Extensions of Dynamic Programming for Combinatorial Optimization and Data Mining

الغلاف الأمامي
Springer, 22‏/05‏/2018 - 280 من الصفحات

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.


 

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المحتوى

1 Introduction
1
Pareto Optimal Points and Decision Tables
14
2 Tools for Study of Pareto Optimal Points
15
3 Some Tools for Decision Tables
23
Part II Decision Trees
32
4 Different Kinds of Decision Trees
35
5 Multistage Optimization of Decision Trees with Some Applications
49
6 More Applications of Multistage Optimization of Decision Trees
73
Cost Versus Uncertainty
173
Part IV Element Partition Trees
190
Main Notions
191
14 Multistage Optimization of Element Partition Trees
207
15 Bicriteria Optimization of Element Partition Trees
225
Part V Combinatorial Optimization Problems
236
16 Matrix Chain Multiplication
237
17 Binary Search Trees
245

Cost Versus Cost
85
Cost Versus Uncertainty
105
Part III Decision Rules and Systems of Decision Rules
123
9 Different Kinds of Rules and Systems of Rules
125
10 Multistage Optimization of Decision Rules
131
Cost Versus Cost
151
18 Global Sequence Alignment
253
19 Optimal Paths in Directed Graphs
261
A Dagger Software System
269
Appendix Final Remarks
274
Index
275
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