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3- Next, a master problem in which we handle the assignment of VMs to servers and connections to specific paths without scheduling them is generated.
We propose three smaller and simpler perturbations of the master problem in the OA algorithm by prioritizing, fixing, eliminating, or limiting exchangers in various ways to avoid premature termination.
Optimality Benders' cuts (18) are added to the master problem in each iteration j in order to adjust the output of gas-fired units according to the impact they have on the gas system operation.
The resulting configuration corresponds to what is known as the master problem in a column generation approach [29], while each IMCC configuration corresponds to what is known as the pricing problem.
Taking into account the production of gas-fired units ((hat{varvec{x}}^{j})) calculated by the master problem in the iteration j, subproblems (19)–(21) calculate the gas network optimization with security constraints.
The full master problem in (5) contains all K link rate vectors, but it is restricted to a subset J ⊆ K of vectors in the restricted master problem (16) used for column generation.
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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.
The interactive MINLP solver is based on the decomposition based MINLP algorithms, where a NLP sub-problem is solved in the innerloop and a MILP master problem is solved in the outer-loop.
Step 2: Solve the master problem as described in Sect.
We decompose the problem to separate the location decisions in the master problem from the inventory decisions in the subproblem.
The maximum order of constraints in the master problem is two, and they are calculated in parallel.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com