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From preface
Optimal resource allocation is an extremely important part of many human activities, including reliability engineering. One of the first problems that arose in this engineering area was optimal allocation of spare units. Then it came to optimization of networks of various natures (communication, transportation, energy transmission, etc.) and now it is an important part of counter-terrorism protection.
In this book is an overview of different approaches of optimal resource allocation, from classical LaGrange methods to modern heuristic algorithms.
This book is not a tutorial in the common sense of the word. It is not a reliability cookbook. It is more a bridge between reliability engineering and applied mathematics in the field of optimal allocation of resources for systems ’ reliability increase. It supplies the reader with basic knowledge in optimization theory and presents examples of application of the corresponding mathematical methods to real world problems. The book ’ s objective is to inspire the reader to visit the wonderful area of applied methods of optimization, rather than to give him or her a mathematical course on optimization.
Basic Mathematical Redundancy Models
Types of Models
Non-repairable Redundant Group with Active Redundant Units
Non-repairable Redundant Group with Standby Redundant Units
Repairable Redundant Group with Active Redundant Units
Repairable Redundant Group with Standby Redundant Units
Multi-level Systems and System Performance Estimation
Brief Review of Other Types of Redundancy
Time Redundancy
Some Additional Optimization Problems
Chronological Bibliography of Main Monographs on Reliability Theory (with topics on Optimization)
Formulation of Optimal Redundancy Problems
Problem Description
Formulation of the Optimal Redundancy Problem with a Single Restriction
Formulation of Optimal Redundancy Problems with Multiple Constraints
Formulation of Multi-Criteria Optimal Redundancy Problems
Chronological Bibliography
Method of Lagrange Multipliers
Chronological Bibliography
Steepest Descent Method
The Main Idea of SDM
Description of the Algorithm
The Stopping Rule
Approximate Solution
Chronological Bibliography
Dynamic Programming
Bellman’s Algorithm
Kettelle’s Algorithm
Chronological Bibliography
Universal Generating Functions
Generating Function
Universal GF (U-function)
Chronological Bibliography
Genetic Algorithms
Structure of Steady-State Genetic Algorithms
Related Techniques
Chronological Bibliography
MonteCarlo Simulation
Introductory Remarks
Formulation of Optimal Redundancy Problems in Statistical Terms
Algorithm for Trajectory Generation
Description of the Idea of the Solution
Inverse Optimization Problem
Direct Optimization Problem
Chronological Bibliography
Comments On Calculation Methods
Comparison of Methods
Sensitivity Analysis of Optimal Redundancy Solutions
Optimal Redundancy with Several Limiting Factors
Method of Weighing Costs
Method of Generalized Generating Functions
Chronological Bibliography
Optimal Redundancy in Multistate Systems
Chronological Bibliography
Case Studies
Spare Supply System for Worldwide Telecommunication System Globalstar
Optimal Capacity Distribution of Telecommunication Backbone Network Resources
Optimal Spare Allocation for Mobile Repair Station
Chronological Bibliography
Counter-Terrorism: Protection Resources Allocation
Written Description of the Problem
Evaluation of Expected Loss
Algorithm of Resource Allocation
Branching System Protection
Fictional Case Study
Measures of Defense, Their Effectiveness, and Related Expenses
Antiterrorism Resource Allocation under Fuzzy Subjective Estimates
Chronological Bibliography
About the author