Comparison Between Two Multi-Objective Optimization Algorithms: PAES and MGDA. Testing MGDA on Kriging Metamodels

  • Adrien Zerbinati
  • Jean-Antoine Désidéri
  • Régis Duvigneau
Part of the Computational Methods in Applied Sciences book series (COMPUTMETHODS, volume 27)


In multi-objective optimization, the knowledge of the Pareto set provides valuable information on the reachable optimal performance. A number of evolutionary strategies (PAES (Knowles and Corne in Evol. Comput. 8(2):149–172, 2000), NSGA-II (Deb et al. in IEEE Trans. Evol. Comput. 6(2):182–197, 2002), etc.), have been proposed in the literature and proved to be successful in identifying the Pareto set. However, these derivative-free algorithms are very demanding in computational time. Today, in many areas of computational sciences, codes are developed that include the calculation of the gradient, cautiously validated and calibrated. Thus, an alternate method applicable when the gradients are known is introduced presently. Using a clever combination of the gradients, a descent direction common to all criteria is identified. As a natural outcome, the Multiple Gradient Descent Algorithm (MGDA) is defined as a generalization of the steepest descent method and compared with the PAES by numerical experiments. Using the MGDA on a multi-objective optimization problem requires the evaluation of a large number of points with regard to criteria and their gradients. In the particular case of CFD problems, each point evaluation is very costly. Thus here we also propose to construct metamodels and to calculate approximate gradients by local finite differences.


Pareto Front Design Point Pareto Optimal Solution Descent Direction Frechet Derivative 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197 CrossRefGoogle Scholar
  2. 2.
    Désidéri J-A (2009) Multiple-gradient descent algorithm (MGDA). INRIA research report 6953, June.
  3. 3.
    Geuzaine C, Remacle JF (2010) A three-dimensional finite element mesh generator with built-in pre- and post-processing facilities. Version 2.5.0, October.
  4. 4.
    Knowles JD, Corne DW (2000) Approximating the nondominated front using the Pareto Archived Evolution Strategy. Evol Comput 8(2):149–172 CrossRefGoogle Scholar
  5. 5.
    Zerbinati A, Désidéri J-A, Duvigneau R (2011) Comparison between MGDA and PAES for multi objective optimization. INRIA research report 7667, June.

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Adrien Zerbinati
    • 1
  • Jean-Antoine Désidéri
    • 1
  • Régis Duvigneau
    • 1
  1. 1.INRIASophia AntipolisFrance

Personalised recommendations