Tuesday, July 20, 2010
Heuristic search is a very general method applicable to a large class of problem . It includes a variety of techniques. In order to choose an appropriate method, it is necessary to analyze the problem with respect to the following considerations.
Is the problem decomposable ?
A very large and composite problem can be easily solved if it can be broken into smaller problems and recursion could be used. Suppose we want to solve.
Ex:- ∫ x2 + 3x+sin2x cos 2x dx
This can be done by breaking it into three smaller problems and solving each by applying specific rules. Adding the results the complete solution is obtained.
2. Can solution steps be ignored or undone?
Problem fall under three classes ignorable , recoverable and irrecoverable. This classification is with reference to the steps of the solution to a problem. Consider thermo proving. We may later find that it is of no help. We can still proceed further, since nothing is lost by this redundant step. This is an example of ignorable solutions steps.
Now consider the 8 puzzle problem tray and arranged in specified order. While moving from the start state towards goal state, we may make some stupid move and consider theorem proving. We may proceed by first proving lemma. But we may backtrack and undo the unwanted move. This only involves additional steps and the solution steps are recoverable.
Lastly consider the game of chess. If a wrong move is made, it can neither be ignored nor be recovered. The thing to do is to make the best use of current situation and proceed. This is an example of an irrecoverable solution steps.
1. Ignorable problems Ex:- theorem proving
· In which solution steps can be ignored.
2. Recoverable problems Ex:- 8 puzzle
· In which solution steps can be undone
3. Irrecoverable problems Ex:- Chess
· In which solution steps can’t be undone
A knowledge of these will help in determining the control structure.
3.. Is the Universal Predictable?
Problems can be classified into those with certain outcome (eight puzzle and water jug problems) and those with uncertain outcome ( playing cards) . in certain – outcome problems, planning could be done to generate a sequence of operators that guarantees to a lead to a solution. Planning helps to avoid unwanted solution steps. For uncertain out come problems, planning can at best generate a sequence of operators that has a good probability of leading to a solution. The uncertain outcome problems do not guarantee a solution and it is often very expensive since the number of solution and it is often very expensive since the number of solution paths to be explored increases exponentially with the number of points at which the outcome can not be predicted. Thus one of the hardest types of problems to solve is the irrecoverable, uncertain – outcome problems ( Ex:- Playing cards).
4. Is good solution absolute or relative ?
(Is the solution a state or a path ?)
There are two categories of problems. In one, like the water jug and 8 puzzle problems, we are satisfied with the solution, unmindful of the solution path taken, whereas in the other category not just any solution is acceptable. We want the best, like that of traveling sales man problem, where it is the shortest path. In any – path problems, by heuristic methods we obtain a solution and we do not explore alternatives. For the best-path problems all possible paths are explored using an exhaustive search until the best path is obtained.
5. The knowledge base consistent ?
In some problems the knowledge base is consistent and in some it is not. For example consider the case when a Boolean expression is evaluated. The knowledge base now contains theorems and laws of Boolean Algebra which are always true. On the contrary consider a knowledge base that contains facts about production and cost. These keep varying with time. Hence many reasoning schemes that work well in consistent domains are not appropriate in inconsistent domains.
Ex.Boolean expression evaluation.
6. What is the role of Knowledge?
Though one could have unlimited computing power, the size of the knowledge base available for solving the problem does matter in arriving at a good solution. Take for example the game of playing chess, just the rues for determining legal moves and some simple control mechanism is sufficient to arrive at a solution. But additional knowledge about good strategy and tactics could help to constrain the search and speed up the execution of the program. The solution would then be realistic.
Consider the case of predicting the political trend. This would require an enormous amount of knowledge even to be able to recognize a solution , leave alone the best.
Ex:- 1. Playing chess 2. News paper understanding
7. Does the task requires interaction with the person.
The problems can again be categorized under two heads.
1. Solitary in which the computer will be given a problem description and will produce an answer, with no intermediate communication and with he demand for an explanation of the reasoning process. Simple theorem proving falls under this category . given the basic rules and laws, the theorem could be proved, if one exists.
Ex:- theorem proving (give basic rules & laws to computer)
2. Conversational, in which there will be intermediate communication between a person and the computer, wither to provide additional assistance to the computer or to provide additional informed information to the user, or both problems such as medical diagnosis fall under this category, where people will be unwilling to accept the verdict of the program, if they can not follow its reasoning.
Ex:- Problems such as medical diagnosis.
8. Problem Classification
Actual problems are examined from the point of view , the task here is examine an input and decide which of a set of known classes.
Ex:- Problems such as medical diagnosis , engineering design.
Posted by Gurram. Veera Raghavavaiah at 3:10 AM