IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v138y2008i3d10.1007_s10957-008-9394-2.html
   My bibliography  Save this article

Improved ε-Constraint Method for Multiobjective Programming

Author

Listed:
  • M. Ehrgott

    (University of Auckland
    Université de Nantes)

  • S. Ruzika

    (Technische Universität Kaiserslautern)

Abstract

In this paper, we revisit one of the most important scalarization techniques used in multiobjective programming, the ε-constraint method. We summarize the method and point out some weaknesses, namely the lack of easy-to-check conditions for properly efficient solutions and the inflexibility of the constraints. We present two modifications that address these weaknesses by first including slack variables in the formulation and second elasticizing the constraints and including surplus variables. We prove results on (weakly, properly) efficient solutions. The improved ε-constraint method that we propose combines both modifications.

Suggested Citation

  • M. Ehrgott & S. Ruzika, 2008. "Improved ε-Constraint Method for Multiobjective Programming," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 375-396, September.
    • Handle: RePEc:spr:joptap:v:138:y:2008:i:3:d:10.1007_s10957-008-9394-2
    DOI: 10.1007/s10957-008-9394-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-008-9394-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-008-9394-2?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. JosÉ Figueira & Salvatore Greco & Matthias Ehrogott, 2005. "Multiple Criteria Decision Analysis: State of the Art Surveys," International Series in Operations Research and Management Science, Springer, number 978-0-387-23081-8, April.
    2. P. H. Sach, 2003. "Nearly Subconvexlike Set-Valued Maps and Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 119(2), pages 335-356, November.
    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. Julio Mar-Ortiz & Alex J. Ruiz Torres & Belarmino Adenso-Díaz, 2022. "Scheduling in parallel machines with two objectives: analysis of factors that influence the Pareto frontier," Operational Research, Springer, vol. 22(4), pages 4585-4605, September.
    2. Sergio García García & Vicente Rodríguez Montequín & Marina Díaz Piloñeta & Susana Torno Lougedo, 2021. "Multi-Objective Optimization of Steel Off-Gas in Cogeneration Using the ε-Constraint Method: A Combined Coke Oven and Converter Gas Case Study," Energies, MDPI, vol. 14(10), pages 1-21, May.
    3. Mesquita-Cunha, Mariana & Figueira, José Rui & Barbosa-Póvoa, Ana Paula, 2023. "New ϵ−constraint methods for multi-objective integer linear programming: A Pareto front representation approach," European Journal of Operational Research, Elsevier, vol. 306(1), pages 286-307.
    4. Alcaraz, Javier & Landete, Mercedes & Monge, Juan F. & Sainz-Pardo, José L., 2020. "Multi-objective evolutionary algorithms for a reliability location problem," European Journal of Operational Research, Elsevier, vol. 283(1), pages 83-93.
    5. Steuer, Ralph E. & Utz, Sebastian, 2023. "Non-contour efficient fronts for identifying most preferred portfolios in sustainability investing," European Journal of Operational Research, Elsevier, vol. 306(2), pages 742-753.
    6. Vandana Goyal & Namrata Rani & Deepak Gupta, 2022. "An algorithm for quadratically constrained multi-objective quadratic fractional programming with pentagonal fuzzy numbers," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 32(1), pages 49-71.
    7. Ghasemi, Peiman & Khalili-Damghani, Kaveh & Hafezalkotob, Ashkan & Raissi, Sadigh, 2020. "Stochastic optimization model for distribution and evacuation planning (A case study of Tehran earthquake)," Socio-Economic Planning Sciences, Elsevier, vol. 71(C).
    8. Hartillo-Hermoso, María Isabel & Jiménez-Tafur, Haydee & Ucha-Enríquez, José María, 2020. "An exact algebraic ϵ-constraint method for bi-objective linear integer programming based on test sets," European Journal of Operational Research, Elsevier, vol. 282(2), pages 453-463.
    9. Masar Al-Rabeeah & Santosh Kumar & Ali Al-Hasani & Elias Munapo & Andrew Eberhard, 2019. "Bi-objective integer programming analysis based on the characteristic equation," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(5), pages 937-944, October.
    10. Shijin Wang & Xiaodong Wang & Xin Liu & Jianbo Yu, 2018. "A Bi-Objective Vehicle-Routing Problem with Soft Time Windows and Multiple Depots to Minimize the Total Energy Consumption and Customer Dissatisfaction," Sustainability, MDPI, vol. 10(11), pages 1-21, November.
    11. Mavrotas, George & Florios, Kostas, 2013. "An improved version of the augmented epsilon-constraint method (AUGMECON2) for finding the exact Pareto set in Multi-Objective Integer Programming problems," MPRA Paper 105034, University Library of Munich, Germany.
    12. R. S. Burachik & C. Y. Kaya & M. M. Rizvi, 2014. "A New Scalarization Technique to Approximate Pareto Fronts of Problems with Disconnected Feasible Sets," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 428-446, August.
    13. Zhou, Liping & Geng, Na & Jiang, Zhibin & Wang, Xiuxian, 2018. "Multi-objective capacity allocation of hospital wards combining revenue and equity," Omega, Elsevier, vol. 81(C), pages 220-233.
    14. Hamdan, Bayan & Diabat, Ali, 2020. "Robust design of blood supply chains under risk of disruptions using Lagrangian relaxation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 134(C).
    15. Diabat, Ali & Jabbarzadeh, Armin & Khosrojerdi, Amir, 2019. "A perishable product supply chain network design problem with reliability and disruption considerations," International Journal of Production Economics, Elsevier, vol. 212(C), pages 125-138.
    16. Ma, Zhenjun & Xia, Lei & Gong, Xuemei & Kokogiannakis, Georgios & Wang, Shugang & Zhou, Xinlei, 2020. "Recent advances and development in optimal design and control of ground source heat pump systems," Renewable and Sustainable Energy Reviews, Elsevier, vol. 131(C).
    17. Cristina Lopes & Ana Maria Rodrigues & Valeria Romanciuc & José Soeiro Ferreira & Elif Göksu Öztürk & Cristina Oliveira, 2023. "Divide and Conquer: A Location-Allocation Approach to Sectorization," Mathematics, MDPI, vol. 11(11), pages 1-19, June.
    18. Holzmann, Tim & Smith, J.C., 2018. "Solving discrete multi-objective optimization problems using modified augmented weighted Tchebychev scalarizations," European Journal of Operational Research, Elsevier, vol. 271(2), pages 436-449.

    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. Fancello, Giovanna & Tsoukiàs, Alexis, 2021. "Learning urban capabilities from behaviours. A focus on visitors values for urban planning," Socio-Economic Planning Sciences, Elsevier, vol. 76(C).
    2. Bana e Costa, Carlos A. & Oliveira, Carlos S. & Vieira, Victor, 2008. "Prioritization of bridges and tunnels in earthquake risk mitigation using multicriteria decision analysis: Application to Lisbon," Omega, Elsevier, vol. 36(3), pages 442-450, June.
    3. Denys Yemshanov & Frank H. Koch & Yakov Ben‐Haim & Marla Downing & Frank Sapio & Marty Siltanen, 2013. "A New Multicriteria Risk Mapping Approach Based on a Multiattribute Frontier Concept," Risk Analysis, John Wiley & Sons, vol. 33(9), pages 1694-1709, September.
    4. Corrente, Salvatore & Figueira, José Rui & Greco, Salvatore, 2014. "The SMAA-PROMETHEE method," European Journal of Operational Research, Elsevier, vol. 239(2), pages 514-522.
    5. Comino, E. & Ferretti, V., 2016. "Indicators-based spatial SWOT analysis: supporting the strategic planning and management of complex territorial systems," LSE Research Online Documents on Economics 64142, London School of Economics and Political Science, LSE Library.
    6. Kaveh Madani & Laura Read & Laleh Shalikarian, 2014. "Voting Under Uncertainty: A Stochastic Framework for Analyzing Group Decision Making Problems," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 28(7), pages 1839-1856, May.
    7. Kadziński, MiŁosz & Greco, Salvatore & SŁowiński, Roman, 2012. "Extreme ranking analysis in robust ordinal regression," Omega, Elsevier, vol. 40(4), pages 488-501.
    8. Haurant, P. & Oberti, P. & Muselli, M., 2011. "Multicriteria selection aiding related to photovoltaic plants on farming fields on Corsica island: A real case study using the ELECTRE outranking framework," Energy Policy, Elsevier, vol. 39(2), pages 676-688, February.
    9. Growiec, Jakub, 2018. "Factor-specific technology choice," Journal of Mathematical Economics, Elsevier, vol. 77(C), pages 1-14.
    10. José M. Merigó & Anna M. Gil-Lafuente & Daniel Palacios-Marqués, 2014. "A new method for fuzzy decision making under risk and uncertainty," International Journal of Business Continuity and Risk Management, Inderscience Enterprises Ltd, vol. 5(1), pages 29-42.
    11. Franceschini, Fiorenzo & Maisano, Domenico, 2015. "Checking the consistency of the solution in ordinal semi-democratic decision-making problems," Omega, Elsevier, vol. 57(PB), pages 188-195.
    12. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, II: More than two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 246-276, April.
    13. Grabisch, Michel & Kojadinovic, Ivan & Meyer, Patrick, 2008. "A review of methods for capacity identification in Choquet integral based multi-attribute utility theory: Applications of the Kappalab R package," European Journal of Operational Research, Elsevier, vol. 186(2), pages 766-785, April.
    14. Pablo Aragonés‐Beltrán & Mª. Carmen González‐Cruz & Astrid León‐Camargo & Rosario Viñoles‐Cebolla, 2023. "Assessment of regional development needs according to criteria based on the Sustainable Development Goals in the Meta Region (Colombia)," Sustainable Development, John Wiley & Sons, Ltd., vol. 31(2), pages 1101-1121, April.
    15. Boris Yatsalo & Sergey Gritsyuk & Terry Sullivan & Benjamin Trump & Igor Linkov, 2016. "Multi-criteria risk management with the use of DecernsMCDA: methods and case studies," Environment Systems and Decisions, Springer, vol. 36(3), pages 266-276, September.
    16. Juliana Martins Ruzante & Valerie J. Davidson & Julie Caswell & Aamir Fazil & John A. L. Cranfield & Spencer J. Henson & Sven M. Anders & Claudia Schmidt & Jeffrey M. Farber, 2010. "A Multifactorial Risk Prioritization Framework for Foodborne Pathogens," Risk Analysis, John Wiley & Sons, vol. 30(5), pages 724-742, May.
    17. Becchio, Cristina & Bottero, Marta Carla & Corgnati, Stefano Paolo & Dell’Anna, Federico, 2018. "Decision making for sustainable urban energy planning: an integrated evaluation framework of alternative solutions for a NZED (Net Zero-Energy District) in Turin," Land Use Policy, Elsevier, vol. 78(C), pages 803-817.
    18. Tunjo Perić & Zoran Babić & Josip Matejaš, 2018. "Comparative analysis of application efficiency of two iterative multi objective linear programming methods (MP method and STEM method)," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(3), pages 565-583, September.
    19. Morgenroth, Edgar & FitzGerald, John & FitzGerald, John, 2006. "Summary and Conclusions," Book Chapters, in: Morgenroth, Edgar (ed.),Ex-Ante Evaluation of the Investment Priorities for the National Development Plan 2007-2013, chapter 24, pages 317-333, Economic and Social Research Institute (ESRI).
      • Baker, Terence J. & FitzGerald, John & Honohan, Patrick & FitzGerald, John & Honohan, Patrick, 1996. "Summary and Conclusions," Book Chapters, in: Baker, Terence J. (ed.),Economic Implications for Ireland of EMU, chapter 12, pages 339-352, Economic and Social Research Institute (ESRI).
    20. Fernandez, Eduardo & Navarro, Jorge & Bernal, Sergio, 2010. "Handling multicriteria preferences in cluster analysis," European Journal of Operational Research, Elsevier, vol. 202(3), pages 819-827, May.

    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:138:y:2008:i:3:d:10.1007_s10957-008-9394-2. 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.