Heuristic Search. Theory and Applications. Stefan Edelkamp. Stefan Schrodl ELSEVIER. Morgan Kaufmann is an imprint of Elsevier HEIDELBERG LONDON

Transcription

1 Heuristic Search Theory and Applications Stefan Edelkamp Stefan Schrodl AMSTERDAM BOSTON HEIDELBERG LONDON ELSEVIER NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY» TOKYO Morgan Kaufmann is an imprint of Elsevier

2 Contents List of Algorithms Preface xxul PART I HEURISTIC SEARCH PRIMER CHAPTER 1 Introduction Notational and Mathematical Background Pseudocode Computability Theory Complexity Theory Asymptotic Resource Consumption Symbolic Logic Search Success Stories State Space Problems Problem Graph Representations Heuristics Examples of Search Problems Sliding-Tile Puzzles Rubik's Cube Sokoban Route Planning TSP Multiple Sequence Alignment General State Space Descriptions Action Planning *Production Systems Markov Decision Processes Generic Search Model Summary Exercises Bibliographic Notes 45 CHAPTER 2 Basic Search Algorithms Uninformed Graph Search Algorithms Depth-First Search Breadth-First Search Dijkstra's Algorithm 53 V

3 vi Contents Negatively Weighted Graphs Relaxed Node Selection * Algorithm of Bellman-Ford Dynamic Programming Informed Optimal Search A* On the Optimal Efficiency of A* *General Weights Cost Algebras Multiobjective Search Summary Exercises Bibliographic Notes 86 CHAPTER 3 *Dictionary Data Structures Priority Queues Bucket Data Structures Heap Data Structures Hash Tables Hash Dictionaries Ill Hash Functions Hashing Algorithms Memory-Saving Dictionaries Approximate Dictionaries Subset Dictionaries Arrays and Lists Tries Hashing Unlimited Branching Trees String Dictionaries Suffix Trees Generalized Suffix Trees Summary Exercises Bibliographic Notes 157 CHAPTER 4 Automatically Created Heuristics Abstraction Transformations Valtorta's Theorem hierarchical A* Pattern Databases 167

4 4.4.1 Fifteen-Puzzle Rubik's Cube Directed Search Graphs Korf's Conjecture Multiple Pattern Databases Disjoint Pattern Databases *Customized Pattern Databases Pattern Selection Symmetry and Dual Pattern Databases Bounded Pattern Databases On-Demand Pattern Databases Compressed Pattern Databases Compact Pattern Databases Summary Exercises Bibliographic Notes 190 PART II HEURISTIC SEARCH UNDER MEMORY CONSTRAINTS CHAPTER 5 Linear-Space Search ^Logarithmic Space Algorithms Divide-and-Conquer BFS Divide-and-Conquer Shortest Paths Search Exploring the Search Tree Branch-and-Bound Iterative-Deepening Search Iterative-Deepening A* Prediction of IDA* Search Asymptotic Branching Factors IDA* Search Tree Prediction *Convergence Criteria * Refined Threshold Determination *Recursive Best-First Search Summary Exercises Bibliographic Notes 223 CHAPTER 6 Memory-Restricted Search Linear Variants Using Additional Memory Transposition Tables Fringe Search 231

5 viii Contents iterative Threshold Search MA*, SMA, and SMAG Nonadmissible Search Enforced Hill-Climbing Weighted A* Overconsistent A* Anytime Repahing A* Jt-Best-First Search Beam Search Partial A* and Partial IDA* Reduction of the Closed List Dynamic Programming in Implicit Graphs Divide-and-Conquer Solution Reconstruction Frontier Search *Sparse Memory Graph Search Breadth-First Heuristic Search Locality Reduction of the Open List Beam-Stack Search Partial Expansion A* Two-Bit Breadth-First Search Summary Exercises Bibliographic Notes 279 CHAPTER 7 Symbolic Search Boolean Encodings for Set of States Binary Decision Diagrams Computing the Image for a State Set Symbolic Blind Search Symbolic Breadth-First Tree Search Symbolic Breadth-First Search Symbolic Pattern Databases Cost-Optimal Symbolic Breadth-First Search Symbolic Shortest Path Search Limits and Possibilities of BDDs Exponential Lower Bound Polynomial Upper Bound Symbolic Heuristic Search Symbolic A* Bucket Implementation 305

6 Contents ix Symbolic Best-First Search Symbolic Breadth-First Branch-and-Bound *Refinements Improving the BDD Size Partitioning Symbolic Algorithms for Explicit Graphs Summary Exercises Bibliographic Notes 317 CHAPTER 8 External Search Virtual Memory Management Fault Tolerance Model of Computation Basic Primitives External Explicit Graph Search * External Priority Queues External Explicit Graph Depth-First Search External Explicit Graph Breadth-First Search External Implicit Graph Search Delayed Duplicate Detection for BFS *External Breadth-First Branch-and-Bound *External Enforced Hill-Climbing External A* *Lower Bound for Delayed Duplicate Detection *Refinements Hash-Based Duplicate Detection Structured Duplicate Detection Pipelining External Iterative-Deepening A* Search External Explicit-State Pattern Databases External Symbolic Pattern Databases External Relay Search *External Value Iteration Forward Phase: State Space Generation Backward Phase: Update of Values *Flash Memory Hashing Mapping Compressing Flushing 358

7 x Contents 8.10 Summary Exercises Bibliographic Notes 364 PART III HEURISTIC SEARCH UNDER TIME CONSTRAINTS CHAPTER 9 Distributed Search Parallel Processing Motivation for Practical Parallel Search Space Partitioning Depth Slicing Lock-Free Hashing Parallel Depth-First Search *Parallel Branch-and-Bound Stack Splitting Parallel IDA* Asynchronous IDA* Parallel Best-First Search Algorithms Parallel Global A* Parallel Local A* Parallel External Search Parallel External Breadth-First Search Parallel Structured Duplicate Detection Parallel External A* Parallel Pattern Database Search Parallel Search on the GPU GPU Basics GPU-Based Breadth-First Search Bitvector GPU Search Bidirectional Search Bidirectional Front-to-End Search *Biclirectional Front-to-Front Search Perimeter Search Bidirectional Symbolic Breadth-First Search *Island Search *Multiple-Goal Heuristic Search Summary Exercises Bibliographic Notes 425

8 Contents xi CHAPTER 10 State Space Pruning Admissible State Space Pruning Substring Pruning Pruning Dead-Ends Penalty Tables Symmetry Reduction Nonadmissible State Space Pruning Macro Problem Solving Relevance Cuts Partial Order Reduction Summary Exercises Bibliographic Notes 463 CHAPTER 11 Real-Time Search LRTA* LRTA* with Lookahead One Analysis of the Execution Cost of LRTA* Upper Bound on the Execution Cost of LRTA* Lower Bound on the Execution Cost of LRTA* Features of LRTA* Heuristic Knowledge Fine-Grained Control Improvement of Execution Cost Variants of LRTA* Variants with Local Search Spaces of Varying Sizes Variants with Minimal Lookahead Variants with Faster Value Updates Variants That Detect Convergence Variants That Speed Up Convergence Nonconverging Variants Variants for Nondeterministic and Probabilistic State Spaces How to Use Real-Time Search Case Study. Off line Search Case Study: Goal-Directed Navigation in Unknown Terrain Case Study: Coverage Case Study: Localization Summary Exercises Bibliographic Notes 514

9 xii Contents PART IV HEURISTIC SEARCH VARIANTS CHAPTER 12 Adversary Search Two-Player Games Game Tree Search aj3-pruning Transposition Tables *Searching with Restricted Windows Accumulated Evaluations *Partition Search *Other Improvement Techniques Learning Evaluation Functions Retrograde Analysis *Symbolic Retrograde Analysis *Multiplayer Games General Game Playing AND/OR Graph Search AO* *IDAO* *LAO* Summary Exercises Bibliographic Notes 567 CHAPTER 13 Constraint Search Constraint Satisfaction Consistency Arc Consistency Bounds Consistency *Path Consistency Specialized Consistency Search Strategies Backtracking Backjumping Dynamic Backtracking Backmarking Search Strategies NP-Hard Problem Solving Boolean Satisfiability Number Partition 596

10 Contents xiii *Bin Packing * Rectangle Packing * Vertex Cover, Independent Set, Clique *Graph Partition Temporal Constraint Networks Simple Temporal Network *PERT Scheduling * Path Constraints Formula Progression Automata Translation * Soft and Preference Constraints Constraint Optimization Summary Exercises Bibliographic Notes 629 CHAPTER 14 Selective Search From State Space Search to Minimization Hill-Climbing Search Simulated Annealing Tabu Search Evolutionary Algorithms Randomized Local Search and (1 + 1) EA Simple GA Insights to Genetic Algorithm Search Approximate Search Approximating TSP Approximating MAX-fc-SAT Randomized Search Ant Algorithms Simple Ant System Algorithm Flood Vertex Ant Walk * Lagrange Multipliers Saddle-Point Conditions Partitioned Problems *No-Free-Lunch Summary Exercises Bibliographic Notes 668

11 xiv Contents PART V HEURISTIC SEARCH APPLICATIONS CHAPTER 15 Action Planning Optimal Planning Graphplcm 675 \5A.2 Satplan Dynamic Programming Planning Pattern Databases Suboptimal Planning Causal Graphs Metric Planning Temporal Planning Derived Predicates Timed Initial Literals State Trajectory Constraints Preference Constraints Bibliographic Notes 697 CHAPTER 16 Automated System Verification Model Checking Temporal Logics The Role of Heuristics Communication Protocols Formula-Based Heuristic Activeness Heuristic Trail-Directed Heuristics Liveness Model Checking Planning Heuristics Program Model Checking Analyzing Petri Nets Exploring Real-Time Systems Timed Automata Linearly Priced Timed Automata Traversal Politics Analyzing Graph Transition Systems Anomalies in Knowledge Bases Diagnosis General Diagnostic Engine Symbolic Propagation 729

12 Contents xv 16.9 Automated Theorem Proving Heuristics Functional A* Search Bibliographic Notes 734 CHAPTER 17 Vehicle Navigation Components of Route Guidance Systems Generation and Preprocessing of Digital Maps Positioning Systems Map Matching Geocoding and Reverse Geocoding User Interface Routing Algorithms Heuristics for Route Planning Time-Dependent Routing Stochastic Time-Dependent Routing Cutting Corners Geometric Container Pruning Localizing A* Bibliographic Notes 756 CHAPTER 18 Computational Biology Biological Pathway Multiple Sequence Alignment Bounds Iterative-Deepening Dynamic Programming Main Loop Sparse Representation of Solution Paths Use of Improved Heuristics Bibliographic Notes 771 CHAPTER 19 Robotics Search Spaces Search under Incomplete Knowledge Fundamental Robot-Navigation Problems Search Objective Search Approaches Optimal Offline Search Greedy On line Search 784

13 xvi Contents 19.6 Greedy Localization Greedy Mapping Search with the Freespace Assumption Bibliographic Notes 791 Bibliography 793 Index 825