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A mesh adaptive direct search algorithm for multiobjective optimization

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. Hansen, Pierre & Mladenovic, Nenad, 2001. "Variable neighborhood search: Principles and applications," European Journal of Operational Research, Elsevier, vol. 130(3), pages 449-467, May.
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    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 & 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. Wang, Honggang, 2017. "Multi-objective retrospective optimization using stochastic zigzag search," European Journal of Operational Research, Elsevier, vol. 263(3), pages 946-960.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    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.

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