Solution of the configuration design problem

To solve the configuration design problem means to assign a value to each active parameter in such a way that no active constraint is violated. The design process can be represented by a trajectory in two dimensional design state space where the

x-axis represents the number of active unassigned parameters
y-axis represents the number of violated active constraints

(the constraint validity of which cannot be checked because this constraint is defined over an unassigned parameter is not considered to be violated).

The search for the solution can be depicted in the design state space as the transition from the initial state to the goal state. At the beginning of the search all parameters are unbounded and no constraint is violated. As a result, the initial point of the trajectory is located on the x-axis and its distance to the origin is equal to the number of parameters which are active at the beginning of the search. Since the successful solution stands for the case when all active parameters are assigned and no active constraint is violated, the trajectory in this case ends in the origin of the system of coordinates. If the trajectory ends above the x-axis, not all constraints are satisfied and the search fails. The final point of the trajectory on the x-axis but not in the origin indicates that some parameters remain unbound (and they are not important for the final solution or there is no knowledge available how to assign a value to them).

There are many strategies how to solve configuration design problems. Every strategy can produce the trajectory of a characteristic shape in the design state space (an example of such a trajectory is here). In general, the solution consists of various design steps. There are several different basic types of steps:

The assignment step assigns one parameter. This assignment can violate some constraints. The step is represented in the state space by an arrow pointing to the left (it is parallel to the x-axis if the step does not violate any constraint).
The corrective step modifies the values of some parameters in order to remove a constraint violation. It is represented by an arrow parallel to the y-axis (if the number of violated constraint decreases, the arrow is pointing downwards).
The activation step activates one or more parameters and puts them into the current solution. Since activated parameters are unbound, the step is represented in the state space by an arrow parallel to the x-axis and pointing to the right.
The inactivation step inactivates one or more parameters and deletes them from the current solution. The step can induce the inactivation of some constraints associated with inactivated parameters. It is represented in the state space by an arrow pointing to the left (it is parallel to the x-axis if no constraint is inactivated).
The relaxation step inactivates some constraints and activates others. The step is represented in the design state space by an arrow parallel to the y-axis.

Various strategies can be constructed using these steps. One of them is the Complete-Revise-Optimize (CRO) strategy which is closely related to the strategy Complete Model and Revise.