Overview
- Presents different dynamic programming applications in the areas of (i) optimization of decision trees, (ii) optimization of decision rules and systems of decision rules, (iii) optimization of element partition trees, which are used in finite element methods for solving partial differential equations (PDEs), and (iv) study of combinatorial optimization problems
- Studies optimal element partition trees for rectangular meshes
- Creates a multi-stage optimization approach for classic combinatorial optimization problems such as matrix chain multiplication, binary search trees, global sequence alignment, and shortest paths
Part of the book series: Intelligent Systems Reference Library (ISRL, volume 146)
Access this book
Tax calculation will be finalised at checkout
Other ways to access
Table of contents (19 chapters)
-
Front Matter
-
Common Tools: Pareto Optimal Points and Decision Tables
-
Front Matter
-
-
Decision Trees
-
Front Matter
-
-
Decision Rules and Systems of Decision Rules
-
Front Matter
-
-
Element Partition Trees
-
Front Matter
-
Keywords
About this book
Dynamic programming is an efficient technique for solving optimization problems. It is based on breaking the initial problem down into simpler ones and solving these sub-problems, beginning with the simplest ones. A conventional dynamic programming algorithm returns an optimal object from a given set of objects. This book develops extensions of dynamic programming, enabling us to (i) describe the set of objects under consideration; (ii) perform a multi-stage optimization of objects relative to different criteria; (iii) count the number of optimal objects; (iv) find the set of Pareto optimal points for bi-criteria optimization problems; and (v) to study relationships between two criteria. It considers various applications, including optimization of decision trees and decision rule systems as algorithms for problem solving, as ways for knowledge representation, and as classifiers; optimization of element partition trees for rectangular meshes, which are used in finite element methods for solving PDEs; and multi-stage optimization for such classic combinatorial optimization problems as matrix chain multiplication, binary search trees, global sequence alignment, and shortest paths. The results presented are useful for researchers in combinatorial optimization, data mining, knowledge discovery, machine learning, and finite element methods, especially those working in rough set theory, test theory, logical analysis of data, and PDE solvers. This book can be used as the basis for graduate courses.
Authors and Affiliations
Bibliographic Information
Book Title: Extensions of Dynamic Programming for Combinatorial Optimization and Data Mining
Authors: Hassan AbouEisha, Talha Amin, Igor Chikalov, Shahid Hussain, Mikhail Moshkov
Series Title: Intelligent Systems Reference Library
DOI: https://doi.org/10.1007/978-3-319-91839-6
Publisher: Springer Cham
eBook Packages: Intelligent Technologies and Robotics, Intelligent Technologies and Robotics (R0)
Copyright Information: Springer International Publishing AG, part of Springer Nature 2019
Hardcover ISBN: 978-3-319-91838-9Published: 31 May 2018
Softcover ISBN: 978-3-030-06309-2Published: 25 January 2019
eBook ISBN: 978-3-319-91839-6Published: 22 May 2018
Series ISSN: 1868-4394
Series E-ISSN: 1868-4408
Edition Number: 1
Number of Pages: XVI, 280
Number of Illustrations: 69 b/w illustrations, 3 illustrations in colour