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In the general case, constraint problems can be much harder, and may not be expressible in some of these simpler systems. "Real life" examples include automated planning, [6] [7] lexical disambiguation, [8] [9] musicology, [10] product configuration [11] and resource allocation. [12] The existence of a solution to a CSP can be viewed as a ...
Other considered kinds of constraints are on real or rational numbers; solving problems on these constraints is done via variable elimination or the simplex algorithm. Constraint satisfaction as a general problem originated in the field of artificial intelligence in the 1970s (see for example (Laurière 1978)).
An example: a binary constraint satisfaction problem (join-tree clustering can also be applied to non-binary constraints.) This graph is not chordal (x3x4x5x6 form a cycle of four nodes having no chord). The graph is made chordal. The algorithm analyzes the nodes from x6 to x1.
As a result, the constraint satisfaction problem can be used to set a constraint whose relation is the table on the right, which may not be in the constraint language. As a result, if a constraint satisfaction problem has the table on the left as its set of solutions, every relation can be expressed by projecting over a suitable set of variables.
In constraint satisfaction, local search is an incomplete method for finding a solution to a problem. It is based on iteratively improving an assignment of the variables until all constraints are satisfied. In particular, local search algorithms typically modify the value of a variable in an assignment at each step.
In artificial intelligence and operations research, a Weighted Constraint Satisfaction Problem (WCSP), also known as Valued Constraint Satisfaction Problem (VCSP), is a generalization of a constraint satisfaction problem (CSP) where some of the constraints can be violated (according to a violation degree) and in which preferences among solutions can be expressed.
If the problem mandates that the constraints be satisfied, as in the above discussion, the constraints are sometimes referred to as hard constraints.However, in some problems, called flexible constraint satisfaction problems, it is preferred but not required that certain constraints be satisfied; such non-mandatory constraints are known as soft constraints.
A constraint is composed of a sequence of variables, called its scope, and a set of their evaluations, which are the evaluations satisfying the constraint. The constraint satisfaction problems referred to in this article are assumed to be in a special form.