Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization
Proceedings of the 5th International Conference on Genetic Algorithms
On classes of functions for which No Free Lunch results hold
Information Processing Letters
Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy
Evolutionary Computation
Focused no free lunch theorems
Proceedings of the 10th annual conference on Genetic and evolutionary computation
No free lunch and free leftovers theorems for multiobjective optimisation problems
EMO'03 Proceedings of the 2nd international conference on Evolutionary multi-criterion optimization
No free lunch theorems for optimization
IEEE Transactions on Evolutionary Computation
Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach
IEEE Transactions on Evolutionary Computation
A fast and elitist multiobjective genetic algorithm: NSGA-II
IEEE Transactions on Evolutionary Computation
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The No Free Lunch theorem (Schumacher et al., 2001; Wolpert and Macready, 1997 [8,10]) is a foundational impossibility result in black-box optimization stating that no optimization technique has performance superior to any other over any set of functions closed under permutation. This paper considers situations in which there is some form of structure on the set of objective values other than the typical total ordering (e.g., Pareto dominance in multi-objective optimization). It is shown that in such cases, when attention is restricted to natural measures of performance and optimization algorithms that measure performance and optimize with respect to this structure, that a No Free Lunch result holds for any class of problems which is structurally closed under permutation. This generalizes the Sharpened No Free Lunch theorem of Schumacher et al. (2001) [8] to non-totally ordered objective spaces.