In this study, the subproblem
which had a global optimal solution was formulated to the priority structure using LINGO software as follows:
It is easy to verify that every subproblem
in (2.5) must have a unique solution because of strict convexity.
The scholarship assignment problem discussed above can be deemed as a combination of two subproblems
. The first subproblem
is to search for all feasible assignment schemes which meet the practical constraints and the basic equity requirement simultaneously.
When each element in the [W.sup.c] matrix is updated, the remaining elements in [W.sup.c] matrix and [S.sup.c] matrix are fixed; at this time, the objective function is changed into an L2-norm constrained least-squares minimization subproblem
. Similarly, when each element in [S.sup.c] matrix is updated, [W.sup.c] matrix and the remaining elements in [S.sup.c] matrix are fixed.
In particular, the PV here represents the population that consists of the solutions of its corresponding representative subproblem
and this problem's neighbor subproblems
The Benders decomposition method consists in dividing the original problem into a master problem and an easier subproblem
. In a minimization problem, the master problem solution provides a lower bound (LB) and the subproblem
solution provides an upper bound (UB) to the original problem.
The algorithm we propose here is based on the classical SA algorithm whose subproblem
must be solved exactly to generate the next iterate point.
2 only subjects to the space-time flow balance and binary constraints, the second part can be easily regarded as a time-dependent shortest path problem that can be solved to the optimum using some exact solution approach, such as forward DP, label setting, and label correcting (Mahmoudi and Zhou , Yin et al.
1: Design a Finite Dimensional PI Controller for Just SOF Stabilization.
HTUC problem can be divided into two subproblems
, hydro subproblem
and unit commitment coordination subproblem
(2) Solving the Second Subproblem
. Similarly, update L:
Note that [mathematical expression not reproducible] in (9) is well defined, since subproblem
(9) has a unique solution.