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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 ...
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 ...
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.
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 ...
Domain-specific constraints may come to the constraint store both from the body of a clauses and from equating a literal with a clause head: for example, if the interpreter rewrites the literal A(X+2) with a clause whose fresh variant head is A(Y/2), the constraint X+2=Y/2 is added to the constraint store. If a variable appears in a real or ...
Each constraint is a boolean mapping indicating if the joint assignment (,) violates a constraint, and is the penalty incurred for violating the constraints. Constraints assigned an infinite penalty are known as hard constraints, and represent unfeasible assignments to the optimization problem.
Geometric programming is a technique whereby objective and inequality constraints expressed as posynomials and equality constraints as monomials can be transformed into a convex program. Integer programming studies linear programs in which some or all variables are constrained to take on integer values. This is not convex, and in general much ...
Constraint programming states relations between variables in the form of constraints that specify the properties of the target solution. The set of constraints is solved by giving a value to each variable so that the solution is consistent with the maximum number of constraints. Constraint programming often complements other paradigms ...