{"id":{"repo_id":"vt","oai_identifier":"oai:vtechworks.lib.vt.edu:10919/28514"},"canonical_url":"https://search.dev.ndltd.org/etd/vt/oai:vtechworks.lib.vt.edu:10919/28514","repository":{"repo_id":"vt","name":"Virginia Tech","base_url":"https://vtechworks.lib.vt.edu/oai/request"},"display":{"title":"Simultaneous Generalized Hill Climbing Algorithms for Addressing Sets of Discrete Optimization Problems","abstract":"Generalized hill climbing (GHC) algorithms provide a framework for using local search algorithms to address intractable discrete optimization problems. Many well-known local search algorithms can be formulated as GHC algorithms, including simulated annealing, threshold accepting, Monte Carlo search, and pure local search (among others). This dissertation develops a mathematical framework for simultaneously addressing a set of related discrete optimization problems using GHC algorithms. The resulting algorithms, termed simultaneous generalized hill climbing (SGHC) algorithms, can be applied to a wide variety of sets of related discrete optimization problems. The SGHC algorithm probabilistically moves between these discrete optimization problems according to a problem generation probability function. This dissertation establishes that the problem generation probability function is a stochastic process that satisfies the Markov property. Therefore, given a SGHC algorithm, movement between these discrete optimization problems can be modeled as a Markov chain. Sufficient conditions that guarantee that this Markov chain has a uniform stationary probability distribution are presented. Moreover, sufficient conditions are obtained that guarantee that a SGHC algorithm will visit the globally optimal solution over all the problems in a set of related discrete optimization problems. Computational results are presented with SGHC algorithms for a set of traveling salesman problems. For comparison purposes, GHC algorithms are also applied individually to each traveling salesman problem. These computational results suggest that optimal/near optimal solutions can often be reached more quickly using a SGHC algorithm.","abstract_html":"Generalized hill climbing (GHC) algorithms provide a framework for using local search algorithms to address intractable discrete optimization problems. Many well-known local search algorithms can be formulated as GHC algorithms, including simulated annealing, threshold accepting, Monte Carlo search, and pure local search (among others). This dissertation develops a mathematical framework for simultaneously addressing a set of related discrete optimization problems using GHC algorithms. The resulting algorithms, termed simultaneous generalized hill climbing (SGHC) algorithms, can be applied to a wide variety of sets of related discrete optimization problems. The SGHC algorithm probabilistically moves between these discrete optimization problems according to a problem generation probability function. This dissertation establishes that the problem generation probability function is a stochastic process that satisfies the Markov property. Therefore, given a SGHC algorithm, movement between these discrete optimization problems can be modeled as a Markov chain. Sufficient conditions that guarantee that this Markov chain has a uniform stationary probability distribution are presented. Moreover, sufficient conditions are obtained that guarantee that a SGHC algorithm will visit the globally optimal solution over all the problems in a set of related discrete optimization problems. Computational results are presented with SGHC algorithms for a set of traveling salesman problems. For comparison purposes, GHC algorithms are also applied individually to each traveling salesman problem. These computational results suggest that optimal/near optimal solutions can often be reached more quickly using a SGHC algorithm.","abstract_has_math":false,"creators":["Vaughan, Diane Elizabeth"],"institution":"Virginia Tech","degree_name":"Ph. D.","degree_level":"doctoral","degree_discipline":"Industrial and Systems Engineering","degree_department":"Industrial and Systems Engineering","school":null,"contributors":[],"advisors":[],"committee_chairs":["Koelling, C. 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Sufficient conditions that guarantee that this Markov chain has a uniform stationary probability distribution are presented. Moreover, sufficient conditions are obtained that guarantee that a SGHC algorithm will visit the globally optimal solution over all the problems in a set of related discrete optimization problems. Computational results are presented with SGHC algorithms for a set of traveling salesman problems. For comparison purposes, GHC algorithms are also applied individually to each traveling salesman problem. These computational results suggest that optimal/near optimal solutions can often be reached more quickly using a SGHC algorithm."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Ph. D."]},{"key":"dc:title","label":"Title","values":["Simultaneous Generalized Hill Climbing Algorithms for Addressing Sets of Discrete Optimization Problems"]}]}],"canonical_facts":{"dc:contributor.committeechair":["Koelling, C. 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