Solving Problems by searching

Well defined problems

A probem is well defined if it is easy to automatically asses the validity (utility) of any proposed solution.

(By easy is meant e.g. Polynomial time. However, to find an optimal solution may be computationally hard.)

There are two important types of well defined problems:

Path problems and Constraint Satisfaction Problems

Path problemsA path problem may often be defines by the following information:

• a state space

• a known initial state

• a definition of a goal state

• a set of possible actions with well defined

preconditions and effects

• a cost function of the path

Constraint Satisfaction Problems (CSP)

CSP consists of

• a domain

• a set of variables

• a set of constraints on these variables

• an optimality function (optimising criterion)

CSP are solved by carefully searching the search space making choices that restrain the search space as much as possible.

Problem overview

Problems

Well Defined Problems(Validated in Polynomial Time)

Ill-Defined Problems

Path ProblemsConstraint Satisfaction Problems

Constructive Methods Repair Methods (Local Search)

Constraint Handling

Generate & Test(Logic Programming)

Constrain & Generate(Constraint Logic Programming)

Contraint Propagation

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