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A step toward constant time local search for optimizing pseudo boolean functions

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dc.contributor.authorChen, Wenxiang, author
dc.contributor.authorWhitley, L. Darrell, advisor
dc.contributor.authorHowe, Adele E., advisor
dc.contributor.authorCheney, Margaret, committee member
dc.date.accessioned2007-01-03T06:10:14Z
dc.date.available2007-01-03T06:10:14Z
dc.date.issued2013
dc.description.abstractPseudo Boolean Functions (PBFs) are the objective functions for a wide class of hard optimization problems, such as MAX-SAT and MAX-CUT. Since these problems are NP-Hard, researchers and practitioners rely on incomplete solvers, such as Stochastic Local Search (SLS), for large problems. Best-Improvement Local Search (BILS) is a common form of SLS, which always takes the move yielding the highest improvement in the objective function. Generally, the more runtime SLS is given, the better solution can be obtained. This thesis aims at algorithmically accelerating SLS for PBFs using Walsh Analysis. The contributions of this thesis are threefold. First, a general approach for executing an approximate best-improvement move in constant time on average using Walsh analysis, "Walsh-LS", is described. Conventional BILS typically requires examining all n neighbors to decide which move to take, given the number of variables is n. With Walsh analysis, however, we can determine which neighbors need to be checked. As long as the objective function is epistatically bounded by a constant k (k is the number of variables per subfunctions), the number of neighbors that need to be checked is constant regardless of problem size. An impressive speedup of runtime (up to 449 times) is observed in our empirical studies. Second, in the context of Walsh-LS, we empirically study two key components of SLS from the perspectives of both efficiency and effectiveness: 1) Local optimum escape method: hard random or soft restarts; 2) Local search strategy: first-improvement or best-improvement. Lastly, on average we can perform approximate BILS using the mean over a Hamming region of arbitrary radius as a surrogate objective function. Even though the number of points is exponential in the radius of the Hamming region, BILS using the mean value of points in the Hamming region as a surrogate objective function can still take each move in time independent of n on average. According to our empirical studies, using the average over a Hamming region as a surrogate objective function can yield superior performance results on neutral landscapes like NKq-landscapes.
dc.format.mediumborn digital
dc.format.mediummasters theses
dc.identifierChen_colostate_0053N_12060.pdf
dc.identifierETDF2013500363COMS
dc.identifier.urihttp://hdl.handle.net/10217/81007
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.subjectcomplexity per move
dc.subjectstochastic local search
dc.subjectpseudo Boolean optimization
dc.subjectNK-landscapes
dc.titleA step toward constant time local search for optimizing pseudo boolean functions
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineComputer Science
thesis.degree.grantorColorado State University
thesis.degree.levelMasters
thesis.degree.nameMaster of Science (M.S.)

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