Titlebook: Decision Diagrams for Optimization; David Bergman,Andre A. Cire,John Hooker Book 2016 The Editor(s) (if applicable) and The Author(s), und

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Ceremony

Introduction,onstraint propagation, primal heuristics, and intelligent modeling. It presents a simple example to illustrate how decision diagrams can be used to solve an optimization problem. It concludes with a brief outline of the book.

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Exact Decision Diagrams,constraint separation. We illustrate our framework on a number of classical combinatorial optimization problems: maximum independent set, set covering, set packing, single machine scheduling, maximum cut, and maximum 2-satisfiability.

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Restricted Decision Diagrams,of the feasible set, the objective function, or both. We first show how to modify the top-down compilation approach to generate restricted diagrams that observe an input-specified width. Next, we provide a computational study of the bound provided by restricted diagrams, particularly focusing on the set covering and set packing problems.

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Variable Ordering,the exact decision diagram for particular classes of graphs. For general graphs, we show that the size is bounded by the Fibonacci numbers. Lastly, we demonstrate experimentally that variable orderings that produce small exact decision diagrams also produce better bounds from relaxed decision diagrams.

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Dimension Reduction and Feature Selectionombinatorial optimization problems, and compare our solution technology with mixed-integer linear programming. Finally, we conclude by showing how the diagram-based branch-and-bound procedure is suitable for ., and provide empirical evidence of almost linear speedups on the maximum independent set problem.