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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.
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 ...
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 ...
Arc consistency can also be defined relative to a specific binary constraint: a binary constraint is arc consistent if every value of one variable has a value of the second variable such that they satisfy the constraint. This definition of arc consistency is similar to the above, but is given specific to a constraint. This difference is ...
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.
In artificial intelligence and operations research, constraint satisfaction is the process of finding a solution through a set of constraints that impose conditions that the variables must satisfy. [1] A solution is therefore an assignment of values to the variables that satisfies all constraints—that is, a point in the feasible region.
Constraint propagation works by reducing domains of variables, strengthening constraints, or creating new ones. This leads to a reduction of the search space, making the problem easier to solve by some algorithms. Constraint propagation can also be used as an unsatisfiability checker, incomplete in general but complete in some particular cases.