Computation Results of Finding All Efficient Points in Multiobjective Combinatorial Optimization

Milan Stanojevic, Mirko Vujoševic, Bogdana Stanojevic

Abstract


The number of efficient points in criteria space of multiple objective combinatorial optimization problems is considered in this paper. It is concluded that under certain assumptions, that number grows polynomially although the number of Pareto optimal solutions grows exponentially with the problem size. In order to perform experiments, an original algorithm for obtaining all efficient points was formulated and implemented for three classical multiobjective combinatorial optimization problems. Experimental results with the shortest path problem, the Steiner tree problem on graphs and the traveling salesman problem show that the number of efficient points is much lower than a polynomial upper bound.

Keywords


multiple objective optimization, combinatorial optimization, complexity of computation

Full Text:

PDF

References


M. Ehrgott, Multicriteria Optimization, Springer-Verlag, 2000.
http://dx.doi.org/10.1007/978-3-662-22199-0

M. Ehrgott, X. Gandibleux, A Survey and Annotated Bibliography of Multiobjective Combinatorial Optimization, OR Spektrum, Vol. 22, pp. 425-46 2000.
http://dx.doi.org/10.1007/s002910000046

V.A. Emelichev, V.A. Perepelitsa, On Cardinality of the Set of Alternatives in Discrete Manycriterion Problems, Discrete Math. Appl. Vol. 2, pp. 461-471, 1992.
http://dx.doi.org/10.1515/dma.1992.2.5.461

H.W. Hamacher, G. Ruhe, On Spanning Tree Problems with Multiple Objectives, Ann. Oper. Res., Vol. 52, pp. 209-230, 1994.
http://dx.doi.org/10.1007/BF02032304

I.V. Sergienko, V.A. Perepelitsa, Finding the Set of Alternatives in Discrete Multicriterion Problems, Cybernetics Vol. 23, pp. 673-683, 1987.
http://dx.doi.org/10.1007/BF01074927

M. Stanojevic, M. Vujosevic, B. Stanojevic, Number of Efficient Points in Some Multiobjective Combinatorial Optimization Problems, International Journal of Computers, Communications & Control, Vol.III (supl. issue), pp. 497-502, 2008.

M. Visée, J. Teghem, M. Pirlot, E.L. Ulungu, Two-phases Method and Branch and Bound Procedures to Solve the Bi-objective Knapsack Problem, J. Glob. Optim., Vol. 12, pp. 139-155, 1998.
http://dx.doi.org/10.1023/A:1008258310679

M. Vujoševic, M. Stanojevi’c, Multiobjective Traveling Salesman Problem and a Fuzzy Set Approach to Solving It. In: D. Ivanchev, M.D. Todorov (eds), Applications of Mathematics in Engeneering and Economics, Heron Press, Sofia, pp. 111-118, 2002.

M. Vujoševic, M. Stanojevi’c, A Bicriterion Steiner Tree Problem on Graph", Yugosl. J. Oper. Res., Vol. 13, pp. 25-33, 2003.
http://dx.doi.org/10.2298/YJOR0301025V




DOI: https://doi.org/10.15837/ijccc.2008.4.2405



Copyright (c) 2017 Milan Stanojevic, Mirko Vujoševic, Bogdana Stanojevic

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

CC-BY-NC  License for Website User

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.