Notes

Outline

CS 371: Introduction to Artificial Intelligence Informed Search

Outline Q/A Time Overview of My Code, Java Concepts Informed Search Methods Memory Bounded Search Iterative Improvement Search Heuristic Functions Game-Playing Worked Examples

Overview of Code Abstract classes form “templates” helpful for: Generalizing problem solving methods (factoring out common code, enabling reuse) Making the problem formalization clear Providing a language construct to guide fill-in-the-blank implementation

Abstract Classes for Search Operator – operator encodings may take on many different forms State – “search state” or node really.  The encoding of the “state” of the agent is internal and unspecified Searcher – could have added on thread support for anytime algorithm, but kept it simple for now

Informed Search Methods Best-First Search Greedy Search A* Worked examples Admissibility, monotonicity, pathmax, optimality, completeness, complexity

Best-First Search Describe General Search Evaluation Function f(n) - desirability of node n for expansion Best-First Search: General Search with queueing ordered by f  (A heap rather than a queue, really.)

Best-First Search (cont.) Let g(n) = pathCost(n).  What search do you have if f(n) = g(n)?

Greedy Search Heuristic Function h(n) - estimated cost of the cheapest path from n to a goal node Greedy Search: Best-First Search with f(n) = h(n) “Always choose the node that looks closest to the goal next.” Can think of h as the height of a “search terrain”.  In greedy search, you would look for the next biggest step down from where you’ve been.

Example: Route Finding

Example: Route Finding (cont.) h(n) = straight-line distance to goal city

A* Search Path Cost g(n) - cost from initial state to n Uniform Cost Search expands minimum g(n) Greedy Search expands minimum h(n) Search algorithm “A” expands minimum estimated total cost f(n)=g(n)+h(n) Worked example

Behavior of A* Admissible h never overestimates the cost to reach the goal (e.g. route finding, sliding tile puzzle) h admissible Þ A is called A* Monotonicity of f – f doesn’t decrease along a path h admissible Þ f monotonic? h admissible Þ pathmax equation forces monotonicity: f(n’) = max(f(n), g(n’)+h(n’)) Monotonicity à search contours

Search Contours

Properties of A* A* is optimal – finds optimal path to goal A* is optimally efficient - no other algorithm is guaranteed to expand fewer nodes A* is complete on locally finite graphs (finite branching factor, minimum cost constant) Complexity exponential unless h is very accurate (error grows no faster than log of actual path cost)

Iterative Deepening A* Basic intuition: iterative deepening DFS with increasing f-limit rather than increasing depth-limit.

Heuristic Functions Fundamental tradeoff Inventing heuristics: 8-puzzle example Relaxed problem – problem with constraints removed Relax: A tile can move from A to B if A adjacent to B and B is empty. A tile can move from A to B if A adjacent to B. A tile can move from A to B if A is empty. A tile can move from A to B. The cost of an exact solution to a relaxed problem can provide a good heuristic h.

Developing a Heuristic for TripleCross Pretend tiles can be shifted independently with 4 operators. Pretend subgoals (solve circle, line of dots, “Binary Arts”) can be solved independently with parallel operations. Other ideas?

Developing a Heuristic Tradeoff between quality of h and efficiency of search. Extreme cases: h(n) = 0  (admissible, but equivalent to uniform cost search) h(n) = exact optimal cost remaining (search goes directly to goal, but full problem solved for each step!)

Memory-Bounded Search Space-complexity the main drawback with A* IDA* - Iterative deepening search along f contours Good for simple problems with few contours.  What to do if there are many unique path-cost values?

SMA* Argument: IDA* uses too little memory SMA* - Simplified Memory-bounded A* Korf: SMA* 20x slower on 15 tile puzzle Tradeoff: wasted work searching vs. wasted work checking repeated states. Can there be a good balance?

Iterative Improvement Search Hill-Climbing – greedy wandering, no queue, no backtracking Should be called “hill-descending” or “local optimization” Gets caught in local minima Local optimization with random restarts Local optimization with % random steps

Simulated Annealing Simulated Annealing – local optimization with % random steps, with % decreasing slowly over time Analogy to statistical mechanics, process of annealing metals, forming crystalline structures. Applet demo by Dudu Noy http://www.math.tau.ac.il/~dudunoy/ex2/tsp.html Another applet demo by Wesley Perkins: http://www.starbath.com/Optimization/Gacut.htm

Genetic Algorithms Analogy to genetic evolution: Encoding (of characteristics, behaviors) Population Fitness (evaluation function, survival of fittest) Crossover, mutation from one generation to the next Koza video Biomorph demo by Jean-Philippe Rennard http://www.rennard.org/alife/english/jpmain.html?border.html&entete.html&gavgb.html