CONVEX EXTENSION OF DISCRETE-CONVEX FUNCTIONS AND APPLICATIONS IN OPTIMIZATION THE STRUCTURE OF PARALLEL AND DISTRIBUTED PROCESSING SYSTEMS

 

Tiit Riismaa

 

Abstract

 

A method of description and optimization of the structure of multi-level parallel and distributed processing systems is presented. The set of feasible structures for such class of systems is defined. The representation of this set is constructed in terms of the graph theory. A recursive algorithm is constructed to solve the general problem of optimal multi-level paralleling procedure. For the reduced statement two types of variable parameters are defined: for the level size and for the relations of adjacent levels. Two different classes of iteration methods are developed. For solving the reduced problem the recursive algorithm is constructed, where index of level is the index of recursion. Also a numerical method of local searching is developed. On each step of the iteration the calculation of the value of objective function is required only on some vertices of some kind of unit cube. Modelling and optimization of the structure of multi-level processing system illustrate the considered approach.

 

Lecture Notes in Management Science (2011) Vol. 3: 75-90

3rd International Conference on Applied Operational Research, Proceedings

© Tadbir Operational Research Group Ltd. All rights reserved.

www.tadbir.ca

 

ISSN 2008-0050 (Print)

ISSN 1927-0097 (Online)

 

ARTICLE OUTLINE

 

·         Introduction

·         Feasible Set Of Multi-Level Parallel And Distributed Processing System

·         The Problem Of Optimal Multi-Level Parallel And Distributed Processing System

·         Recursive Algorithm For Solving The General Problem Of Optimal Multi-Level Parallel And Distributed Processing System

·         Reduced Problem Of Optimal Parallel And Distributed Processing System

·         Recursive Algorithm For Solving The Reduced Problem Of Optimal Parallel And Distributed Processing System

·         Mathematical Properties Of The Reduced Problem Of Optimal Parallel And Distributed Processing System

·         Algorithm Of Local Searching For The Reduced Problem Of Optimal Multi-Level Parallel And Distributed Processing System

·         Academic Example: Optimization The Structure Of Multi-Level Parallel And Distributed Processing System

·         Conclusion          

·         References

 

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