Nested Partitions Method, Theory and Applications

1. Front Matter

   Pages I-X

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2. Introduction

   1. Front Matter

      Pages 1-1

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   2. Introduction

      • Leyuan Shi, Sigurdur Ólafsson

      Pages 1-15

3. Methodology

   1. Front Matter

      Pages 17-17

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   2. The Nested Partitions Method

      • Leyuan Shi, Sigurdur Ólafsson

      Pages 19-46

   3. Noisy Objective Functions

      • Leyuan Shi, Sigurdur Ólafsson

      Pages 47-68

   4. Mathematical Programming in the NP Framework

      • Leyuan Shi, Sigurdur Ólafsson

      Pages 69-83

   5. Hybrid Nested Partitions Algorithm

      • Leyuan Shi, Sigurdur Ólafsson

      Pages 85-103

4. Applications

   1. Front Matter

      Pages 105-105

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   2. Flexible Resource Scheduling

      • Leyuan Shi, Sigurdur Ólafsson

      Pages 107-124

   3. Feature Selection

      • Leyuan Shi, Sigurdur Ólafsson

      Pages 125-155

   4. Supply Chain Network Design

      • Leyuan Shi, Sigurdur Ólafsson

      Pages 157-171

   5. Beam Angle Selection

      • Leyuan Shi, Sigurdur Ólafsson

      Pages 173-191

   6. Local Pickup and Delivery Problem

      • Leyuan Shi, Sigurdur Ólafsson

      Pages 193-206

   7. Extended Job Shop Scheduling

      • Leyuan Shi, Sigurdur Ólafsson

      Pages 207-225

   8. Resource Allocation under Uncertainty

      • Leyuan Shi, Sigurdur Ólafsson

      Pages 227-246

5. Back Matter

   Pages 247-257

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Thesubjectofthisbookisthenested partitions method(NP),arelativelynew optimization method that has been found to be very e?ective solving discrete optimization problems. Such discrete problems are common in many practical applications and the NP method is thus useful in diverse application areas. It can be applied to both operational and planning problems and has been demonstrated to e?ectively solve complex problems in both manufacturing and service industries. To illustrate its broad applicability and e?ectiveness, in this book we will show how the NP method has been successful in solving complex problems in planning and scheduling, logistics and transportation, supply chain design, data mining, and health care. All of these diverse app- cationshaveonecharacteristicincommon:theyallleadtocomplexlarge-scale discreteoptimizationproblemsthatareintractableusingtraditionaloptimi- tion methods. 1.1 Large-Scale Optimization IndevelopingtheNPmethodwewillconsideroptimization problemsthatcan be stated mathematically in the following generic form: minf(x), (1.1) x?X where the solution space or feasible region X is either a discrete or bounded ? set of feasible solutions. We denote a solution to this problem x and the ? ? objective function value f = f (x ).

• Manufacturing
• Multimedia
• Scheduling
• Stochastic Optimization
• algorithm
• algorithms
• combinatorial optimization
• communication
• complex systems
• data mining
• genetic algorithms
• meta-heuristics
• mixed integer programming
• optimization
• programming

• University of Wisconsin-Madison, USA

  Leyuan Shi

• Iowa State University, USA

  Sigurdur Ólafsson

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