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Integrating Pareto Optimization into Dynamic Programming

Faculty of Technology and Center for Biotechnology, Bielefeld University, 33501 Bielefeld, Germany
Author to whom correspondence should be addressed.
Academic Editor: Jesper Jansson
Algorithms 2016, 9(1), 12;
Received: 18 November 2015 / Revised: 11 January 2016 / Accepted: 18 January 2016 / Published: 27 January 2016
PDF [2400 KB, uploaded 27 January 2016]


Pareto optimization combines independent objectives by computing the Pareto front of the search space, yielding a set of optima where none scores better on all objectives than any other. Recently, it was shown that Pareto optimization seamlessly integrates with algebraic dynamic programming: when scoring schemes A and B can correctly evaluate the search space via dynamic programming, then so can Pareto optimization with respect to A and B. However, the integration of Pareto optimization into dynamic programming opens a wide range of algorithmic alternatives, which we study in substantial detail in this article, using real-world applications in biosequence analysis, a field where dynamic programming is ubiquitous. Our results are two-fold: (1) We introduce the operation of a “Pareto algebra product” in the dynamic programming framework of Bellman’s GAP. Users of this framework can now ask for Pareto optimization with a single keystroke. Careful evaluation of the implementation alternatives by means of an extended Bellman’s GAP compiler demonstrates the dependence of the best implementation choice on the application at hand. (2) We extract from our experiments several pieces of advice to programmers who do not use a system such as Bellman’s GAP, but who choose to hand-craft their dynamic programming recurrences, incorporating Pareto optimization from scratch. View Full-Text
Keywords: pareto optimization; algebraic dynamic programming; sorting algorithms pareto optimization; algebraic dynamic programming; sorting algorithms

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Gatter, T.; Giegerich, R.; Saule, C. Integrating Pareto Optimization into Dynamic Programming. Algorithms 2016, 9, 12.

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