In the present manuscript, we investigate and demonstrate the use of outer approximation methods for simultaneously optimising the placement and operation of control valves in water distribution networks.
The extended incremental method, as well as the outer approximation method, were applied for the linearization of the nonlinear equations that govern the physics of gas transport and for the coupling constraint of the two energy systems.
All CFETR PF coil are fabricated by stacking several double-pancakes (DP), due to the complex structure, the common outer heating method can hardly satisfy the curing temperature requirement.
The public model library (PML) of gPROMS is used to simulate the process and the built-in optimization package of gPROMS is used to solve the MIDO via the deterministic outer approximation method.
We propose for the stacking sequence optimization an outer approximation method which iteratively solves a set of mixed integer linear problems associated to the evaluation of the constraint margin function.
If (mathrm{RES}= vert (Au^{ k+1)}+q)^{T} u^{ k+1)}-m u^{ k+1)}-m u^{ k+1psilon), then stop; otherwise, set (k:=k+1) and return to step 2. From Method 3.1 or Method 3.2 we can see that the MMS iteration method belongs to a class of inner-outer iteration methods.
After taking a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution, the time derivative is estimated and used in an (outer) Runge Kutta method of arbitrary order.
This solution coincides with the one obtained by Dasika and Maranas using the outer approximation method [ 17].
Dasika and Maranas [ 17] developed an optimization framework for the design of biocircuits, based on the circuit modeling formulation by Hasty [ 19] and a multistart local outer approximation method for the optimization.
Whereas the time reported to find the optimum with the outer approximation method was of 200 minutes in an Intel 3.4 GHz Xeon processor [ 17], MITS arrived to the same solution in less than 200 seconds using an Intel 2.8 GHz Xeon, thus reducing the computational cost at least by a factor of 60.
The outer-approximation method was originally introduced by Haugazeau in 1968 and was successfully generalized and extended in recent papers [11 14].
