Integrating Pareto Optimization into Dynamic Programming

Thomas Gatter,Cédric Saule,Robert Giegerich

doi:10.3390/a9010012

Abstract

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.

Highlights

Pareto optimization addresses optimization under multiple, independent objectives [1].It allows one to compute a well-defined set of extremal solutions from the search space, the Pareto front
The outcome is of interest for programmers who consider Pareto optimization, but not necessarily in a dynamic programming context
In an algebraic dynamic programming application, the case of simultaneously merging two or more sorted sublists can occur in Equations (15) and (16)

Summary

Introduction

It allows one to compute a well-defined set of extremal solutions from the search space, the Pareto front. This set holds all solutions that are optimal in one objective, in the sense that the value of the objective function cannot be improved without weakening values in other objectives. Pareto optimization is used widely in combinatorial optimization; see [2,3,4] for recent applications. It is often employed, albeit in a heuristic fashion, with genetic algorithms. This happens, e.g., for biologically-motivated problems in [5,6,7]

Objectives

Results

Conclusion