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The Belchertown Intrusive Complex is a ~164 km2 Devonian pluton that intruded Paleozoic metasedimentary and metavolcanic rocks in west-central Massachusetts. Intrusion of the pluton was synchronous with Acadian deformation (Ashwal, 1974). The complex is concentrically zoned, with a core of orthopyroxene-biotite monzodiorite, a middle zone of clinopyroxene-hornblende-biotite granodiorite, and an outermost zone of hornblende-biotite granodiorite. Zoning from a more to less hydrous mineral suite from the outside to the inside of the pluton led Ashwal (1974) to suggest that metamorphic hydration most strongly affected the outermost zones of the complex. Basaltic inclusions occur most commonly near the edges of the pluton. Many of these inclusions preserve textures suggestive of mafic-felsic magma interaction. The abundance of basaltic enclaves on the edges of the complex may suggest a bowl-shaped structure, with lower more mafic-dominated rocks exposed on the edges of the complex. Bulk rock major element analyses of granitoids, basalts and gabbros, and diorites from all zones of the complex show that intermediate samples, regardless of zone, plot on a mixing line between mafic and felsic end members, supporting a model in which mafic and felsic magmas may have mingled and mixed. Trace element analyses of intermediate-composition samples are similar across the entire complex, with enrichment in large ion lithophile elements and a pronounced Nb trough. In contrast, trace element concentrations in both the mafic rocks (basaltic enclaves and gabbroic inclusions), and in the granitoids, show considerable variation. The diversity of composition within both the mafic and felsic end-members suggests that either fractionation or differing degrees of partial melting of source rocks may account for these compositional ranges. Sanukitoids comprise a majority of the inner zone, and point to the mixing of parental melts at depth in a subduction tectonic regime as a likely model of petrogenesis for the complex.

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. / Ph. D.

Generalized hill climbing (GHC) algorithms provide a unifying framework for describing several discrete optimization problem local search heuristics, including simulated annealing and tabu search. A necessary and a sufficient convergence condition for GHC algorithms are presented. The convergence conditions presented in this dissertation are based upon a new iteration classification scheme for GHC algorithms. The convergence theory for particular formulations of GHC algorithms is presented and the implications discussed. Examples are provided to illustrate the relationship between the new convergence conditions and previously existing convergence conditions in the literature. The contributions of the necessary and the sufficient convergence conditions for GHC algorithms are discussed and future research endeavors are suggested. / Ph. D.