Forward checking:

Whether to add some sophistication to the search method there constraint solvers use a technique called as forward checking. So here the general idea is to work the like as a backtracking search but, where checking compliance with constraints behind assigning a  value to a variable there the agent also checks when this assignment is going to break constraints with  future variable assignments. Hence is supposing that V_c has been assigned to the current variable c, after then for each unassigned variable x_i, as temporarily remove all values from D_i that along with V_c break a constraint. Thus it may be that in doing so, D_i becomes empty. Because the choice of V_c for the current variable is bad  -  so however it will not find its way into a solution to the problem just because there's no way to assign a value to xi without breaking a constraint. In that condition even though the assignment of V_c may not break any constraints such that already assigned variables so a new value is chosen as or backtracking occurs whether there are no values left, just because we know that V  is a bad assignment. 

Here the next diagram like again, taken from Smith's tutorial to shows how forward checking improves the search for a solution to the 4-queens problem as;:. 

In such a scenario to forward checking, to improve the intelligence of the constraint solving agent so there are some possibilities for a heuristic search. Therefore firstly, our agent can worry about the order such that looks at the variables, that is, in example of the 4-queens problem so it might try to put a queen in row 2, after then one in row 3, one in row 1 and then finally one in row 4. Moreover a solver taking such care is said to be utilizing a variable-ordering heuristic. Conversely the ordering of variables can be done earlier than a search  is started and rigidly adhered to during the search. In fact this might be a good idea whether there is extra knowledge about the problem, like an example that a particular variable should be assigned a value sooner quite than later. In such a scenario  the ordering of the variables can be done dynamically so in response to some information gathered about that how the search is progressing during the search procedure.