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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 ...
Every variable is associated a bucket of constraints; the bucket of a variable contains all constraints having the variable has the highest in the order. Bucket elimination proceed from the last variable to the first. For each variable, all constraints of the bucket are replaced as above to remove the variable.
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 ...
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 ...
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.
As a result, the other term can replace the variable in the current goal and constraint store, thus practically removing the variable from consideration. In the particular case of equality of a variable with itself, the constraint can be removed as always satisfied. In this form of constraint satisfaction, variable values are terms.
Objective: Elected functional combination of variables (to be maximized or minimized) Constraints: Combination of Variables expressed as equalities or inequalities that must be satisfied for any acceptable design alternative; Feasibility: Values for set of variables that satisfies all constraints and minimizes/maximizes Objective.