Search Algorithms in Artificial Intelligence: State Space Search and Problem Solving, Lecture notes of Artificial Intelligence

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Artificial Intelligence

(part 4a)

Problem Solving Using Search:

Structures and Strategies for

State Space Search

Course Contents

Again..Selected topics for our course. Covering all of AI is impossible!

Key topics include: Introduction to Artificial Intelligence (AI) Knowledge Representation and Search Introduction to AI Programming Problem Solving Using Search: Structure & Strategy Exhaustive Search Algorithm Heuristic Search Techniques and Mechanisms of Search Algorithm Knowledge Representation Issues and Concepts Strong Method Problem Solving Reasoning in Uncertain Situations Soft Computing and Machine Learning

Search as Problem-Solving Strategy

• many problems can be viewed as reaching a goal

state from a given starting point

• often there is an underlying state space that defines the problem and its possible solutions in a more formal way
• the space can be traversed by applying a successor function (operators) to proceed from one state to the next
• if possible, information about the specific problem or the general domain is used to improve the search - experience from previous instances of the problem - strategies expressed as heuristics - simpler versions of the problem - constraints on certain aspects of the problem

Examples – Search as Problem Solving

• getting from home to FSKSM
  • start: home in Kolej Perdana
  • goal: UTM FSKSM.
  • operators: move three blocks, turn

● loading a moving truck -start: apartment full of boxes and furniture -goal: empty apartment, all boxes and furniture in the truck -operators: select item, carry item from apartment to truck, load item

● getting settled -start: items randomly distributed over the place -goal: satisfactory arrangement of items -operators: select item, move item

Objectives

• formulate appropriate problems as search tasks
  • states, initial state, goal state, successor functions (operators), cost
• know the fundamental search strategies and algorithms
  • uninformed search
    • breadth-first, depth-first, uniform-cost, iterative deepening, bi-directional
  • informed search
    • best-first (greedy, A*), heuristics, memory-bounded, iterative improvement
• evaluate the suitability of a search strategy for a problem
  • completeness, time & space complexity, optimality

Evaluation Criteria

• formulation of a problem as search task
• basic search strategies
• important properties of search strategies
• selection of search strategies for specific tasks
• development of task-specific variations of search

strategies

Graph theory

• tool for reasoning about the structure of objects and

relations

• Structure of the problem can be VISUALISED more

directly.

• Invented by Swiss Mathematician Leonhard to solve

“Bridges of Konigsberg Problem” (Newman 1965)

• Problem: IS THERE A WALK AROUND THE

CITY THAT CROSSES EACH BRIDGE EXACTLY

ONCE??

The city of Königsberg- 2 islands, 2 riverbanks and 7 bridges

Give a predicate to indicate the relation direction between nodes RB and I? connect(X,Y,Z)

GRAPH THEORY: STRUCTURE a) A labeled directed graph- arrow indicate directions

{a, b, c, d, e} Arcs? {(a,b),(a,d), (b,c),(c,b),(c,d),(d,a),(d,e),(e,c),(e,d)}

Nodes

b) A rooted tree, exemplifying family relationships(parents, child, sibling) -path from root to all nodes -directed graph with arcs having one direction ~no cycle -i.e. game players cannot UNDO moves

Ancestor_of g, h and i

GRAPH THEORY: STRUCTURE

Leaf or tip

Root

parent

child

1

2

3

4

5

Diagram: Models and the Real World

Real World

Model

Problem Solutions

Problem: What is the best transportation method to get from SLO to Fresno?

Experimental Approach: Try all the options out, and then decide.

Analytical Approach: Assemble essential information about the different methods, determine an evaluation method, evaluate them, and decide.

State Space Representation

of a Problem

• In a graph:
  • nodes- are problem solution states
  • Arcs- are steps in problem solving
• State Space Search
  • finding a solution path from start state to goal
  • Means to determine complexity of problem
  • Chess, tic-tac-toe have exponential complexity, impossible to search exhaustively
  • Strategies to search large space need heuristic to reduce complexity

State space of the 8-puzzle generated by “move blank” operations

State Space Representation

of a Problem..8 puzzle

State Space Representation of a Problem..TSP

An instance of the traveling salesperson problem. Complexity of exhaustive search is (N-1)! What is N??

In the graph above, what is the complexity of this problem?