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(No) Free Lunch Theorems for Multiobjective Optimization
Joshua D. Knowles
IRIDIA, CP 194/6
Université Libre de Bruxelles
Brussels, Belgium
jknowles@ulb.ac.be

Abstract

The classic No Free Lunch (NFL) theorem for optimization (Wolpert and Macready 1995, 1997) states that all black-box search algorithms perform identically when performance is aggregated over the set of all discrete optimization problems. Thus, unqualified statements of the form: "Algorithm A outperforms Algorithm B" for any two black-box search algorithms A and B, whatever, are always untrue. Recent work by Corne and Knowles has extended the NFL theorem to the case of (Pareto) multiobjective optimization, yielding four new No Free and Free Lunch theorems. The talk will endeavour to explain these new results, following a gentle introduction to NFL. [In the spirit of the talk No Free Beer will be provided this time ;-) ]

Keywords

No Free Lunch theorem, Multiobjective optimization

References

  1. D.W. Corne and J.D. Knowles. (2003) No Free Lunch and Free Leftovers Theorems for Multiobjective Optimization Problems. In Evolutionary Multi-Criterion Optimization (EMO 2003) Second International Conference. pp. 327-341.
    See http://iridia.ulb.ac.be/~jknowles/CorneKnowlesEMO2003-NFL.pdf
  2. D.W. Corne and J.D. Knowles. (2003) Some Multiobjective Optimizers are Better than Others. In Proceedings of the IEEE Congress on Evolutionary Computation. To Appear.
    See http://iridia.ulb.ac.be/~jknowles/CorneKnowlesCEC2003.pdf