Sentence examples for violation vectors from inspiring English sources
The mathematical formulae for calculating the interval violation vectors of a design vector corresponding to various constraint functions are provided.
Then the objective and feasibility robustness indices of various design vectors can be calculated based on their values of total interval violation vectors.
A novel concept of interval violation vector was proposed for evaluating the feasibility robustness of a design vector, the mathematical formulae for calculating the interval violation vectors of various constraint functions were also provided.
Definition 1 (Interval violation vector).
The feasibility robustness index can be calculated from the total interval violation vector of all the constraints in the robust optimization model considering that the total interval violation vector reversely reflects the feasibility robustness of a constraint function.
Then the formula for calculating the interval violation vector of such a constraint should be adjusted as Eq. (4).
The improvement is gained from the definition of interval violation vector and the robustness-based preferential guidelines.
In fact, (delta_{phs}) is the violation vector showing the infeasibility level in control constraint (29) under a given scenario.
And then the formula for calculating the interval violation vector for such a constraint will be simplified as Eq. (6).
As can be seen from Eq. (10), the larger total interval violation vector will lead to the smaller feasibility robustness index for a design vector.
To locate the optimal solution of objective and feasibility robustness, a new concept of interval violation vector and its calculation formulae corresponding to different constraint functions are proposed.
