10.1016/j.orl.2008.07.006
   Web of Science ®Google Scholar
• R. Marler and J. Arora, Survey of multi-objective optimization methods for engineering, Struct. Multidiscip. Optim. 26 (2004), pp. 369–395. doi: 10.1007/s00158-003-0368-6
   Web of Science ®Google Scholar
• K. Miettinen, Nonlinear Multiobjective Optimization, Kluwer Academic Publishers, Boston, 1999.
   Google Scholar
• K. Miettinen, Introduction to multiobjective optimization: Noninteractive approaches, in Multiobjective Optimization: Interactive and Evolutionary Approaches, J. Branke, K. Deb, K. Miettinen, and R. Slowinski, eds., Lecture Notes in Computer Science, vol. 5252, Springer, Berlin, 2008, pp. 1–26.
   Google Scholar
• M. Molga and C. Smutnicki, Test functions for optimization needs, 2005. Available at http://www.zsd.ict.pwr.wroc.pl/files/docs/functions.pdf
   Google Scholar
• J. Nast, Idea Mapping: How to Access Your Hidden Brain Power, Learn Faster, Remember More, and Achieve Success in Business, Wiley, Hoboken, NJ.
   Google Scholar
• C.D. Nikolakakou, T.N. Grapsa, I.A. Nikas, and G.S. Androulakis, A lexicographic approach on unconstrained optimization, in Book of Abstracts of the 23rd European Conference on Operational Research, Bonn, Germany, 2009, pp. 90.
   Google Scholar
• C.D. Nikolakakou, T.N. Grapsa, and G.S. Androulakis, Integrating Taylor's expansion on the lexicographic approach for unconstrained optimization, in Book of Abstracts of the 24rd European Conference on Operational Research, Lisbon, Portugal, 2010, pp. 192.
   Google Scholar
• C.D. Nikolakakou, T.N. Grapsa, and G.S. Androulakis, Integrating Taylor's expansion on the lexicographic approach for unconstrained optimization, in Proceedings of the 1st International Symposium & 10th Balkan Conference on Operational Research, Thessaloniki, Greece, 2011, pp. 354–361.
   Google Scholar
• J. Nocedal and S.J. Wright, Numerical Optimization, 2nd ed., Springer, New York, 2006.
   Google Scholar
• H. Pohlheim, GEATbx examples, examples of objective functions, December 2006. Available at http://www.geatbx.com/download/GEATbx_ObjFunExpl_v38.pdf
   Google Scholar
• R Development Core Team, R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria, 2011. Available at http://www.R-project.org/, ISBN3-900051-07-0.
   Google Scholar
• S.S. Rao, Optimization Theory and Applications, 2nd ed., 7th reprint, Wiley Eastern Limited, New Delhi, 1992.
   Google Scholar
• M. Zarepisheh and E. Khorram, On the transformation of lexicographic nonlinear multiobjective programs to single objective programs, Math. Meth. Oper. Res. 74 (2011), pp. 217–231. 10.1007/s00186-011-0360-7 doi: 10.1007/s00186-011-0360-7
   Web of Science ®Google Scholar
• A. Zykina, A lexicographic optimization algorithm, Autom. Remote Control 65 (2004), pp. 363–368. doi: 10.1023/B:AURC.0000019366.84601.8e
   Web of Science ®Google Scholar