Keywords

Optimization, theory, discrete optimization, blackbox complexity, optimal elimination of fitness functions, generalized onemax, generalized leading ones, problem learning

Abstract

The modern view of optimization is that optimization algorithms are not designed in a vacuum, but can make use of information regarding the broad class of objective functions from which a problem instance is drawn. Using this knowledge, we want to design optimization algorithms that execute quickly (efficiency), solve the objective function with minimal samples (performance), and are applicable over a wide range of problems (abstraction). However, we present a new theory for blackbox optimization from which, we conclude that of these three desired characteristics, only two can be maximized by any algorithm. We put forward an alternate view of optimization where we use knowledge about the problem class and samples from the problem instance to identify which problem instances from the class are being solved. From this Elimination of Fitness Functions approach, an idealized optimization algorithm that minimizes sample counts over any problem class, given complete knowledge about the class, is designed. This theory allows us to learn more about the difficulty of various problems, and we are able to use it to develop problem complexity bounds. We present general methods to model this algorithm over a particular problem class and gain efficiency at the cost of specifically targeting that class. This is demonstrated over the Generalized Leading-Ones problem and a generalization called LO∗∗ , and efficient algorithms with optimal performance are derived and analyzed. We also iii tighten existing bounds for LO∗∗∗. Additionally, we present a probabilistic framework based on our Elimination of Fitness Functions approach that clarifies how one can ideally learn about the problem class we face from the objective functions. This problem learning increases the performance of an optimization algorithm at the cost of abstraction. In the context of this theory, we re-examine the blackbox framework as an algorithm design framework and suggest several improvements to existing methods, including incorporating problem learning, not being restricted to blackbox framework and building parametrized algorithms. We feel that this theory and our recommendations will help a practitioner make substantially better use of all that is available in typical practical optimization algorithm design scenarios.

Notes

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Graduation Date

2012

Semester

Fall

Advisor

Wu, Annie

Degree

Doctor of Philosophy (Ph.D.)

College

College of Engineering and Computer Science

Department

Computer Science

Degree Program

Computer Science

Format

application/pdf

Identifier

CFE0004511

URL

http://purl.fcla.edu/fcla/etd/CFE0004511

Language

English

Release Date

December 2012

Length of Campus-only Access

None

Access Status

Doctoral Dissertation (Open Access)

Subjects

Dissertations, Academic -- Engineering and Computer Science, Engineering and Computer Science -- Dissertations, Academic

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