Nested Partitions Method, Theory and Applications

Transcription

1 Nested Partitions Method, Theory and Applications

2 Recent titles in the INTERNATIONAL SERIES IN OPERATIONS RESEARCH & MANAGEMENT SCIENCE Frederick S. Hillier, Series Editor, Stanford University Gass & Assad/ AN ANNOTATED TIMELINE OF OPERATIONS RESEARCH: An Informal History Greenberg/ TUTORIALS ON EMERGING METHODOLOGIES AND APPLICATIONS IN OPERATIONS RESEARCH Weber/ UNCERTAINTY IN THE ELECTRIC POWER INDUSTRY: Methods and Models for Decision Support Figueira, Greco & Ehrgott/ MULTIPLE CRITERIA DECISION ANALYSIS: State of the Art Surveys Reveliotis/ REAL-TIME MANAGEMENT OF RESOURCE ALLOCATIONS SYSTEMS: A Discrete Event Systems Approach Kall & Mayer/ STOCHASTIC LINEAR PROGRAMMING: Models, Theory, and Computation Sethi, Yan & Zhang/ INVENTORY AND SUPPLY CHAIN MANAGEMENT WITH FORECAST UPDATES Cox/ QUANTITATIVE HEALTH RISK ANALYSIS METHODS: Modeling the Human Health Impacts of Antibiotics Used in Food Animals Ching & Ng/MARKOV CHAINS: Models, Algorithms and Applications Li & Sun/ NONLINEAR INTEGER PROGRAMMING Kaliszewski/ SOFT COMPUTING FOR COMPLEX MULTIPLE CRITERIA DECISION MAKING Bouyssou et al/ EVALUATION AND DECISION MODELS WITH MULTIPLE CRITERIA: Stepping stones for the analyst Blecker & Friedrich/ MASS CUSTOMIZATION: Challenges and Solutions Appa, Pitsoulis & Williams/ HANDBOOK ON MODELLING FOR DISCRETE OPTIMIZATION Herrmann/ HANDBOOK OF PRODUCTION SCHEDULING Axsäter/ INVENTORY CONTROL, 2 nd Ed. Hall/ PATIENT FLOW: Reducing Delay in Healthcare Delivery Józefowska & Wȩglarz/ PERSPECTIVES IN MODERN PROJECT SCHEDULING Tian & Zhang/ VACATION QUEUEING MODELS: Theory and Applications Yan, Yin & Zhang/ STOCHASTIC PROCESSES, OPTIMIZATION, AND CONTROL THEORY APPLICATIONS IN FINANCIAL ENGINEERING, QUEUEING NETWORKS, AND MANUFACTURING SYSTEMS Saaty & Vargas/ DECISION MAKING WITH THE ANALYTIC NETWORK PROCESS: Economic, Political, Social & Technological Applications w. Benefits, Opportunities, Costs & Risks Yu/ TECHNOLOGY PORTFOLIO PLANNING AND MANAGEMENT: Practical Concepts and Tools Kandiller/ PRINCIPLES OF MATHEMATICS IN OPERATIONS RESEARCH Lee & Lee/ BUILDING SUPPLY CHAIN EXCELLENCE IN EMERGING ECONOMIES Weintraub/ MANAGEMENT OF NATURAL RESOURCES: A Handbook of Operations Research Models, Algorithms, and Implementations Hooker/ INTEGRATED METHODS FOR OPTIMIZATION Dawande et al/ THROUGHPUT OPTIMIZATION IN ROBOTIC CELLS Friesz/ NETWORK SCIENCE, NONLINEAR SCIENCE AND DYNAMIC GAME THEORY APPLIED TO THE STUDY OF INFRASTRUCTURE SYSTEMS Cai, Sha & Wong/ TIME-VARYING NETWORK OPTIMIZATION Mamon & Elliott/ HIDDEN MARKOV MODELS IN FINANCE del Castillo/ PROCESS OPTIMIZATION: A Statistical Approach Józefowska/JUST-IN-TIME SCHEDULING: Models & Algorithms for Computer & Manufacturing Systems Yu,Wang&Lai/FOREIGN-EXCHANGE-RATE FORECASTING WITH ARTIFICIAL NEURAL NETWORKS Beyer et al/ MARKOVIAN DEMAND INVENTORY MODELS A list of the early publications in the series is at the end of the book

3 Nested Partitions Method, Theory and Applications Leyuan Shi University of Wisconsin-Madison, WI, USA Sigurdur Ólafsson Iowa State University, IA, USA 123

4 Leyuan Shi University of Wisconsin-Madison WI,USA Sigurdur Ólafsson Iowa State University IA,USA ISBN: e-isbn: Library of Congress Control Number: c Springer Science+Business Media, LLC 2009 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now know or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper springer.com

5 To my parents Dangping Shi and Wanrong Shen LS To ömmu Lilju, mömmu, and Jenny SÓ

6 Contents 1 Introduction Large-Scale Optimization Exact Solution Methods Heuristic Solution Methods TheNPmethod Application Examples Resource-Constrained Project Scheduling Feature Selection Radiation Treatment Planning AbouttheBook Part I Methodology 2 The Nested Partitions Method Nested Partitions Framework Partitioning A Generic Partitioning Method Intelligent Partitioning for TSP Intelligent Partitioning for Feature Selection General Intelligent Partitioning Randomly Generating Feasible Solutions Biased Random Sampling Incorporating Heuristics in Generating Solutions Determining the Total Sampling Effort Backtracking and Initialization Promising Index Convergence Analysis Finite Time Convergence for COPs Time until Convergence Continuous Optimization Problems

7 viii Contents 3 Noisy Objective Functions Convergence Analysis Basic Properties Global Convergence SelectingtheCorrectMove Ordinal Optimization Ranking and Selection Time Until Convergence Mathematical Programming in the NP Framework Mathematical Programming Relaxations Column Generation NP and Mathematical Programming Branch-and-Bound Dynamic Programming Intelligent Partitioning Generating Feasible Solutions Promising Index Non-linear Programming Hybrid Nested Partitions Algorithm Greedy Heuristics in the NP Framework Generating Good Feasible Solutions Intelligent Partitioning RandomSearchintheNPFramework NP with Genetic Algorithm NP with Tabu Search NP with Ant Colony Optimization Domain Knowledge in the NP Framework Part II Applications 6 Flexible Resource Scheduling ThePMSFRProblem Reformulation of the PMSFR Problem NP Algorithm for the PMSFR Problem Partitioning Generating Feasible Solutions NumericalExample Conclusions Feature Selection NP Method for Feature Selection

8 Contents ix Intelligent Partitioning Generating Feasible Solutions NP-Wrapper and NP-Filter Algorithm NP Filter Algorithm NP Wrapper Example Numerical Comparison with Other Methods Value of Feature Selection Comparison with Simple Entropy Filter The Importance of Intelligent Partitioning Scalability of NP Filter Improving Efficiency through Instance Sampling Adaptive NP-Filter Conclusions Supply Chain Network Design Multicommodity Capacitated Facility Location Background Problem Formulation Mathematical Programming Solutions HybridNP/CPLEXforMCFLP Partitioning Generating Feasible Solutions Hybrid NP/CPLEX Algorithm ExperimentalResults Conclusions Beam Angle Selection Introduction Intensity-Modulated Radiation Therapy Beam Angle Selection NP for Beam Angle Selection Partitioning Generating Feasible Solutions Defining the Promising Index Computational Results Using LP To Evaluate NP Solutions Using Condor for Parallel Sample Evaluation Using Pinnacle To Evaluate NP Samples Conclusions Local Pickup and Delivery Problem Introduction LPDP Formulation NP Method for LPDP Intelligent Partitioning

9 x Contents Generating Feasible Solutions Numerical Results Test Instances Algorithm Setting Test Results Conclusions Extended Job Shop Scheduling Introduction Extended Job Shop Formulation Bill-of-Materials Constraints Work Shifts Constraints Dispatching Rules (DR) NP Method for Extended Job Shop Scheduling Partitioning Generating Feasible Sample Solutions Estimating the Promising Index and Backtracking DR-Guided Nested Partitions (NP-DR) Computational Results Effectiveness of Weighted Sampling α Sensitivity β Sensitivity Conclusions Resource Allocation under Uncertainty Introduction Optimal Computing Budget Allocation Stochastic Resource Allocation Problems NP Method for Resource Allocation Calculating the Promising Index through Ordinal Optimization The OCBA Technique The NP Hybrid Algorithm Implementation Numerical Results A Reduced Problem The Original Resource Allocation Problem A More Complex and Less Structured Problem Conclusions References Index...255