IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v204y2010i3p545-556.html
   My bibliography  Save this article

A mesh adaptive direct search algorithm for multiobjective optimization

Author

Listed:
  • Audet, Charles
  • Savard, Gilles
  • Zghal, Walid

Abstract

This work studies multiobjective optimization (MOP) of nonsmooth functions subject to general constraints. We first present definitions and optimality conditions as well as some single-objective formulations of MOP, parameterized with respect to some reference point in the space of objective functions. Next, we propose a new algorithm called MultiMads (multiobjective mesh adaptive direct search) for MOP. MultiMads generates an approximation of the Pareto front by solving a series of single-objective formulations of MOP generated using the NBI (natural boundary intersection) framework. These single-objective problems are solved using the Mads (mesh adaptive direct search) algorithm for constrained nonsmooth optimization. The Pareto front approximation is shown to satisfy some first-order necessary optimality conditions based on the Clarke calculus. MultiMads is then tested on problems from the literature with different Pareto front landscapes and on a styrene production process simulation problem from chemical engineering.

Suggested Citation

  • Audet, Charles & Savard, Gilles & Zghal, Walid, 2010. "A mesh adaptive direct search algorithm for multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 204(3), pages 545-556, August.
    • Handle: RePEc:eee:ejores:v:204:y:2010:i:3:p:545-556
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(09)00860-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Hansen, Pierre & Mladenovic, Nenad, 2001. "Variable neighborhood search: Principles and applications," European Journal of Operational Research, Elsevier, vol. 130(3), pages 449-467, May.
    2. K Deb, 2001. "Nonlinear goal programming using multi-objective genetic algorithms," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 52(3), pages 291-302, March.
    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. Cédric Durantin & Julien Marzat & Mathieu Balesdent, 2016. "Analysis of multi-objective Kriging-based methods for constrained global optimization," Computational Optimization and Applications, Springer, vol. 63(3), pages 903-926, April.
    2. Wenyu Wang & Christine A. Shoemaker, 2023. "Reference Vector Assisted Candidate Search with Aggregated Surrogate for Computationally Expensive Many Objective Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 35(2), pages 318-334, March.
    3. Wenyu Wang & Taimoor Akhtar & Christine A. Shoemaker, 2022. "Integrating $$\varepsilon $$ ε -dominance and RBF surrogate optimization for solving computationally expensive many-objective optimization problems," Journal of Global Optimization, Springer, vol. 82(4), pages 965-992, April.
    4. Juliane Müller & Jangho Park & Reetik Sahu & Charuleka Varadharajan & Bhavna Arora & Boris Faybishenko & Deborah Agarwal, 2021. "Surrogate optimization of deep neural networks for groundwater predictions," Journal of Global Optimization, Springer, vol. 81(1), pages 203-231, September.
    5. Srikanth Reddy, K. & Panwar, Lokesh & Panigrahi, B.K. & Kumar, Rajesh, 2018. "Modeling and analysis of profit based self scheduling of GENCO in electricity markets with renewable energy penetration and emission constraints," Renewable Energy, Elsevier, vol. 116(PA), pages 48-63.
    6. Wang, Honggang, 2017. "Multi-objective retrospective optimization using stochastic zigzag search," European Journal of Operational Research, Elsevier, vol. 263(3), pages 946-960.
    7. Alberto Lovison & Kaisa Miettinen, 2021. "On the Extension of the DIRECT Algorithm to Multiple Objectives," Journal of Global Optimization, Springer, vol. 79(2), pages 387-412, February.
    8. Jean Bigeon & Sébastien Le Digabel & Ludovic Salomon, 2021. "DMulti-MADS: mesh adaptive direct multisearch for bound-constrained blackbox multiobjective optimization," Computational Optimization and Applications, Springer, vol. 79(2), pages 301-338, June.
    9. A. L. Custódio & J. F. A. Madeira, 2018. "MultiGLODS: global and local multiobjective optimization using direct search," Journal of Global Optimization, Springer, vol. 72(2), pages 323-345, October.
    10. Svenson, Joshua & Santner, Thomas, 2016. "Multiobjective optimization of expensive-to-evaluate deterministic computer simulator models," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 250-264.
    11. Audet, Charles & Bigeon, Jean & Cartier, Dominique & Le Digabel, Sébastien & Salomon, Ludovic, 2021. "Performance indicators in multiobjective optimization," European Journal of Operational Research, Elsevier, vol. 292(2), pages 397-422.
    12. Amaioua, Nadir & Audet, Charles & Conn, Andrew R. & Le Digabel, Sébastien, 2018. "Efficient solution of quadratically constrained quadratic subproblems within the mesh adaptive direct search algorithm," European Journal of Operational Research, Elsevier, vol. 268(1), pages 13-24.

    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. S Dhouib & A Kharrat & H Chabchoub, 2011. "Goal programming using multiple objective hybrid metaheuristic algorithm," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 677-689, April.
    2. Maenhout, Broos & Vanhoucke, Mario, 2010. "A hybrid scatter search heuristic for personalized crew rostering in the airline industry," European Journal of Operational Research, Elsevier, vol. 206(1), pages 155-167, October.
    3. Pokharel, Shaligram, 2008. "A two objective model for decision making in a supply chain," International Journal of Production Economics, Elsevier, vol. 111(2), pages 378-388, February.
    4. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2018. "Minimizing Piecewise-Concave Functions Over Polyhedra," Mathematics of Operations Research, INFORMS, vol. 43(2), pages 580-597, May.
    5. Amina Lamghari & Roussos Dimitrakopoulos & Jacques Ferland, 2015. "A hybrid method based on linear programming and variable neighborhood descent for scheduling production in open-pit mines," Journal of Global Optimization, Springer, vol. 63(3), pages 555-582, November.
    6. Patricia Domínguez-Marín & Stefan Nickel & Pierre Hansen & Nenad Mladenović, 2005. "Heuristic Procedures for Solving the Discrete Ordered Median Problem," Annals of Operations Research, Springer, vol. 136(1), pages 145-173, April.
    7. Ali Shahabi & Sadigh Raissi & Kaveh Khalili-Damghani & Meysam Rafei, 2021. "Designing a resilient skip-stop schedule in rapid rail transit using a simulation-based optimization methodology," Operational Research, Springer, vol. 21(3), pages 1691-1721, September.
    8. Wilson, Duncan T. & Hawe, Glenn I. & Coates, Graham & Crouch, Roger S., 2013. "A multi-objective combinatorial model of casualty processing in major incident response," European Journal of Operational Research, Elsevier, vol. 230(3), pages 643-655.
    9. Felipe, Ángel & Ortuño, M. Teresa & Righini, Giovanni & Tirado, Gregorio, 2014. "A heuristic approach for the green vehicle routing problem with multiple technologies and partial recharges," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 71(C), pages 111-128.
    10. Fowler, John W. & Mönch, Lars, 2022. "A survey of scheduling with parallel batch (p-batch) processing," European Journal of Operational Research, Elsevier, vol. 298(1), pages 1-24.
    11. Miglierina, E. & Molho, E. & Recchioni, M.C., 2008. "Box-constrained multi-objective optimization: A gradient-like method without "a priori" scalarization," European Journal of Operational Research, Elsevier, vol. 188(3), pages 662-682, August.
    12. Véronique François & Yasemin Arda & Yves Crama, 2019. "Adaptive Large Neighborhood Search for Multitrip Vehicle Routing with Time Windows," Transportation Science, INFORMS, vol. 53(6), pages 1706-1730, November.
    13. Tino Henke & M. Grazia Speranza & Gerhard Wäscher, 2014. "The Multi-Compartment Vehicle Routing Problem with Flexible Compartment Sizes," FEMM Working Papers 140006, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
    14. Timo Hintsch, 2019. "Large Multiple Neighborhood Search for the Soft-Clustered Vehicle-Routing Problem," Working Papers 1904, Gutenberg School of Management and Economics, Johannes Gutenberg-Universität Mainz.
    15. Olcay Polat & Can B. Kalayci & Özcan Mutlu & Surendra M. Gupta, 2016. "A two-phase variable neighbourhood search algorithm for assembly line worker assignment and balancing problem type-II: an industrial case study," International Journal of Production Research, Taylor & Francis Journals, vol. 54(3), pages 722-741, February.
    16. Janssens, Jochen & Van den Bergh, Joos & Sörensen, Kenneth & Cattrysse, Dirk, 2015. "Multi-objective microzone-based vehicle routing for courier companies: From tactical to operational planning," European Journal of Operational Research, Elsevier, vol. 242(1), pages 222-231.
    17. Jiang, Min & Huang, George Q., 2022. "Intralogistics synchronization in robotic forward-reserve warehouses for e-commerce last-mile delivery," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).
    18. Xiao, Yiyong & Kaku, Ikou & Zhao, Qiuhong & Zhang, Renqian, 2011. "A reduced variable neighborhood search algorithm for uncapacitated multilevel lot-sizing problems," European Journal of Operational Research, Elsevier, vol. 214(2), pages 223-231, October.
    19. Bani, Abderrahman & El Hallaoui, Issmail & Corréa, Ayoub Insa & Tahir, Adil, 2023. "Solving a real-world multi-depot multi-period petrol replenishment problem with complex loading constraints," European Journal of Operational Research, Elsevier, vol. 311(1), pages 154-172.
    20. Roe, R.A. & Smeelen, M. & Hoefeld, C., 2005. "Outsourcing and organizational change : an employee perspective," Research Memorandum 045, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

    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:eee:ejores:v:204:y:2010:i:3:p:545-556. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.