There are a variety of combinatorial optimization problems that are relevant to the examination of statistical data. Combinatorial problems arise in the clustering of a collection of objects, the seriation (sequencing or ordering) of objects, and the selection of variables for subsequent multivariate statistical analysis such as regression. The options for choosing a solution strategy in combinatorial data analysis can be overwhelming. Because some problems are too large or intractable for an optimal solution strategy, many researchers develop an over-reliance on heuristic methods to solve all combinatorial problems. However, with increasingly accessible computer power and ever-improving methodologies, optimal solution strategies have gained popularity for their ability to reduce unnecessary uncertainty. In this monograph, optimality is attained for nontrivially sized problems via the branch-and-bound paradigm.

This book provides explanatory text, illustrative mathematics and algorithms, demonstrations of the iterative process, pseudocode, and well-developed examples for (familiar as well as novel) applications of the branch-and-bound paradigm to relevant problems in combinatorial data analysis.

Cluster Analysis-Partitioning.- An Introduction to Branch-and-Bound Methods for Partitioning.- Minimum-Diameter Partitioning.- Minimum Within-Cluster Sums of Dissimilarities Partitioning.- Minimum Within-Cluster Sums of Squares Partitioning.- Multiobjective Partitioning.- Seriation.- to the Branch-and-Bound Paradigm for Seriation.- Seriation-Maximization of a Dominance Index.- Seriation-Maximization of Gradient Indices.- Seriation-Unidimensional Scaling.- Seriation-Multiobjective Seriation.- Variable Selection.- to Branch-and-Bound Methods for Variable Selection.- Variable Selection for Cluster Analysis.- Variable Selection for Regression Analysis.