A Visualization Technique for Accessing Solution Pool in Interactive Methods of Multiobjective Optimization

Ernestas Filatovas, Dmitry Podkopaev, Olga Kurasova

Abstract


Interactive methods of multiobjective optimization repetitively derive Pareto optimal solutions based on decision maker's preference information and present the obtained solutions for his/her consideration. Some interactive methods save the obtained solutions into a solution pool and, at each iteration, allow the decision maker considering any of solutions obtained earlier. This feature contributes to the flexibility of exploring the Pareto optimal set and learning about the optimization problem. However, in the case of many objective functions, the accumulation of derived solutions makes accessing the solution pool cognitively difficult for the decision maker. We propose to enhance interactive methods with visualization of the set of solution outcomes using dimensionality reduction and interactive mechanisms for exploration of the solution pool. We describe a proposed visualization technique and demonstrate its usage with an example problem solved using the interactive method NIMBUS.

Keywords


Multiobjective optimization, interactive methods, Pareto front visualization, dimensionality reduction, multidimensional scaling.

Full Text:

PDF

References


Belton, V., Branke, J., Eskelinen, P., Greco, S., Molina, J., Ruiz, F., Słowiński, R. (2008); Interactive multiobjective optimization from a learning perspective, in Branke, J., Deb, K., Miettinen, K., Słowiński, R., editors, Multiobjective Optimization (Lecture Notes in Computer Science, 5252), Springer, ISBN 978-3-540-88907-6, 405–433.

Borg, I., Groenen, P. J. (2005); Modern multidimensional scaling: Theory and applications, Springer, ISBN 978-0-387-25150-9.

Branke, J., Deb, K., Miettinen, K., Słowiński, R. (2008); Multiobjective optimization: Interactive and evolutionary approaches (Lecture Notes in Computer Science 5252), Springer, ISBN 978-3-540-88908-3.

Castelletti, A., Lotov, A. V., Soncini-Sessa, R. (2010); Visualization-based multi-objective improvement of environmental decision-making using linearization of response surfaces, Environmental Modelling & Software, ISSN 1364-8152, 25(12): 1552–1564.

Dzemyda, G., Kurasova, O., Žilinskas, J. (2013); Multidimensional Data Visualization: Methods and Applications (Springer Optimization and Its Applications, 75), Springer, ISBN 978- 1-4419-0235-1.

Filatovas, E., Kurasova, O. (2011); A decision support system for solving multiple criteria optimization problems. Informatics in Education, ISSN 1648-5831, 10(2): 213–224.

Gardiner, L., Vanderpooten, D. (1997); Interactive multiple criteria procedures: Some reflections. In Climaco, J., editor, Multicriteria Analysis, Springer, ISBN 978-3-642-64500-6, 290–301.
http://dx.doi.org/10.1007/978-3-642-60667-0_28

Jaszkiewicz, A., Słowiński, R. (1999). The "light beam search" approach - an overview of methodology and applications. European Journal of Operational Research, ISSN 0377-2217, 113(2): 300–314.

Visualization in the multiple objective decision-making framework, in Branke, J., Deb, K., Miettinen, K., Słowiński, R., editors, Multiobjective Optimization (Lecture Notes in Computer Science, 5252), Springer, ISBN 978-3-540-88907-6, 195–212.

Kurasova, O., Petkus, T., Filatovas, E. (2013); Visualization of pareto front points when solving multi-objective optimization problems. Information Technology And Control, ISSN 1392-124, 42(4): 353–361.
http://dx.doi.org/10.5755/j01.itc.42.4.3209

Laukkanen, T., Tveit, T.-M., Ojalehto, V., Miettinen, K., Fogelholm, C.-J. (2010); An interactive multi-objective approach to heat exchanger network synthesis. Computers & Chemical Engineering, ISSN 0098-1354, 34(6): 943–952.
http://dx.doi.org/10.1016/j.compchemeng.2010.01.002

Lotov, A., Bushenkov, V., Kamenev, G. (2004); Interactive Decision Maps, Approximation and Visualization of Pareto Frontier (Applied Optimization, 89), Springer, ISBN 978-1-4419- 8851-5.

Lotov, A. V., Miettinen, K. (2008); Visualizing the Pareto frontier, in Branke, J., Deb, K., Miettinen, K., Słowiński, R., editors, Multiobjective Optimization (Lecture Notes in Computer Science, 5252), Springer, ISBN 978-3-540-88907-6, 5252: 213–243.

Luque, M., Ruiz, F., Miettinen, K. (2011); Global formulation for interactive multiobjective optimization. OR Spectrum, ISSN 0171-6468, 33(1): 27–48.
http://dx.doi.org/10.1007/s00291-008-0154-3

Visual PROMETHEE: Developments of the PROMETHEE & GAIA multicriteria decision aid methods, in Proceedings of IEEE International Conference on Industrial Engineering and Engineering Management, 2009, e- ISBN 978-1-4244-4870-8, 1646–1649.

Miettinen, K. (1999); Nonlinear multiobjective optimization (International Series in Operations Research & Management Science, 12), Springer, ISBN 978-1-4615-5563-6.

Miettinen, K. (2014); Survey of methods to visualize alternatives in multiple criteria decision making problems. OR Spectrum, ISSN 0171-6468, 36(1): 3–37.
http://dx.doi.org/10.1007/s00291-012-0297-0

Interactive nonlinear multiobjective optimization methods. In Ehrgott, M., Figueia, J., and Greco, S., editors, Multiple Criteria Decision Analysis: State of the Art Surveys, Springer, (to appear).

Miettinen, K., Mäkelä, M. (1995); Interactive bundle-based method for nondifferentiable multiobjective optimization: NIMBUS. Optimization, ISSN 0233-1934, 34(3): 231–246.

Interactive method NIMBUS for nondifferentiable multiobjective optimization problems, in Climaco, J., editor, Multicriteria Analysis, Springer, ISBN 978-3-642-64500-6, 310–319.

Miettinen, K., Mäkelä, M. M. (2000); Interactive multiobjective optimization system WWW-NIMBUS on the Internet. Computers & Operations Research, ISSN 0305-0548, 27(7): 709–723.
http://dx.doi.org/10.1016/s0305-0548(99)00115-x

Miettinen, K., Mäkelä, M. M. (2006); Synchronous approach in interactive multiobjective optimization. European Journal of Operational Research, ISSN 0377-2217, 170(3): 909–922.
http://dx.doi.org/10.1016/j.ejor.2004.07.052

Miettinen, K., Mäkelä, M. M., Kaario, K. (2006); Experiments with classification-based scalarizing functions in interactive multiobjective optimization. European Journal of Operational Research, ISSN 0377-2217, 175(2): 931–947.
http://dx.doi.org/10.1016/j.ejor.2005.06.019

Miettinen, K., Mustajoki, J., Stewart, T. J. (2014b); Interactive multiobjective optimization with NIMBUS for decision making under uncertainty. OR Spectrum, ISSN 0171-6468, 36(1): 39–56.

Introduction to multiobjective optimization: Interactive approaches, in Branke, J., Deb, K., Miettinen, K., Słowiński, R., editors, Multiobjective Optimization: Interactive and Evolutionary Approaches (Lecture Notes in Computer Science, 5252), Springer, ISBN 978-3-540-88908-3, 27–57.

Narula, S. C., Weistroffer, H. (1989); A flexible method for nonlinear multicriteria decisionmaking problems. IEEE Transactions on Systems, Man and Cybernetics, ISSN 1083-4419, 19(4): 883–887.

Naud, A., Duch, W. (2000); Interactive data exploration using MDS mapping, in Proceedings of the Fifth Conference: Neural Networks and Soft Computing, ISBN 83-908587-2-X, 255–260.

Ojalehto, V., Miettinen, K., Laukkanen, T. (2014); Implementation aspects of interactive multiobjective optimization for modeling environments: the case of GAMS-NIMBUS. Computational Optimization and Applications, ISSN 0926-6003, 58(3): 757–779.
http://dx.doi.org/10.1007/s10589-014-9639-y

Ojalehto, V., Miettinen, K., Mäkelä, M. (2007); Interactive software for multiobjective optimization: IND-NIMBUS, WSEAS Transactions on Computers, ISSN 2224-2872, 6(1): 87– 94.

Petkus, T., Filatovas, E., Kurasova, O. (2009); Investigation of human factors while solving multiple criteria optimization problems in computer network. Technological and Economic Development of Economy, ISSN 2029-4913, 15(3): 464–479.
http://dx.doi.org/10.3846/1392-8619.2009.15.464-479

Pohlheim, H. (2006); Multidimensional scaling for evolutionary algorithms – visualization of the path through search space and solution space using Sammon mapping. Artificial Life, ISSN 1064-5462, 12(2): 203–209.

Saaty, T., Ozdemir, M. (2003); Why the magic number seven plus or minus two, Mathematical and Computer Modelling, ISSN 0895-7177, 38(3–4): 33–244.

Steuer, R. E. (1989); The Tchebycheff procedure of interactive multiple objective programming, in Karpak, B., Zionts, S., editors, Multiple Criteria Decision Making and Risk Analysis Using Microcomputers (NATO ASI Series, 56), Springer, ISBN 978-3-642-74919-3, 235–249.
http://dx.doi.org/10.1007/978-3-642-74919-3_8

Valdés, J. J., Barton, A. J. (2007); Visualizing high dimensional objective spaces for multiobjective optimization: A virtual reality approach, in Proceedings of the IEEE Congress on Evolutionary Computation(CEC 2007), IEEE, ISBN 978-1-4244-1339-3, 4199–4206.

Walker, D. J., Everson, R. M., Fieldsend, J. E. (2013); Visualizing mutually nondominating solution sets in many-objective optimization. IEEE Transactions on Evolutionary Computation, ISSN 1089-778X, 17(2): 165–184.
http://dx.doi.org/10.1109/tevc.2012.2225064

Yoshimi, M., Kuhara, T., Nishimoto, K., Miki, M., Hiroyasu, T. (2012). Visualization of pareto solutions by spherical self-organizing map and it's acceleration on a GPU. Journal of Software Engineering & Applications, ISSN 1945-3116, 5(3): 129–137.




DOI: https://doi.org/10.15837/ijccc.2015.4.1672



Copyright (c) 2017 Ernestas Filatovas, Dmitry Podkopaev, Olga Kurasova

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

IJCCC is an Open Access Journal : CC-BY-NC.

Articles published in IJCCC user license are protected by copyright.

Users can access, download, copy, translate the IJCCC articles for non-commercial purposes provided that users, but cannot redistribute, display or adapt:

  • Cite the article using an appropriate bibliographic citation: author(s), article title, journal, volume, issue, page numbers, year of publication, DOI, and the link to the definitive published version on IJCCC website;
  • Maintain the integrity of the IJCCC article;
  • Retain the copyright notices and links to these terms and conditions so it is clear to other users what can and what cannot be done with the  article;
  • Ensure that, for any content in the IJCCC article that is identified as belonging to a third party, any re-use complies with the copyright policies of that third party;
  • Any translations must prominently display the statement: "This is an unofficial translation of an article that appeared in IJCCC. Agora University  has not endorsed this translation."

This is a non commercial license where the use of published articles for commercial purposes is forbiden. 

Commercial purposes include: 

  • Copying or downloading IJCCC articles, or linking to such postings, for further redistribution, sale or licensing, for a fee;
  • Copying, downloading or posting by a site or service that incorporates advertising with such content;
  • The inclusion or incorporation of article content in other works or services (other than normal quotations with an appropriate citation) that is then available for sale or licensing, for a fee;
  • Use of IJCCC articles or article content (other than normal quotations with appropriate citation) by for-profit organizations for promotional purposes, whether for a fee or otherwise;
  • Use for the purposes of monetary reward by means of sale, resale, license, loan, transfer or other form of commercial exploitation;

    The licensor cannot revoke these freedoms as long as you follow the license terms.

[End of CC-BY-NC  License for Website User]


INTERNATIONAL JOURNAL OF COMPUTERS COMMUNICATIONS & CONTROL (IJCCC), With Emphasis on the Integration of Three Technologies (C & C & C),  ISSN 1841-9836.

IJCCC was founded in 2006,  at Agora University, by  Ioan DZITAC (Editor-in-Chief),  Florin Gheorghe FILIP (Editor-in-Chief), and  Misu-Jan MANOLESCU (Managing Editor).

Ethics: This journal is a member of, and subscribes to the principles of, the Committee on Publication Ethics (COPE).

Ioan  DZITAC (Editor-in-Chief) at COPE European Seminar, Bruxelles, 2015:

IJCCC is covered/indexed/abstracted in Science Citation Index Expanded (since vol.1(S),  2006); JCR2018: IF=1.585..

IJCCC is indexed in Scopus from 2008 (CiteScore2018 = 1.56):

Nomination by Elsevier for Journal Excellence Award Romania 2015 (SNIP2014 = 1.029): Elsevier/ Scopus

IJCCC was nominated by Elsevier for Journal Excellence Award - "Scopus Awards Romania 2015" (SNIP2014 = 1.029).

IJCCC is in Top 3 of 157 Romanian journals indexed by Scopus (in all fields) and No.1 in Computer Science field by Elsevier/ Scopus.

 

 Impact Factor in JCR2018 (Clarivate Analytics/SCI Expanded/ISI Web of Science): IF=1.585 (Q3). Scopus: CiteScore2018=1.56 (Q2);

SCImago Journal & Country Rank

Editors-in-Chief: Ioan DZITAC & Florin Gheorghe FILIP.