Paper Info
Title
A No Free Lunch theorem for multi-objective optimization
Abstract
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.
Year
DOI
Venue
2010
10.1016/j.ipl.2010.07.026
Inf. Process. Lett.
Keywords
DocType
Volume
optimization technique,optimization algorithm,multi-objective optimization,measure performance,Free Lunch theorem,objective space,No Free Lunch result,foundational impossibility result,No Free Lunch theorem,black-box optimization
Journal
110
Issue
ISSN
Citations 
21
0020-0190
1
PageRank 
References 
Authors
0.35
8
1
Name
Order
Citations
PageRank
Travis C. Service1395.18