Ai lecture 9(unit02)
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The document discusses the concept of Constraint Satisfaction Problems (CSP) in artificial intelligence, explaining its definition and application. It outlines the components of CSP, including variables, domains, and constraints, using examples such as Sudoku, graph coloring, and the n-queens problem. Each example illustrates how constraints dictate the possible solutions within the defined parameters.
Ai lecture 9(unit02)
- 1. Topic To Be Covered: Constraint Satisfaction Problem(Approach) In AI Jagdamba Education Society's SND College of Engineering & Research Centre Department of Computer Engineering SUBJECT: Artificial Intelligence & Robotics Lecture No-09(UNIT-02) Prof.Dhakane Vikas N
- 2. Constraint Satisfaction Problem In AI What is CSP???? In artificial intelligence and operations research, constraint satisfaction is the process of finding a solution to a problem by satisfying set of constraints. It is heuristic based Technique. CSP is also called as decision problem.
- 3. Constraint Satisfaction Problem In AI What is CSP???? Way of representation of problem in CSP is different from state space representation Some popular example of Constraint satisfaction problem are like Map (Graph) Coloring problem-N-Queens Problem & Sudoku etc.
- 4. Constraint Satisfaction Problem In AI What is CSP???? For Example-01(Sudoku): Sudoku is played on a grid of 9 x 9 spaces. Within the rows and columns are 9 “squares” (made up of 3 x 3 spaces). Each row, column and square (9 spaces each) needs to be filled out with the numbers 1-9, without repeating any numbers within the row, column or square. As you can see from the image below of an actual Sudoku grid, each Sudoku grid comes with a few spaces already filled in; the more spaces filled in, the easier the game – the more difficult Sudoku puzzles have very few spaces that are already filled in.
- 5. Constraint Satisfaction Problem In AI What is CSP???? Following are main Components of CSP CSP consist of three Components:(V,D,C) 1)V is the set of finite variables {V1,V2,V3…Vn } -In given Sudoku example, available spaces where we have to make entry of data(value) is called as VARIABLES…. 2)D is the set of Domains {D1,D2,D3..Dn} one for each variable. -Here in given Sudoku example domains are values(1-9) that has to be placed in certain variables.
- 6. Constraint Satisfaction Problem In AI What is CSP???? Following are main Components of CSP CSP consist of three Components:(V,D,C) 3) C is the set of Constraints(Rules) that specify allowable combinations of values.(C1,C2,C3) -Which value to place in which variable by selecting it from its domain is based on set of constraints. -For given Sudoku example Constraints are as follows: a)Use value from 1-9 b)No repetition of values on same row, column & square box.
- 7. Constraint Satisfaction Problem In AI
- 8. Constraint Satisfaction Problem In AI What is CSP???? For Example-02(GCP):Graph Coloring Problem For Example(GCP):Vertex coloring is the most common graph coloring problem. The problem is, given m colors, find a way of coloring the vertices of a graph such that no two adjacent vertices are colored using same color. (m=3 & node=10)
- 9. Constraint Satisfaction Problem In AI What is CSP???? For Example-03(N-queens Problem) This problem is to find an arrangement of N queens on a chess board, such that no queen can attack any other queens on the board. The N Queen is the problem of placing N chess queens on an N×N chessboard so that no two queens attack each other. Queen can attack each other if they are in same column, row & diagonal. Example:-04 queen