Heuristic search : theory and applications · Heuristic Search Theoryand Applications Stefan...
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Heuristic Search Theory and Applications Stefan Edelkamp Stefan Schrodl AMSTERDAM • BOSTON • HEIDELBERG • LONDON NEW YORK • OXFORD • PARIS • SAN DIEGO SAN FRANCISCO • SINGAPORE • SYDNEY » TOKYO ELSEVIER Morgan Kaufmann is an imprint of Elsevier
Transcript of Heuristic search : theory and applications · Heuristic Search Theoryand Applications Stefan...
Heuristic Search
Theory and Applications
Stefan Edelkamp
Stefan Schrodl
AMSTERDAM • BOSTON • HEIDELBERG • LONDON
NEW YORK • OXFORD • PARIS • SAN DIEGO
SAN FRANCISCO • SINGAPORE • SYDNEY » TOKYO
ELSEVIER Morgan Kaufmann is an imprint of Elsevier
Contents
List of AlgorithmsPreface xxul
PART I HEURISTIC SEARCH PRIMER
CHAPTER 1 Introduction 3
1.1 Notational and Mathematical Background 3
1.1.1 Pseudocode 3
1.1.2 Computability Theory 4
1.1.3 Complexity Theory 5
1.1.4 Asymptotic Resource Consumption 7
1.1.5 Symbolic Logic 8
1.2 Search 9
1.3 Success Stories 9
1.4 State Space Problems 12
1.5 Problem Graph Representations 14
1.6 Heuristics 15
1.7 Examples of Search Problems 19
1.7.1 Sliding-Tile Puzzles 19
1.7.2 Rubik's Cube 22
1.7.3 Sokoban 22
1.7.4 Route Planning 24
1.7.5 TSP 25
1.7.6 Multiple Sequence Alignment 26
1.8 General State Space Descriptions 29
1.8.1 Action Planning 29
1.8.2 *Production Systems 32
1.8.3 Markov Decision Processes 35
1.8.4 Generic Search Model 36
1.9 Summary 37
1.10 Exercises 39
1.11 Bibliographic Notes 45
CHAPTER 2 Basic Search Algorithms 47
2.1 Uninformed Graph Search Algorithms 48
2.1.1 Depth-First Search 50
2.1.2 Breadth-First Search 51
2.1.3 Dijkstra's Algorithm 53
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vi Contents
2.1.4 Negatively Weighted Graphs 57
2.1.5 Relaxed Node Selection 58
2.1.6 *Algorithm of Bellman-Ford 60
2.1.7 Dynamic Programming 62
2.2 Informed Optimal Search 68
2.2.1 A* 69
2.2.2 On the Optimal Efficiency of A* 74
2.3 *General Weights 75
2.3.1 Cost Algebras 76
2.3.2 Multiobjective Search 79
2.4 Summary 80
2.5 Exercises 82
2.6 Bibliographic Notes 86
CHAPTER 3 *Dictionary Data Structures 89
3.1 Priority Queues 89
3.1.1 Bucket Data Structures 90
3.1.2 Heap Data Structures 97
3.2 Hash Tables 110
3.2.1 Hash Dictionaries Ill
3.2.2 Hash Functions 112
3.2.3 Hashing Algorithms 121
3.2.4 Memory-Saving Dictionaries 130
3.2.5 Approximate Dictionaries 134
3.3 Subset Dictionaries 138
3.3.1 Arrays and Lists 139
3.3.2 Tries 139
3.3.3 Hashing 139
3.3.4 Unlimited Branching Trees 141
3.4 String Dictionaries 142
3.4.1 Suffix Trees 143
3.4.2 Generalized Suffix Trees 146
3.5 Summary 151
3.6 Exercises 154
3.7 Bibliographic Notes 157
CHAPTER 4 Automatically Created Heuristics 161
4.1 Abstraction Transformations 162
4.2 Valtorta's Theorem 164
4.3 hierarchical A* 165
4.4 Pattern Databases 167
4.4.1 Fifteen-Puzzle 168
4.4.2 Rubik's Cube 169
4.4.3 Directed Search Graphs 170
4.4.4 Korf's Conjecture 170
4.4.5 Multiple Pattern Databases 172
4.4.6 Disjoint Pattern Databases 173
4.5 *Customized Pattern Databases 177
4.5.1 Pattern Selection 178
4.5.2 Symmetry and Dual Pattern Databases 179
4.5.3 Bounded Pattern Databases 180
4.5.4 On-Demand Pattern Databases 183
4.5.5 Compressed Pattern Databases 183
4.5.6 Compact Pattern Databases 185
4.6 Summary 185
4.7 Exercises 187
4.8 Bibliographic Notes 190
PART II HEURISTIC SEARCH UNDER MEMORY CONSTRAINTS
CHAPTER 5 Linear-Space Search 195
5.1 ^Logarithmic Space Algorithms 195
5.1.1 Divide-and-Conquer BFS 196
5.1.2 Divide-and-Conquer Shortest Paths Search 196
5.2 Exploring the Search Tree 197
5.3 Branch-and-Bound 198
5.4 Iterative-Deepening Search 201
5.5 Iterative-Deepening A* 204
5.6 Prediction of IDA* Search 206
5.6.1 Asymptotic Branching Factors 206
5.6.2 IDA* Search Tree Prediction 212
5.6.3 *Convergence Criteria 217
5.7 * Refined Threshold Determination 218
5.8 *Recursive Best-First Search 219
5.9 Summary 220
5.10 Exercises 222
5.11 Bibliographic Notes 223
CHAPTER 6 Memory-Restricted Search 227
6.1 Linear Variants Using Additional Memory 228
6.1.1 Transposition Tables 228
6.1.2 Fringe Search 231
viii Contents
6.1.3 iterative Threshold Search 233
6.1.4 MA*, SMA, and SMAG 235
6.2 Nonadmissible Search 240
6.2.1 Enforced Hill-Climbing 240
6.2.2 Weighted A* 243
6.2.3 Overconsistent A* 244
6.2.4 Anytime Repahing A* 246
6.2.5 Jt-Best-First Search 250
6.2.6 Beam Search 251
6.2.7 Partial A* and Partial IDA* 251
6.3 Reduction of the Closed List 254
6.3.1 Dynamic Programming in Implicit Graphs 255
6.3.2 Divide-and-Conquer Solution Reconstruction 255
6.3.3 Frontier Search 257
6.3.4 *Sparse Memory Graph Search 259
6.3.5 Breadth-First Heuristic Search 261
6.3.6 Locality 264
6.4 Reduction of the Open List 266
6.4.1 Beam-Stack Search 266
6.4.2 Partial Expansion A* 270
6.4.3 Two-Bit Breadth-First Search 271
6.5 Summary 273
6.6 Exercises 275
6.7 Bibliographic Notes 279
CHAPTER 7 Symbolic Search 283
7.1 Boolean Encodings for Set of States 284
7.2 Binary Decision Diagrams 286
7.3 Computing the Image for a State Set 290
7.4 Symbolic Blind Search 291
7.4.1 Symbolic Breadth-First Tree Search 291
7.4.2 Symbolic Breadth-First Search 293
7.4.3 Symbolic Pattern Databases 294
7.4.4 Cost-Optimal Symbolic Breadth-First Search 296
7.4.5 Symbolic Shortest Path Search 298
7.5 Limits and Possibilities of BDDs 299
7.5.1 Exponential Lower Bound 299
7.5.2 Polynomial Upper Bound 300
7.6 Symbolic Heuristic Search 302
7.6.1 Symbolic A* 302
7.6.2 Bucket Implementation 305
Contents ix
7.6.3 Symbolic Best-First Search 307
7.6.4 Symbolic Breadth-First Branch-and-Bound 308
7.7 *Refinements 309
7.7.1 Improving the BDD Size 309
7.7.2 Partitioning 310
7.8 Symbolic Algorithms for Explicit Graphs 311
7.9 Summary 311
7.10 Exercises 313
7.11 Bibliographic Notes 317
CHAPTER 8 External Search 319
8.1 Virtual Memory Management 320
8.2 Fault Tolerance 321
8.3 Model of Computation 321
8.4 Basic Primitives 323
8.5 External Explicit Graph Search 324
8.5.1 *External Priority Queues 324
8.5.2 External Explicit Graph Depth-First Search 325
8.5.3 External Explicit Graph Breadth-First Search 326
8.6 External Implicit Graph Search 328
8.6.1 Delayed Duplicate Detection for BFS 328
8.6.2 *External Breadth-First Branch-and-Bound 330
8.6.3 *External Enforced Hill-Climbing 332
8.6.4 External A* 334
8.6.5 *Lower Bound for Delayed Duplicate Detection 340
8.7 *Refinements 342
8.7.1 Hash-Based Duplicate Detection 342
8.7.2 Structured Duplicate Detection 343
8.7.3 Pipelining 344
8.7.4 External Iterative-Deepening A* Search 345
8.7.5 External Explicit-State Pattern Databases 346
8.7.6 External Symbolic Pattern Databases 348
8.7.7 External Relay Search 348
8.8 *External Value Iteration 349
8.8.1 Forward Phase: State Space Generation 349
8.8.2 Backward Phase: Update of Values 349
8.9 *Flash Memory 353
8.9.1 Hashing 354
8.9.2 Mapping 354
8.9.3 Compressing 356
8.9.4 Flushing 358
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8.10 Summary 358
8.11 Exercises 361
8.12 Bibliographic Notes 364
PART III HEURISTIC SEARCH UNDER TIME CONSTRAINTS
CHAPTER 9 Distributed Search 369
9.1 Parallel Processing 370
9.1.1 Motivation for Practical Parallel Search 374
9.1.2 Space Partitioning 374
9.1.3 Depth Slicing 375
9.1.4 Lock-Free Hashing 378
9.2 Parallel Depth-First Search 379
9.2.1 *Parallel Branch-and-Bound 379
9.2.2 Stack Splitting 380
9.2.3 Parallel IDA* 382
9.2.4 Asynchronous IDA* 382
9.3 Parallel Best-First Search Algorithms 385
9.3.1 Parallel Global A* 385
9.3.2 Parallel Local A* 387
9.4 Parallel External Search 388
9.4.1 Parallel External Breadth-First Search 388
9.4.2 Parallel Structured Duplicate Detection 391
9.4.3 Parallel External A* 392
9.4.4 Parallel Pattern Database Search 398
9.5 Parallel Search on the GPU 400
9.5.1 GPU Basics 401
9.5.2 GPU-Based Breadth-First Search 401
9.5.3 Bitvector GPU Search 407
9.6 Bidirectional Search 408
9.6.1 Bidirectional Front-to-End Search 409
9.6.2 *Biclirectional Front-to-Front Search 410
9.6.3 Perimeter Search 412
9.6.4 Bidirectional Symbolic Breadth-First Search 416
9.6.5 *Island Search 416
9.6.6 *Multiple-Goal Heuristic Search 418
9.7 Summary 419
9.8 Exercises 422
9.9 Bibliographic Notes 425
Contents xi
CHAPTER 10 State Space Pruning 429
10.1 Admissible State Space Pruning 430
10.1.1 Substring Pruning 430
10.1.2 Pruning Dead-Ends 440
10.1.3 Penalty Tables 445
10.1.4 Symmetry Reduction 447
10.2 Nonadmissible State Space Pruning 449
10.2.1 Macro Problem Solving 449
10.2.2 Relevance Cuts 452
10.2.3 Partial Order Reduction 453
10.3 Summary 458
10.4 Exercises 460
10.5 Bibliographic Notes 463
CHAPTER 11 Real-Time Search 465
11.1 LRTA* 466
11.2 LRTA* with Lookahead One 473
11.3 Analysis of the Execution Cost of LRTA* 474
11.3.1 Upper Bound on the Execution Cost of LRTA* 476
11.3.2 Lower Bound on the Execution Cost of LRTA* 477
11.4 Features of LRTA* 479
11.4.1 Heuristic Knowledge 479
11.4.2 Fine-Grained Control 479
11.4.3 Improvement of Execution Cost 480
11.5 Variants of LRTA* 482
11.5.1 Variants with Local Search Spaces of Varying Sizes 482
11.5.2 Variants with Minimal Lookahead 482
11.5.3 Variants with Faster Value Updates 484
11.5.4 Variants That Detect Convergence 488
11.5.5 Variants That Speed Up Convergence 488
11.5.6 Nonconverging Variants 491
11.5.7 Variants for Nondeterministic and Probabilistic State Spaces 494
11.6 How to Use Real-Time Search 496
11.6.1 Case Study. Off line Search 496
11.6.2 Case Study: Goal-Directed Navigation in Unknown Terrain 497
11.6.3 Case Study: Coverage 500
11.6.4 Case Study: Localization 501
11.7 Summary 507
11.8 Exercises 509
11.9 Bibliographic Notes 514
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PART IV HEURISTIC SEARCH VARIANTS
CHAPTER 12 Adversary Search 519
12.1 Two-Player Games 520
12.1.1 Game Tree Search 524
12.1.2 aj3-Pruning 525
12.1.3 Transposition Tables 530
12.1.4 *Searching with Restricted Windows 530
12.1.5 Accumulated Evaluations 534
12.1.6 *Partition Search 535
12.1.7 *Other Improvement Techniques 537
12.1.8 Learning Evaluation Functions 538
12.1.9 Retrograde Analysis 543
12.1.10 *Symbolic Retrograde Analysis 544
12.2 *Multiplayer Games 547
12.3 General Game Playing 550
12.4 AND/OR Graph Search 552
12.4.1 AO* 554
12.4.2 *IDAO* 554
12.4.3 *LAO* 557
12.5 Summary 559
12.6 Exercises 563
12.7 Bibliographic Notes 567
CHAPTER 13 Constraint Search 571
13.1 Constraint Satisfaction 572
13.2 Consistency 575
13.2.1 Arc Consistency 575
13.2.2 Bounds Consistency 577
13.2.3 *Path Consistency 578
13.2.4 Specialized Consistency 579
13.3 Search Strategies 580
13.3.1 Backtracking 581
13.3.2 Backjumping 583
13.3.3 Dynamic Backtracking 584
13.3.4 Backmarking 585
13.3.5 Search Strategies 587
13.4 NP-Hard Problem Solving 591
13.4.1 Boolean Satisfiability 592
13.4.2 Number Partition 596
Contents xiii
13.4.3 *Bin Packing 598
13.4.4 *Rectangle Packing 601
13.4.5 *Vertex Cover, Independent Set, Clique 604
13.4.6 *Graph Partition 606
13.5 Temporal Constraint Networks 609
13.5.1 Simple Temporal Network 609
13.5.2 *PERT Scheduling 611
13.6 *Path Constraints 612
13.6.1 Formula Progression 614
13.6.2 Automata Translation 615
13.7 *Soft and Preference Constraints 617
13.8 Constraint Optimization 618
13.9 Summary 619
13.10 Exercises 623
13.11 Bibliographic Notes 629
CHAPTER 14 Selective Search 633
14.1 From State Space Search to Minimization 634
14.2 Hill-Climbing Search 635
14.3 Simulated Annealing 637
14.4 Tabu Search 638
14.5 Evolutionary Algorithms 639
14.5.1 Randomized Local Search and (1 + 1) EA 639
14.5.2 Simple GA 641
14.5.3 Insights to Genetic Algorithm Search 643
14.6 Approximate Search 645
14.6.1 Approximating TSP 646
14.6.2 Approximating MAX-fc-SAT 646
14.7 Randomized Search 647
14.8 Ant Algorithms 652
14.8.1 Simple Ant System 652
14.8.2 Algorithm Flood 654
14.8.3 Vertex Ant Walk 654
14.9 *Lagrange Multipliers 657
14.9.1 Saddle-Point Conditions 658
14.9.2 Partitioned Problems 661
14.10 *No-Free-Lunch 662
14.11 Summary 662
14.12 Exercises 664
14.13 Bibliographic Notes 668
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PART V HEURISTIC SEARCH APPLICATIONS
CHAPTER 15 Action Planning 673
15.1 Optimal Planning 675
15.1.1 Graphplcm 675
\5A.2 Satplan 677
15.1.3 Dynamic Programming 678
15.1.4 Planning Pattern Databases 680
15.2 Suboptimal Planning 685
15.2.1 Causal Graphs 685
15.2.2 Metric Planning 687
15.2.3 Temporal Planning 691
15.2.4 Derived Predicates 695
15.2.5 Timed Initial Literals 696
15.2.6 State Trajectory Constraints 696
15.2.7 Preference Constraints 697
15.3 Bibliographic Notes 697
CHAPTER 16 Automated System Verification 701
16.1 Model Checking 702
16.1.1 Temporal Logics 702
16.1.2 The Role of Heuristics 703
16.2 Communication Protocols 705
16.2.1 Formula-Based Heuristic 705
16.2.2 Activeness Heuristic 707
16.2.3 Trail-Directed Heuristics 709
16.2.4 Liveness Model Checking 710
16.2.5 Planning Heuristics 710
16.3 Program Model Checking 713
16.4 Analyzing Petri Nets 717
16.5 Exploring Real-Time Systems 721
16.5.1 Timed Automata 721
16.5.2 Linearly Priced Timed Automata 722
16.5.3 Traversal Politics 723
16.6 Analyzing Graph Transition Systems 723
16.7 Anomalies in Knowledge Bases 726
16.8 Diagnosis 727
16.8.1 General Diagnostic Engine 728
16.8.2 Symbolic Propagation 729
Contents xv
16.9 Automated Theorem Proving 730
16.9.1 Heuristics 732
16.9.2 Functional A* Search 733
16.10 Bibliographic Notes 734
CHAPTER 17 Vehicle Navigation 737
17.1 Components of Route Guidance Systems 737
17.1.1 Generation and Preprocessing of Digital Maps 737
17.1.2 Positioning Systems 739
17.1.3 Map Matching 741
17.1.4 Geocoding and Reverse Geocoding 744
17.1.5 User Interface 744
17.2 Routing Algorithms 744
17.2.1 Heuristics for Route Planning 745
17.2.2 Time-Dependent Routing 746
17.2.3 Stochastic Time-Dependent Routing 747
17.3 Cutting Corners 749
17.3.1 Geometric Container Pruning 749
17.3.2 Localizing A* 752
17.4 Bibliographic Notes 756
CHAPTER 18 Computational Biology 759
18.1 Biological Pathway 759
18.2 Multiple Sequence Alignment 760
18.2.1 Bounds 763
18.2.2 Iterative-Deepening Dynamic Programming 763
18.2.3 Main Loop 764
18.2.4 Sparse Representation of Solution Paths 767
18.2.5 Use of Improved Heuristics 769
18.3 Bibliographic Notes 771
CHAPTER 19 Robotics 773
19.1 Search Spaces 773
19.2 Search under Incomplete Knowledge 777
19.3 Fundamental Robot-Navigation Problems 778
19.4 Search Objective 780
19.5 Search Approaches 781
19.5.1 Optimal Offline Search 782
19.5.2 Greedy On line Search 784
xvi Contents
19.6 Greedy Localization 786
19.7 Greedy Mapping 787
19.8 Search with the Freespace Assumption 789
19.9 Bibliographic Notes 791
Bibliography 793
Index 825
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