AH Method: a novel routine for vicinity examination of the optimum found with a genetic algorithm

Piotr Bilski, Daniel Andrzej Piętak, Paweł Jan Napiorkowski


The paper presents a novel heuristic procedure (further called the AH Method) to investigate function shape in the direct vicinity of the found optimum solution. The survey is conducted using only the space sampling collected during the optimization process with an evolutionary algorithm. For this purpose the finite model of point-set is considered. The statistical analysis of the sampling quality based upon the coverage of the points in question over the entire attraction region is exploited. The tolerance boundaries of the parameters are determined for the user-specified increase of the objective function value above the found minimum. The presented test-case data prove that the proposed approach is comparable to other optimum neighborhood examination algorithms. Also, the AH Method requires noticeably shorter computational time than its counterparts. This is achieved by a repeated, second use of points from optimization without additional objective function calls, as well as significant repository size reduction during preprocessing.

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A. P. Engelbrecht: Computational Intelligence, John Wiley & Sons Ltd., 2002

H.-P. Schwefel: Numerical optimization of computer models, Chichester: Wiley & Sons, 1981

J. Arabas: Wykłady z algorytmów ewolucyjnych, WNT, 2004 (in Polish)

D. E. Goldberg: Genetic Algorithms in Search, Optimization and Machine Learning, Kluwer Academic Publishers, Boston, MA, 1989

T. D. Gwiazda: Algorytmy genetyczne kompendium. Tom I, Wydawnictwo Naukowe PWN, 2007 (in Polish)

Z. Michalewicz: Genetic Algorithms + Data Structures = Evolution Programs, Springer-Verlag, 1999

Z. Michalewicz, D. B. Fogel: How to Solve It: Modern Heuristics, Springer Berlin, Heidelberg, 2004

J. Arabas: Approximating the Genetic Diversity of Populations in the Quasi-Equilibrum State, IEEE Transactions on Evolutionary Computation, 16, 5, 2012

D. A. Piętak, P. J. Napiorkowski, Z. Walczak, J. Wojciechowski: Application of Genetic Algorithm with Real Representation to COULEX Data Analysis, Proceedings of the Conference on Evolutionary Computation and Global Optimization, Oficyna Wydawnicza Politechniki Warszawskiej, 2009

M. Ankerst, M. Breunig, H.-P. Kriegel, J. Sander: OPTICS: Ordering points to identify the clustering structure, Proceedings of 1999 ACM-SIGMOD International Conference on Management of Data (SIGMOD'99), pages 49-60, Philadelphia, 1999

M. Ester, H. Kriegel, J. Sander, X. Xu: A density-based algorithm for discovering clusters in large spatial databases with noise, Proceedings of 1998 International Conference on Knowledge Discovery and Data Mining (KDD'96), pages 226-231, Portland Oregon, 1996

J. Han, M. Kamber: Data mining: concepts and techniques, Morgan Kaufmann Publishers, 2000

A. K. Jain, M. N. Murty, P. J. Flyn: Data clustering: A review, ACM Computing Surveys, 31(3): 264-323, 1999

R. Weber, H.-J. Schek, S. Blott: A quantitative analysis and performance study for similarity-search methods in high-dimensional spaces, Proceedings of the Conference on Very Large DataBases (VLDB'98), pages 194-205, New York City, 1998

R. Weber, S. Blott: An approximation based data structure for similarity search, Technical Report 24, ESPRIT project HERMES (no. 9141), 1997

S. Zhou, Y. Zhao, J. Guan, J. Huang: NBC: A Neighborhood-Based Clustering Algorithm, Lecture Notes in Computer Science, Springer Berlin / Heidelberg, 2005

T. Kohonen: Self-Organized Formation of Topologically Correct Feature Maps, Biological Cybernetics, 43(1), 59-69, 1982

J. E. Amaro, R. Navarro Pérez, E. Ruiz Arriola: Error analysis of nuclear matrix elements, Few-Body Systems, 2013

P. R. Bevington, D. K. Robinson: Data Reduction and Error Analysis for the Physical Sciences, McGraw-Hill, 2003

G. E. P. Box, N. R. Draper: Empirical Model Building and Response Surfaces, John Wiley & Sons, New York, 1987

G. E. P. Box: Science and statistics, Journal of American Statistical Association, 71:791, 1976

S. Brandt: Data Analysis. Statistical and Computational Methods for Scientists and Engineers, Fourth Edition, Springer, New York, 2014

J. Dobaczewski, W. Nazarewicz, P.-G. Reinhard: Error Estimates of Theoretical Models: a Guide, Journal of Physics G: Nuclear and Particle Physics, 41, 074001, 2014

W. T. Eadie, D. Drijard, F. E. James, M. Roos, B. Sadoulet: Statistical Methods in Experimental Physics, North-Holland, Amsterdam, 1971

D. Higdon: Statistical approaches for combining model runs with experimental data, Presentation at ISNET Meeting, Glasgow, 2013

International Organization for Standardization (ISO): Guide to the expression of Uncertainty in Measurement (GUM) – Supplement 1: Numerical methods for the propagation of distributions, Report, 2004

Joint Committee for Guides in Metrology (JCGM): JCGM 100:2008 Evaluation of measurement data – Guide to the expression of Uncertainty in Measurement, Report, 2008

Joint Committee for Guides in Metrology (JCGM): JCGM 101:2008 Evaluation of measurement data – Supplement 1 to the „Guide to the expression of Uncertainty in Measurement” – Propagation of distributions using a Monte Carlo method, Report, 2008

Joint Committee for Guides in Metrology (JCGM): JCGM 102:2011 Evaluation of measurement data – Supplement 2 to the „Guide to the expression of Uncertainty in Measurement” – Extension to any number of output quantities, Report, 2011

Joint Committee for Guides in Metrology (JCGM): JCGM 103 Evaluation of measurement data – Supplement 3 to the „Guide to the expression of Uncertainty in Measurement” – Developing and using measurement models, Report, 2018

Joint Committee for Guides in Metrology (JCGM): JCGM 104:2009 Evaluation of measurement data – An introduction to the „Guide to the expression of Uncertainty in Measurement” and related documents, Report, 2009

Joint Committee for Guides in Metrology (JCGM): JCGM 106:2012 Evaluation of measure-ment data – The role of measurement uncertainty in conformity assessment, Report, 2012

Joint Committee for Guides in Metrology (JCGM): JCGM 200:2008 International vocabulary of metrology – basic and general concepts and associated terms, Report, 2008

S. L. Meyer: Data Analysis for Scientists and Engineers, John Wiley, 1975

R. Z. Morawski, A. Miękina: Monte-Carlo evaluation of measurement uncertainty using a new generator of pseudo-random numbers, PAK vol. 59, nr 5, 2013

E. M. Pugh, G. H. Winslow: The Analysis of Physical Measurements, Addison-Wesley, 1966

A. Saltelli, S. Funtowicz: When all models are wrong, Issues in Science and Technology, Fall 2013:79, 2013

A. Tarantola: Inverse problem theory and methods for model parameter estimation, SIAM, Philadelphia, 2005

J. R. Taylor: An Introduction to Error Analysis, Oxford University Press, 1982

B. A. Wichmann, I. D. Hill: Generating good pseudo-random numbers, Computational Statistics and Data Analysis 51, pages 1614-1622, 2006

A. Björck, G. Dahlquist: Numerical methods, Prentice-Hall, 1974

B. M. Adams, W. J. Bohnhoff, K. R. Dalbey, J. P. Eddy, M. S. Eldred, D. M. Gay, K. Haskell, P. D. Hough, L. P. Swiler: DAKOTA, A Multilevel Parallel Object-Oriented Framework for Design Optimization, Parameter Estimation, Uncertainty Quantification and Sensitivity Analysis: Version 5.0 User’s Manual, Sandia Technical Report, SAND2010-2183, 2009

The MathWorks: Matlab User's Manual, MathWorks Inc., Natick, Mass., USA, 1992

C. B. Moler: Numerical computing with MATLAB, SIAM, Philadelphia, 2004

T. Williams, C. Kelley: Gnuplot 5.3. An Interactive Plotting Program, 2018, in: http://www.gnuplot.info/docs_5.5/gnuplot.pdf, access: August 2022

D. A. Piętak: Statistical distribution of the genetic algorithm sampling with Schwefel's F7 objective function, Proceedings of the IEEE International Conference on Signals and Electronic Systems (ICSES), Gliwice, 2010

D. A. Piętak, J. Wojciechowski, P. J. Napiorkowski: A Front-Line algorithm for error estimation in datasets with nonuniform sampling distribution, Proceedings of the 20th European Conference on Circuit Theory and Design (ECCTD), 6043319, pp. 210-213, Linköping, Szwecja, 2011

D. Cline, T. Czosnyka, A. B. Hayes, P. J. Napiorkowski, N. Warr, C. Y. Wu: GOSIA User Manual for Simulation and Analysis of Coulomb Excitation Experiments, http://www.pas.rochester.edu/~cline/Gosia/Gosia_Manual_20120510.pdf, 2012

T. Czosnyka, D. Cline, C.Y. Wu: Coulomb excitation data analysis code GOSIA, Rochester, NY 14627, USA, 1983, http://www.slcj.uw.edu.pl/~gosia

T. Czosnyka, D. Cline, C.Y. Wu, Bulletin of the American Physical Society, 28, 745, 1983

P. J. Napiorkowski, K. Hadyńska-Klęk, J. Iwanicki, D. A. Piętak, J. Srebrny, K. Wrzosek-Lipska, M. Zielińska (Warsaw Coulex Group): Coulomb excitation at Warsaw Cyclotron, http://slcj.uw.edu.pl/en/cudac-en/, access: August 2022

D. A. Piętak: Metoda oceny jakości wyników eksperymentów wzbudzień kulombowskich z wykorzystaniem algorytmu genetycznego (The method of results quality validation of Coulomb excitation experiments with the use of a genetic algorithm), PhD thesis, Warsaw University of Technology, 2021


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