Nested Partitions Method, Theory and Applications

By: Leyuan Shi, Sigurdur Olafsson

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Hardcover | 14 November 2008

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272 Pages

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23.39 x 15.6 x 1.6

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There is increasing need to solve large-scale complex optimization problems in a wide variety of science and engineering applications, including designing telecommunication networks for multimedia transmission, planning and scheduling problems in manufacturing and military operations, or designing nanoscale devices and systems. Advances in technology and information systems have made such optimization problems more and more complicated in terms of size and uncertainty. Nested Partitions Method, Theory and Applications provides a cutting-edge research tool to use for large-scale, complex systems optimization.

The Nested Partitions (NP) framework is an innovative mix of traditional optimization methodology and probabilistic assumptions. An important feature of the NP framework is that it combines many well-known optimization techniques, including dynamic programming, mixed integer programming, genetic algorithms and tabu search, while also integrating many problem-specific local search heuristics. The book uses numerous real-world application examples, demonstrating that the resulting hybrid algorithms are much more robust and efficient than a single stand-alone heuristic or optimization technique. This book aims to provide an optimization framework with which researchers will be able to discover and develop new hybrid optimization methods for successful application of real optimization problems.

Researchers and practitioners in management science, industrial engineering, economics, computer science, and environmental science will find this book valuable in their research and study. Because of its emphasis on practical applications, the book can appropriately be used as a textbook in a graduate course.

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Introduction	p. 1
Large-Scale Optimization	p. 1
Exact Solution Methods	p. 2
Heuristic Solution Methods	p. 3
The NP method	p. 4
Application Examples	p. 6
Resource-Constrained Project Scheduling	p. 6
Feature Selection	p. 9
Radiation Treatment Planning	p. 10
About the Book	p. 12
Methodology
The Nested Partitions Method	p. 19
Nested Partitions Framework	p. 19
Partitioning	p. 23
A Generic Partitioning Method	p. 23
Intelligent Partitioning for TSP	p. 25
Intelligent Partitioning for Feature Selection	p. 26
General Intelligent Partitioning	p. 29
Randomly Generating Feasible Solutions	p. 30
Biased Random Sampling	p. 30
Incorporating Heuristics in Generating Solutions	p. 32
Determining the Total Sampling Effort	p. 33
Backtracking and Initialization	p. 33
Promising Index	p. 35
Convergence Analysis	p. 37
Finite Time Convergence for COPs	p. 37
Time until Convergence	p. 40
Continuous Optimization Problems	p. 45
Noisy Objective Functions	p. 47
Convergence Analysis	p. 48
Basic Properties	p. 48
Global Convergence	p. 51
Selecting the Correct Move	p. 57
Ordinal Optimization	p. 57
Ranking and Selection	p. 59
Time Until Convergence	p. 63
Mathematical Programming in the NP Framework	p. 69
Mathematical Programming	p. 70
Relaxations	p. 70
Column Generation	p. 72
NP and Mathematical Programming	p. 73
Branch-and-Bound	p. 73
Dynamic Programming	p. 74
Intelligent Partitioning	p. 76
Generating Feasible Solutions	p. 79
Promising Index	p. 81
Non-linear Programming	p. 81
Hybrid Nested Partitions Algorithm	p. 85
Greedy Heuristics in the NP Framework	p. 85
Generating Good Feasible Solutions	p. 86
Intelligent Partitioning	p. 91
Random Search in the NP Framework	p. 92
NP with Genetic Algorithm	p. 93
NP with Tabu Search	p. 97
NP with Ant Colony Optimization	p. 99
Domain Knowledge in the NP Framework	p. 102
Applications
Flexible Resource Scheduling	p. 107
The PMSFR Problem	p. 108
Reformulation of the PMSFR Problem	p. 110
NP Algorithm for the PMSFR Problem	p. 113
Partitioning	p. 113
Generating Feasible Solutions	p. 117
Numerical Example	p. 120
Conclusions	p. 123
Feature Selection	p. 125
NP Method for Feature Selection	p. 127
Intelligent Partitioning	p. 127
Generating Feasible Solutions	p. 128
NP-Wrapper and NP-Filter Algorithm	p. 130
NP Filter Algorithm	p. 130
NP Wrapper Example	p. 131
Numerical Comparison with Other Methods	p. 136
Value of Feature Selection	p. 136
Comparison with Simple Entropy Filter	p. 137
The Importance of Intelligent Partitioning	p. 139
Scalability of NP Filter	p. 142
Improving Efficiency through Instance Sampling	p. 147
Adaptive NP-Filter	p. 149
Conclusions	p. 154
Supply Chain Network Design	p. 157
Multicommodity Capacitated Facility Location	p. 158
Background	p. 158
Problem Formulation	p. 158
Mathematical Programming Solutions	p. 161
Hybrid NP/CPLEX for MCFLP	p. 162
Partitioning	p. 164
Generating Feasible Solutions	p. 166
Hybrid NP/CPLEX Algorithm	p. 166
Experimental Results	p. 168
Conclusions	p. 170
Beam Angle Selection	p. 173
Introduction	p. 173
Intensity-Modulated Radiation Therapy	p. 174
Beam Angle Selection	p. 175
NP for Beam Angle Selection	p. 176
Partitioning	p. 177
Generating Feasible Solutions	p. 181
Defining the Promising Index	p. 182
Computational Results	p. 182
Using LP To Evaluate NP Solutions	p. 183
Using Condor for Parallel Sample Evaluation	p. 187
Using Pinnacle To Evaluate NP Samples	p. 189
Conclusions	p. 191
Local Pickup and Delivery Problem	p. 193
Introduction	p. 193
LPDP Formulation	p. 195
NP Method for LPDP	p. 197
Intelligent Partitioning	p. 197
Generating Feasible Solutions	p. 199
Numerical Results	p. 201
Test Instances	p. 202
Algorithm Setting	p. 202
Test Results	p. 204
Conclusions	p. 206
Extended Job Shop Scheduling	p. 207
Introduction	p. 207
Extended Job Shop Formulation	p. 208
Bill-of-Materials Constraints	p. 209
Work Shifts Constraints	p. 210
Dispatching Rules (DR)	p. 211
NP Method for Extended Job Shop Scheduling	p. 212
Partitioning	p. 212
Generating Feasible Sample Solutions	p. 213
Estimating the Promising Index and Backtracking	p. 217
DR-Guided Nested Partitions (NP-DR)	p. 218
Computational Results	p. 219
Effectiveness of Weighted Sampling	p. 221
[alpha] Sensitivity	p. 222
[beta] Sensitivity	p. 223
Conclusions	p. 224
Resource Allocation under Uncertainty	p. 227
Introduction	p. 227
Optimal Computing Budget Allocation	p. 227
Stochastic Resource Allocation Problems	p. 228
NP Method for Resource Allocation	p. 230
Calculating the Promising Index through Ordinal Optimization	p. 231
The OCBA Technique	p. 234
The NP Hybrid Algorithm	p. 236
Implementation	p. 238
Numerical Results	p. 242
A Reduced Problem	p. 242
The Original Resource Allocation Problem	p. 244
A More Complex and Less Structured Problem	p. 245
Conclusions	p. 246
References	p. 247
Index	p. 255
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Nested Partitions Method, Theory and Applications

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Hardcover

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