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The integer-infeasible path MINLP approach has been applied to perform an efficient initialization scheme and to halve CPU times for solving MILP master problem of the modified OA/ER algorithm.
The master problem of the two-stage model is the minimization of economic loss for load curtailment under lines reinforcement.
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If any power network violations arise, corresponding Benders cuts are formed and added to the master problem for solving the next iteration of UC.
The solving of linear relaxation LP(M) of the master problem chooses a maximum of N IMCCs each time to serve the N MEC requests.
In these column generation approaches, the master problem is often of a set partitioning type.
This decomposition algorithm solves the problem by iterating between reduced Non Linear Programming (NLP) subproblems and a Mixed-Integer Linear Programming (MILP) master problem that consists of linear approximations in all solution points given for all the NLPs solved previously, using the big-M formulation to relax the linear approximations of the disjunctions.
Branching can be done either on the variables of the master problem using cuts, or on the variables of the pricing problem, using a classic branch-and-bound procedure or cuts.
The master problem determines the assignment of platforms to wells and the planning subproblem calculates the timing for fixed assignments.
The most difficulty associated with the Benders' decomposition is the solution of master problem, as in many real-life problems the model will be NP-hard and very time consuming.
We develop a branch-and-Benders-cut (BBC) method where, in a non-standard fashion, the master problem includes the variables of the Benders subproblem, but relaxes their integrality.
solve the following approximation of master problem (7) (13).
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