1. Informed Search Methods Copyright, 1996 © Dale Carnegie & Associates, Inc. Chapter 4

2. CS 471/598 by H. Liu2 What we’ll learn zInformed search algorithms are more efficient in most cases zWhat are Informed search methods zHow to use problem-specific knowledge zHow to optimize a solution

3. CS 471/598 by H. Liu3 Best-First Search zEvaluation function ygives a measure which node to expand zMinimizing estimated cost to reach a goal zGreedy search at node n yheuristic function h(n) xan example is straight-line distance yThe simple Romania map (Fig 4.2) yFinding the route using greedy search - example

4. CS 471/598 by H. Liu4 Best-first search (2) zh(n) is independent of the path cost g(n) zMinimizing the total path cost yf(n) = g(n) + h(n) estimated cost of the cheapest solution thru n zAdmissible heuristic function h ynever overestimates the cost yoptimistic zExample continued (Fig 4.4)

5. CS 471/598 by H. Liu5 A* search zCharacteristics of A* yMonotonicity - nondescreasing yPathmax to ensure monotonicity yContours (Fig 4.5) - from circle to oval (ellipse) zProof of the optimality of A* zProof of the completeness of A* zComplexity of A* (time and space)

6. CS 471/598 by H. Liu6 Different Search zUniform cost search yminimize the path cost so far zGreedy search yminimize the estimated path cost zA* yminimize the total path cost

7. CS 471/598 by H. Liu7 Heuristic Functions zAn example (sliding puzzle) yHow simple is it? zWhat is a good heuristic? yEffective branching factor - close to 1 (Why?) yValue of h xnot too large - must be admissible (Why?) xnot too small - ineffective (oval to circle) (expanding all nodes with f (n) < f*) yGoodness measure - no. of nodes expanded (Fig 4.8)

8. CS 471/598 by H. Liu8 zDomination translates directly into efficiency yLarger h means smaller branching factor yIf h2 >= h1, is h2 is always better h1? yProof? zInventing heuristic functions yWorking on relaxed problems xremove some constraints xA tile can move from square A to square B if A ~B and B is blank

9. CS 471/598 by H. Liu9 zIf we have admissible h 1 … h m and none dominates, we can have for node n h = max(h 1, …, h m ) zFeature selection and combination yuse only relevant features zThe cost of heuristic function calculation y<= the cost of expanding a node yotherwise, we need to rethink.

10. CS 471/598 by H. Liu10 Iterative Improvement Algorithms zIterative improvement ywhen only the state description really matters (e.g., the path to the goal is irrelevant) ye.g., the 8-queens problem ystart with a complete configuration and iteratively modify it to reach the goal zEvaluation functions yMove around the landscape to find a better position to explore further (Fig 4.13)

11. CS 471/598 by H. Liu11 zHill-climbing (maximization) yWell know drawbacks xLocal maxima xPlateaus xRidges yRandom-restart yGradient descent (minimization) zSimulated annealing yEscaping the local minima

12. CS 471/598 by H. Liu12 Summary zHeuristics are the key to reducing research costs zf(n) = g(n)+h(n) zA* is complete, optimal, and optimally efficient among all optimal search algorithms, but... zIterative improvement algorithms are memory efficient, but...