IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v114y2002i1d10.1023_a1015472306888.html
   My bibliography  Save this article

Stochastic Method for the Solution of Unconstrained Vector Optimization Problems

Author

Listed:
  • S. Schäffler

    (Universität der Bundeswehr, EIT 1)

  • R. Schultz

    (Siemens AG)

  • K. Weinzierl

    (Siemens AG)

Abstract

We propose a new stochastic algorithm for the solution of unconstrained vector optimization problems, which is based on a special class of stochastic differential equations. An efficient algorithm for the numerical solution of the stochastic differential equation is developed. Interesting properties of the algorithm enable the treatment of problems with a large number of variables. Numerical results are given.

Suggested Citation

  • S. Schäffler & R. Schultz & K. Weinzierl, 2002. "Stochastic Method for the Solution of Unconstrained Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 114(1), pages 209-222, July.
    • Handle: RePEc:spr:joptap:v:114:y:2002:i:1:d:10.1023_a:1015472306888
    DOI: 10.1023/A:1015472306888
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1015472306888
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1015472306888?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Ralph L. Keeney, 1972. "Utility Functions for Multiattributed Consequences," Management Science, INFORMS, vol. 18(5-Part-1), pages 276-287, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Stefan Banholzer & Giulia Fabrini & Lars Grüne & Stefan Volkwein, 2020. "Multiobjective Model Predictive Control of a Parabolic Advection-Diffusion-Reaction Equation," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    2. Shukla, Pradyumn Kumar & Deb, Kalyanmoy, 2007. "On finding multiple Pareto-optimal solutions using classical and evolutionary generating methods," European Journal of Operational Research, Elsevier, vol. 181(3), pages 1630-1652, September.
    3. Oliver Schütze & Adanay Martín & Adriana Lara & Sergio Alvarado & Eduardo Salinas & Carlos Coello, 2016. "The directed search method for multi-objective memetic algorithms," Computational Optimization and Applications, Springer, vol. 63(2), pages 305-332, March.
    4. Carlos Ignacio Hernández Castellanos & Oliver Schütze & Jian-Qiao Sun & Guillermo Morales-Luna & Sina Ober-Blöbaum, 2020. "Numerical Computation of Lightly Multi-Objective Robust Optimal Solutions by Means of Generalized Cell Mapping," Mathematics, MDPI, vol. 8(11), pages 1-18, November.
    5. Oliver Schütze & Víctor Adrián Sosa Hernández & Heike Trautmann & Günter Rudolph, 2016. "The hypervolume based directed search method for multi-objective optimization problems," Journal of Heuristics, Springer, vol. 22(3), pages 273-300, June.
    6. Clempner, Julio B. & Poznyak, Alexander S., 2016. "Solving the Pareto front for multiobjective Markov chains using the minimum Euclidean distance gradient-based optimization method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 119(C), pages 142-160.
    7. Bennet Gebken & Sebastian Peitz, 2021. "An Efficient Descent Method for Locally Lipschitz Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 696-723, March.
    8. Fereshteh Akbari & Mehrdad Ghaznavi & Esmaile Khorram, 2018. "A Revised Pascoletti–Serafini Scalarization Method for Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 560-590, August.
    9. O. Schütze & C. Hernández & E-G. Talbi & J. Q. Sun & Y. Naranjani & F.-R. Xiong, 2019. "Archivers for the representation of the set of approximate solutions for MOPs," Journal of Heuristics, Springer, vol. 25(1), pages 71-105, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pierre Picard, 2016. "A Note on Health Insurance under Ex Post Moral Hazard," Risks, MDPI, vol. 4(4), pages 1-9, October.
    2. Hauser, John R. & Urban, Glen L., 1975. "A normative methodology for modeling consumer response to innovation," Working papers 785-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    3. James S. Dyer & James E. Smith, 2021. "Innovations in the Science and Practice of Decision Analysis: The Role of Management Science," Management Science, INFORMS, vol. 67(9), pages 5364-5378, September.
    4. Anderson, Jock R. & Hardaker, J. Brian, 1972. "An Appreciation of Decision Analysis in Management," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 40(04), pages 1-15, December.
    5. Harsha Cheemakurthy & Karl Garme, 2022. "Fuzzy AHP-Based Design Performance Index for Evaluation of Ferries," Sustainability, MDPI, vol. 14(6), pages 1-27, March.
    6. He, Ying & Huang, Rui-Hua, 2008. "Risk attributes theory: Decision making under risk," European Journal of Operational Research, Elsevier, vol. 186(1), pages 243-260, April.
    7. John R. Hauser, 1977. "Consumer Preference Axioms: Behavioral Postulates for Describing and Predicting Stochastic Choice," Discussion Papers 287, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    8. Austen Clark & Matthew J. Friedman, 1982. "The Relative Importance of Treatment Outcomes," Evaluation Review, , vol. 6(1), pages 79-93, February.
    9. Zhang, Junyi & Kuwano, Masashi & Lee, Backjin & Fujiwara, Akimasa, 2009. "Modeling household discrete choice behavior incorporating heterogeneous group decision-making mechanisms," Transportation Research Part B: Methodological, Elsevier, vol. 43(2), pages 230-250, February.
    10. Sven Peters & Mendy Tönsfeuerborn & Rüdiger von Nitzsch, 2024. "Integrating Uncertainties in a Multi-Criteria Decision Analysis with the Entscheidungsnavi," Mathematics, MDPI, vol. 12(11), pages 1-28, June.
    11. Dillon, John L. & Perry, Chad, 1977. "Multiattribute Utility Theory, Multiple Objectives And Uncertainty In Ex Ante Project Evaluation," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 45(01-2), pages 1-25, March.
    12. de Almeida, Jonatas Araujo & Costa, Ana Paula Cabral Seixas & de Almeida-Filho, Adiel Teixeira, 2016. "A new method for elicitation of criteria weights in additive models: Flexible and interactive tradeoffAuthor-Name: de Almeida, Adiel Teixeira," European Journal of Operational Research, Elsevier, vol. 250(1), pages 179-191.
    13. Kubińska, Elżbieta & Adamczyk-Kowalczuk, Magdalena & Andrzejewski, Mariusz & Rozakis, Stelios, 2022. "Incorporating the status quo effect into the decision making process: The case of municipal companies merger," Socio-Economic Planning Sciences, Elsevier, vol. 84(C).
    14. John W. Boudreau, 2004. "50th Anniversary Article: Organizational Behavior, Strategy, Performance, and Design in Management Science," Management Science, INFORMS, vol. 50(11), pages 1463-1476, November.
    15. James E. Smith & Detlof von Winterfeldt, 2004. "Anniversary Article: Decision Analysis in Management Science," Management Science, INFORMS, vol. 50(5), pages 561-574, May.
    16. Voola, Persis & A., Vinaya Babu, 2017. "Study of aggregation algorithms for aggregating imprecise software requirements’ priorities," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1191-1199.
    17. Fry, Phillip C. & Rinks, Dan B. & Ringuest, Jeffrey L., 1996. "Comparing the predictive validity of alternatively assessed multi-attribute preference models when relevant decision attributes are missing," European Journal of Operational Research, Elsevier, vol. 94(3), pages 599-609, November.
    18. Zhang, Junyi & Timmermans, Harry J. P. & Borgers, Aloys, 2005. "A model of household task allocation and time use," Transportation Research Part B: Methodological, Elsevier, vol. 39(1), pages 81-95, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:joptap:v:114:y:2002:i:1:d:10.1023_a:1015472306888. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.