Extensions of Dynamic Programming for Combinatorial Optimization and Data Mining

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.

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

Inhalt
Introduction.- Tools for Study of Pareto Optimal Points.- Some Tools for Decision Tables.- Different Kinds of Decision Trees.- Multi-stage Optimization of Decision Trees with Some Applications.- More Applications of Multi-stage Optimizationof Decision Trees.- Bi-Criteria Optimization Problem for Decision Trees: Cost vs Cost.- Bi-Criteria Optimization Problem for Decision Trees: Cost vs Uncertainty.- Different Kinds of Rules and Systems of Rules