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The second and third lines define two constraints, the first of which is an inequality constraint and the second of which is an equality constraint. These two constraints are hard constraints, meaning that it is required that they be satisfied; they define the feasible set of candidate solutions. Without the constraints, the solution would be ...
Constraints can be either hard constraints, which set conditions for the variables that are required to be satisfied, or soft constraints, which have some variable values that are penalized in the objective function if, and based on the extent that, the conditions on the variables are not satisfied.
() are inequality constraints X {\displaystyle X} is a set constraint that includes additional restrictions on x {\displaystyle x} besides those implied by the equality and inequality constraints. The problem formulation stated above is a convention called the negative null form , since all constraint function are expressed as equalities and ...
A binary constraint, in mathematical optimization, is a constraint that involves exactly two variables. For example, consider the n-queens problem, where the goal is to place n chess queens on an n-by-n chessboard such that none of the queens can attack each other (horizontally, vertically, or diagonally). The formal set of constraints are ...
The constraints S#\=0 and M#\=0 means that these two variables cannot take the value zero. When the interpreter evaluates these constraints, it reduces the domains of these two variables by removing the value 0 from them. Then, the constraint all_different(Digits) is considered; it does not reduce any domain, so it is simply stored. The last ...
Constraint composition operates on a pair of binary constraints ((,),) and ((,),) with a common variable. The composition of such two constraints is the constraint ((,),) that is satisfied by every evaluation of the two non-shared variables for which there exists a value of the shared variable such that the evaluation of these three variables ...
The classic model of Constraint Satisfaction Problem defines a model of static, inflexible constraints. This rigid model is a shortcoming that makes it difficult to represent problems easily. [33] Several modifications of the basic CSP definition have been proposed to adapt the model to a wide variety of problems.
It can be considered what the current substitution is for regular logic programming. When only tree terms are allowed, the constraint store contains constraints in the form t1=t2; these constraints are simplified by unification, resulting in constraints of the form variable=term; such constraints are equivalent to a substitution.