Problem Formulation

There are four components to define a problem formally. The first thing that needs to be done is to mention or define the initial states that the agents start with. Second, the description of the possible actions that are available to the agent. The most common formulation uses a successor functions. The third component is tested goal. It determines whether a given state is goal state or not. There is often an explicit set of possible goal states and the test simply checks if the given state is one of them. But sometimes the goal is specified by an abstract property rather than an explicitly enumerated set of states. The final component is a path cost. A path cost function assigns a numeric cost to each path. The problem-solving agent choose a first function that reflects its one performance measured. We assume that the total cost of the path is sum of cost of individual one.

Summary

There are four components to define a problem formally. The first thing that needs to be done is to mention or define the initial states that the agents start with. Second, the description of the possible actions that are available to the agent. The most common formulation uses a successor functions. The third component is tested goal. It determines whether a given state is goal state or not. There is often an explicit set of possible goal states and the test simply checks if the given state is one of them. But sometimes the goal is specified by an abstract property rather than an explicitly enumerated set of states. The final component is a path cost. A path cost function assigns a numeric cost to each path. The problem-solving agent choose a first function that reflects its one performance measured. We assume that the total cost of the path is sum of cost of individual one.

Things to Remember

  • There are four components to define a problem formally. First thing that needs to be done is to mention or define the initial states that the agents starts with. 
  • Second, the description of the possible actions that are available to the agent. The most common formulation uses a successor functions.
  • The third component is test goal. It determines whether a given state is goal state or not.
  • The final component is a path cost. A path cost function assigns a numeric cost to each path. The problem solving agent choose a first function that reflects its one performance measured. We assume that the total cost of the path is sum of cost of individual one.

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Problem Formulation

Problem Formulation

Problem Formulation

As we discussed in the earlier chapter that there are certain steps that we need to follow in order to solve the problem. For solving any problem the first and foremost step to be taken into account is problem formulation. There are four components to define a problem formally and they are given below:

  1. The first thing that needs to be mentioned or defined are the initial states that the agent starts with.
  2. A description of the possible actions that are available to the agent. The most common formulation uses a successor functions. For a given particular state x, the successor function succ-func(x) returns a set of <action, successor> ordered pair where each action is one of the legal action in state 'x' and each successor is a state that can be reached from 'x' by applying the action..

    { < GO (B), in (B) >,
    < GO (D), in (D) >,
    < GO (G), in (G)>
    }
  3. The third component is tested goal. It determines whether a given state is goal state or not. There is often an explicit set of possible goal states and the test simply checks if the given state is one of them. But sometimes the goal is specified by an abstract property rather than an explicitly enumerated set of states.
    For example: In chess, the goal is to reach the state of check-mate where the opponent's king is under attack and cannot escape.
  4. The final component is a path cost. A path cost function assigns a numeric cost to each path. The problem-solving agent chooses a first function that reflects its one performance measured. We assume that the total cost of the path is the sum of the cost of individual one.

References:

  1. Elaine Rich, Kevin Knight 1991, "Artificial Intelligence".
  2. Nilsson, Nils J. Principles of Artificial Intelligence, Narosa Publishing House New Delhi, 1998.
  3. Norvig, Peter & Russel, Stuart Artificial Intelligence: A modern Approach, Prentice Hall, NJ, 1995
  4. Patterson, Dan W. Introduction to Artificial Intelligence and Expert Systems, Prentice Hall of India Private Limited New Delhi, 1998.

Lesson

Problem solving

Subject

Computer Engineering

Grade

Engineering

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