573 Intelligent Systems

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1 Sri Lanka Institute of Information Technology 3ed July, 2005

2 Course Outline Course Information Course Outline Reading Material Course Setup Intelligent agents. Agent types, agent environments and characteristics. Problem solving through searching. Performance measures in problem solving, search techniques, heuristic search techniques. Knowledge representation and inference. Predicate logic, frames and semantic nets. Planning. Planners, search in planning. Learning algorithms. Concept learning, decision tree learning.

3 Text Book and Other Reading Course Outline Reading Material Course Setup Artificial Intelligence: A modern approach/2e, Stuart Russell and Peter Norvig Pearson Education, Inc ISBN Machine Learning, Tom M. Mitchell McGraw-Hill 1997 ISBN Essentials of Artificial Intelligence, Matt Ginsberg Morgan Kaufman Publishers, Inc ISBN

4 Course Expectations Course Information Course Outline Reading Material Course Setup Some amount of independent study. Occasional Class room discussion on certain topics. Continuous assessment in the form of following assignments Assignments (20%) Final examination (80%) Writing an approximately 10 page report on a selected topic in IS for extra credit. Some amount of home work to supplement the course material in the form of reading and tutorials.

5 Problem Solving and Search Search is a problem solving technique t attempts to find a solution by looking at possible actions and systematically exploring the space of problem states until a solution is found. The Promises: Many problems can be cast as search problems. Search potentially offers generality. Only need to know the rules of the game, not how to play well. The Problems: Search is a weak method (knowledge is poor) Combinatoric explosion (The chess game its ). The Solution: Use domain specific knowledge.

6 Problem Solving Agents A problem solving agent decides what to do by finding sequences of actions that lead to desirable states. The first step is goal formulation. A goal is a set of world states the states in which the goal is satisfied. Goals help organize behavior by limiting the objectives. Actions result in transitions between world states. Problem formulation is the process of deciding what actions and states to consider. This often involves abstracting the problem at the right level of granularity. A search algorithm takes a problem and returns a solution (an action sequence) When a solution is found, the actions recommended can be carried out, which is called the execution phase.

7 Defining the Problem 1. Often we are not given an algorithm to solve a problem, but only a specification of what is a solution we have to search for a solution. 2. Search is a way to implement don t know nondeterminism. 3. We need to know how to convert a semantic problem of finding logical consequence to a search problem of finding derivations.

8 Graph Searching Course Information 1. A graph consists of a set N of nodes and a set A of ordered pairs of nodes, called arcs. 2. Node n 2 is a neighbor of n 1 if there is an arc from n 1 to n 2. That is, if < n 1, n 2 > in A. 3. A path is a sequence of nodes < n 0, n 1,..., n k > such that < n i 1, n i > in A. 4. Given a set of start nodes and goal nodes, a solution is a path from a start node to a goal node.

9 Graph Searching Cont... Generic search algorithm: given a graph, start nodes, and goal nodes, incrementally explore paths from the start nodes. Maintain a frontier of paths from the start node that have been explored. As search proceeds, the frontier expands into the unexplored nodes until a goal node is encountered. The way in which the frontier is expanded defines the search strategy.

10 Graph Searching Example

11 Problem Spaces Course Information Another method of looking at the search problem involves the setting up a problem space as follows. 1. the states of the world that form the search space 2. the operators that can transform one state of the world into another 3. the initial state (Root of the tree), and 4. the goal state (Leaf of the tree).

12 Illustration of Problem Spaces A Water Jug Problem You are given two jugs, a 4-gallon one and a 3-gallon one. Neither has any measuring markers on it. There is a pump that can be used to fill the jugs with water. How can you get exactly 2 gallons of water into the 4-gallon jug? State Space Definition Space consists of a set of ordered pairs (x, y) such that x = 0, 4 and y = 0, 3. x-number of gallons of water in 4-gallon jug; y-number gallons of water in 3-gallon jug. Start state is (0, 0). Goal state is (2, n) for any value of n.

13 Setting up of Problem Unstated assumptions: One can fill a jug from the pump. One can pour water out of a jug onto the ground. One can pour water from one jug to another. No other measuring devices are available. Select rules or actions that will move one state to another. The rules can also have redundant information. In which case the search space will be unnecessarily large and cycles may exist.

14 Example Rules Course Information Initial Final Description (x, y) if x < 4 (4, y) Fill the 4 gallon jug (x, y) if y < 3 (x, 3) Fill the 3 gallon jug (x, y) if x > 0 (0, y) Empty the 4 gallon jug on the ground (x, y) if x > 0 (x d, y) Pour some out of the 4 gallon jug (x, y) if (x + y) 3 and x > 0 (0, x + y) pour from 4gal to 3gal We can use the rules based on the following transitions. Partial fillings are not considered since there are no gradings on the jugs and hence only complete filling and emptying makes sense. The state of only one jug is changed at a time. That is multiple jugs cannot be filled at a time. We only consider the three states, filling one jug at a time from the tap, filling one jug from the other, emptying one jug at a time.

15 Questions to be answered Can redundant information be removed from the search tree? How do we determine if the search is optimal? Is the number of steps an appropriate choice? What is the difference between the following two solutions? (0, 0) (0, 3) (3, 0) (3, 3) (4, 2) (0, 2) (2, 0). (0, 0) (4, 0) (1, 3) (1, 0) (0, 1) (4, 1) (2, 3). Draw the search space eliminating redundant information.

16 Missionaries and Cannibals Problem: On one bank of a river there are three missionaries and three cannibals. There is one row-boat available that can hold up to two people and that they would like to use to cross the river. If the cannibals ever outnumber the missionaries on either of the river s banks (including the occupants of the boat), the missionaries will get eaten, How can the row-boat be used to safely carry all of the missionaries and cannibals across the river? Draw the search space for this problem. Use the breath first search to solve it. Use the depth first to solve this. What is preferable and why?

17 General Procedure to Solve a Search Problem 1. Set L to be a list of the initial nodes in the problem. At any given point in time, L s a list of nodes that have not yet been examined by the program. 2. If L is empty, fail. Otherwise pick a node n from L. 3. If n is a goal node, stop and return in and the path from the initial node to n. 4. Otherwise, remove n from L and add to L all of n s children, labeling each with its path from e initial node. Return to Step 2.

18 Search Techniques Categories Blind Search (uninformed search, Brute force search): e.g. Depth-first search, breadth-first search algorithms etc. This type uses no information other than the initial state, the search operators, and a test for a solution. Time consuming. Heuristic (informed search): e.g. hill climbing, best-first search etc. Uses domain specific knowledge to restrict the search space. Suboptimal solution.

19 Course Information Depth-first search treats the frontier as a stack It always selects one of the last elements added to the frontier. If the frontier is [p 1, p 2,...], p 1 is selected. Paths that extend p 1 are added to the front of the stack (in front of p 2 ). p 2 is only selected when all paths from p 1 have been explored.

20 Illustration

21 Algorithm 1. Set L to be a list of the initial nodes in the problem. 2. Let n be the first node on L. If L is empty, fail. 3. If n is a goal node, stop and return it and the path from the initial node to n. 4. Otherwise, remove n from L and add to front of L all of n s children, labeling each with its path from the initial node. Return to step 2.

22 Complexity of Algorithm Depth-first search isn t guaranteed to halt on infinite graphs or on graphs with cycles. The space complexity is linear in the size of the path being explored. Search is unconstrained by the goal until it happens to stumble on the goal.

23 Analysis of Depth-First Search L is considered a stack. Space requirement: Store b 1 nodes at each depth (the siblings of the nodes that have already been expanded) together with the additional node at depth d = d(b-1)+1 Time requirement: If the goal is at the far left of the tree the time requirement is d + 1; if its on the far right one has to examine the entire tree with a total of b d = bd+1 1 b 1 nodes in all. Take the average to find the average number of nodes that have to be visited.

24 Advantages/Disadvantages of Depth-First Search Less memory is required because nodes on the current path are stored. For a search with many goal locations this method is efficient. Because one can find a solution without searching the entire set of nodes. However can get trapped in a blind alley. Searching a single unfaithful path deeper. Minimality of the solution is not guaranteed.

25 Breadth-First Search Course Information Breadth-first search treats the frontier as a queue. It always selects one of the earliest elements added to the frontier. If the frontier is [p 1, p 2,..., p r ]: p 1 is selected. Its neighbors are added to the end of the queue, after p r. p 2 is selected next.

26 Illustration

27 Algorithm 1. Set L to be a list of the initial nodes in the problem. 2. Let n be the first node on L. If L is empty, fail. 3. If n is a goal node, stop and return it and the path from the initial node to n. 4. Otherwise, remove n from L and add to th end of L all of n s children, labeling each with its path from the initial node. Return to step 2.

28 Complexity of Algorithm The branching factor of a node is the number of its neighbors. If the branching factor for all nodes is finite, breadth-first search is guaranteed to find a solution if one exists. It is guaranteed to find the path with fewest arcs. Time complexity is exponential in the path length: bn, where b is branching factor (number of child branches), n is path length. The space complexity is exponential in path length: bn. Search is unconstrained by the goal.

29 Analysis of Breadth-First Search L is considered a queue. Space requirements: Since the total number of nodes at a depth k is b k, all of these nodes need to be stored before depth k + 1 is examined. Then the requirement is b d 1. Time requirement: A node is checked to see if it is a goal node just before the node is expanded to generate successors, and not when the node itself is added to the list L, in oder to reach a goal at d the internal nodes that need to be examined 1 + b b d 1 = bd 1 b 1

30 Advantages/Disadvantages of Breadth-First Search Minimal solution is guaranteed. Storage is high since all nodes at a level needs to be stored. All parts of a level have to be examined to goto the next level. Hence it takes a long time to reach a goal. Will not get trapped in a blind alley.

31 Measuring Performance in Problem Solving Algorithms Criterion Breadth- Uniform- Depth- Depth- Iterative Bidirectional First Cost First Limited Deepening (if applicable) Time b d b d b m b l b d b d/2 Space b d b d bm bl bd b d/2 Optimal? Yes Yes No No Yes Yes Complete? Yes Yes No Yes, if l d Yes Yes Completeness : guaranteed to find a solution? Time Complexity : How long it takes to find the solution? Space Complexity : How much memory is required to perform the search? Optimality : does it find the highest-quality solution? We will now look at some variations to the basic search methods we have looked into.

32 Uniform Cost Search Course Information Algorithm Explanations Analysis of Algorithms BFS finds the shallowest goal but may not be the least cost. (depends on how cost is defined of course) UCS modifies the BFS by always expanding the lowest-cost node on the fringe rather than the lowest depth. BFS is USC with g(n) = DEPTH(n). The path with the cost value is stored in a queue before the final decision is made. We assume that the costs cannot be negative. If they are positive then a optimal goal is found always. Note the reason why C is not expanded because if it is expanded the cost would be greater than the other two and will be useless exercise. (shown in the next page)