Can we measure the difficulty of an optimization problem?
Date
2014-11
Authors
Alpcan, Tansu
Everitt, Tom
Hutter, Marcus
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Volume Title
Publisher
IEEE
Abstract
an we measure the difficulty of an optimization problem? Although optimization plays a crucial role in modern science and technology, a formal framework that puts problems and solution algorithms into a broader context has not been established. This paper presents a conceptual approach which gives a positive answer to the question for a broad class of optimization problems. Adopting an information and computational perspective, the proposed framework builds upon Shannon and algorithmic information theories. As a starting point, a concrete model and definition of optimization problems is provided. Then, a formal definition of optimization difficulty is introduced which builds upon algorithmic information theory. Following an initial analysis, lower and upper bounds on optimization difficulty are established. One of the upper-bounds is closely related to Shannon information theory and black-box optimization. Finally, various computational issues and future research directions are discussed.
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Source
2014 IEEE Information Theory Workshop (ITW), Hobart, TAS., 2-5 Nov. 2014
Type
Conference paper