State-Space Search: Algorithms, Complexity, Extensions, and Applications

ISBN-13: 9780387988320 / Angielski / Twarda / 1999 / 201 str.

Weixiong Zhang

Opis

This book is about problem solving. Specifically, it is about heuristic state-space search under branch-and-bound framework for solving com binatorial optimization problems. The two central themes of this book are the average-case complexity of heuristic state-space search algorithms based on branch-and-bound, and their applications to developing new problem-solving methods and algorithms. Heuristic state-space search is one of the fundamental problem-solving techniques in Computer Science and Operations Research, and usually constitutes an important component of most intelligent problem-solving systems. The search algorithms considered in this book can be classified into the category of branch-and-bound. Branch-and-bound is a general problem-solving paradigm, and is one of the best techniques for optimally solving computation-intensive problems, such as scheduling and planning. The main search algorithms considered include best-first search, depth first branch-and-bound, iterative deepening, recursive best-first search, and space-bounded best-first search. Best-first search and depth-first branch-and-bound are very well known and have been used extensively in Computer Science and Operations Research. One important feature of depth-first branch-and-bound is that it only requires space this is linear in the maximal search depth, making it very often a favorable search algo rithm over best-first search in practice. Iterative deepening and recursive best-first search are the other two linear-space search algorithms. Iterative deepening is an important algorithm in Artificial Intelligence, and plays an irreplaceable role in building a real-time game-playing program."

Spis treści

1 State-Space Search for Problem Solving.- 1.1 Combinatorial Search Problems.- 1.1.1 Sliding-tile puzzles.- 1.1.2 The symmetric Traveling Salesman Problem.- 1.1.3 The asymmetric Traveling Salesman Problem.- 1.1.4 Maximum boolean satisfiability.- 1.2 Branch-and-Bound Methods.- 1.3 Bibliographical and Historical Remarks.- 2 Algorithms for Combinatorial Optimization.- 2.1 Algorithms for Optimal Solutions.- 2.1.1 State space.- 2.1.2 Cost function and heuristic evaluation.- 2.1.3 Best-first search.- 2.1.4 Depth-first branch-and-bound.- 2.1.5 Iterative deepening.- 2.1.6 Recursive best-first search.- 2.1.7 Space-bounded best-first search.- 2.2 Algorithms for Approximate Solutions.- 2.2.1 Approximation based on branch-and-bound.- 2.2.2 Local search.- 2.3 Bibliographical and Historical Remarks.- 3 Complexity of State-Space Search for Optimal Solutions.- 3.1 Incremental Random Trees.- 3.2 Problem Complexity and Cost of Optimal Goal.- 3.3 Best-First Search.- 3.4 Depth-First Branch-and-Bound.- 3.5 Iterative Deepening.- 3.6 Recursive and Space-Bounded Best-First Searches.- 3.7 Branching Factors.- 3.8 Summary of Search Complexity.- 3.9 Graphs Versus Trees.- 3.10 Bibliographical and Historical Remarks.- 4 Computational Complexity Transitions.- 4.1 Complexity Transition.- 4.1.1 Average-case complexity transition.- 4.1.2 Finding all optimal goals.- 4.1.3 Meaning of zero edge cost.- 4.2 Anomaly in Sliding-Tile Puzzles.- 4.3 Complexity Transition on the Asymmetric Traveling Salesman Problem.- 4.3.1 Complexity transitions on the asymmetric Traveling Salesman Problem.- 4.3.2 Identifying the order parameter.- 4.3.3 Summary.- 4.4 Bibliographical and Historical Remarks.- 5 Algorithm Selection.- 5.1 Comparison on Analytic Model.- 5.1.1 Node expansions.- 5.1.2 Running times.- 5.2 Comparison on Practical Problems.- 5.2.1 Lookahead search on sliding-tile puzzles.- 5.2.2 The asymmetric Traveling Salesman Problem.- 5.3 Summary.- 6 A Study of Branch-and-Bound on the Asymmetric Traveling Salesman Problem.- 6.1 Complexity of Branch-and-Bound Subtour Elimination.- 6.1.1 A debate over polynomial versus exponential complexity.- 6.1.2 Preliminaries.- 6.1.3 A study of the polynomial argument.- 6.1.4 Summary.- 6.2 Local Search for the Asymmetric Traveling Salesman Problem.- 6.3 Finding Initial Tours.- 6.3.1 Initial tour construction heuristics.- 6.3.2 Problem structures.- 6.3.3 Experimental comparison.- 6.4 Depth-First Branch-and-Bound Versus Local Search.- 6.4.1 Truncated depth-first branch-and-bound versus local search.- 6.4.2 Anytime depth-first branch-and-bound versus local search.- 6.4.3 Discussion.- 6.4.4 Summary.- 6.5 Bibliographical and Historical Remarks.- 7 State-Space Transformation for Approximation and Flexible Computation.- 7.1 Anytime Approximation Computation.- 7.2 Flexible Computation.- 7.3 State-Space Transformation.- 7.4 Properties of State-Space Transformation.- 7.4.1 Effectiveness.- 7.4.2 Tradeoff between solution quality and computational complexity.- 7.5 Improvements and Extensions.- 7.5.1 Iterative ?-transformation.- 7.5.2 Actual-value pruning.- 7.6 Learning Edge-Cost Distribution and Branching Factor.- 7.7 Experimental Results.- 7.7.1 Random trees.- 7.7.2 The asymmetric Traveling Salesman Problem.- 7.7.3 Maximum boolean satisfiability.- 7.7.4 Summary.- 7.8 Bibliographical and Historical Remarks.- 8 Forward Pruning for Approximation and Flexible Computation, Part I: Single-Agent Combinatorial Optimization.- 8.1 Forward Pruning.- 8.1.1 Forward pruning.- 8.1.2 Complete forward pruning.- 8.1.3 Complete forward pruning for anytime search.- 8.2 Domain-Independent Pruning Heuristics.- 8.2.1 When to prune a node.- 8.2.2 When not to prune a node.- 8.3 Forward Pruning as State-Space Transformation.- 8.4 Analyses.- 8.4.1 An analytic model.- 8.4.2 Probability of finding a solution.- 8.4.3 Modified pruning rule.- 8.4.4 Tradeoff between complexity and solution quality.- 8.4.5 Anytime features.- 8.5 Learning Edge-Cost Distribution and Setting Parameters.- 8.6 Experimental Results.- 8.6.1 Maximum boolean satisfiability.- 8.6.2 The symmetric Traveling Salesman Problem.- 8.6.3 The asymmetric Traveling Salesman Problem.- 8.7 Summary and Discussion.- 8.8 Bibliographical and Historical Remarks.- 9 Forward Pruning for Approximation and Flexible Computation, Part II: Multiagent Game Playing.- 9.1 Minimax and Alpha-Beta Pruning.- 9.2 Forward Pruning.- 9.2.1 Bounds of minimax values.- 9.2.2 Domain-independent pruning heuristics.- 9.3 Playing Games.- 9.3.1 Random game trees.- 9.3.2 The game of Othello.- 9.4 Summary and Discussion.- 9.5 Bibliographical and Historical Remarks.- A Basic Concepts of Branching Processes.- B Mathematical Notation.- C List of Algorithms.- References.