Pareto optimization in algebraic dynamic programming

Pareto optimization combines independent objectives by computing the Pareto front of its search space, defined as the set of all solutions for which no other candidate solution scores better under all objectives. This gives, in a precise sense, better information than an artificial amalgamation of d...

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Bibliographic Details
Published in:Algorithms for molecular biology Vol. 10; no. 1; p. 22
Main Authors: Saule, Cédric, Giegerich, Robert
Format: Journal Article
Language:English
Published: London BioMed Central 07.07.2015
BioMed Central Ltd
Springer Nature B.V
Subjects:
Algorithms
Bioinformatics
Biomedical and Life Sciences
Cellular and Medical Topics
Computational Biology/Bioinformatics
Life Sciences
Pareto efficiency
Physiological
Pareto optimization
Algebraic dynamic programming
Dynamic programming
Sankoff algorithm
RNA structure
ISSN:1748-7188, 1748-7188
Online Access:Get full text
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Summary:Pareto optimization combines independent objectives by computing the Pareto front of its search space, defined as the set of all solutions for which no other candidate solution scores better under all objectives. This gives, in a precise sense, better information than an artificial amalgamation of different scores into a single objective, but is more costly to compute. Pareto optimization naturally occurs with genetic algorithms, albeit in a heuristic fashion. Non-heuristic Pareto optimization so far has been used only with a few applications in bioinformatics. We study exact Pareto optimization for two objectives in a dynamic programming framework. We define a binary Pareto product operator ∗ Par on arbitrary scoring schemes. Independent of a particular algorithm, we prove that for two scoring schemes A and B used in dynamic programming, the scoring scheme A ∗ Par B correctly performs Pareto optimization over the same search space. We study different implementations of the Pareto operator with respect to their asymptotic and empirical efficiency. Without artificial amalgamation of objectives, and with no heuristics involved, Pareto optimization is faster than computing the same number of answers separately for each objective. For RNA structure prediction under the minimum free energy versus the maximum expected accuracy model, we show that the empirical size of the Pareto front remains within reasonable bounds. Pareto optimization lends itself to the comparative investigation of the behavior of two alternative scoring schemes for the same purpose. For the above scoring schemes, we observe that the Pareto front can be seen as a composition of a few macrostates, each consisting of several microstates that differ in the same limited way. We also study the relationship between abstract shape analysis and the Pareto front, and find that they extract information of a different nature from the folding space and can be meaningfully combined.
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ISSN:1748-7188
1748-7188
DOI:10.1186/s13015-015-0051-7