The problem is solved by a domain decomposition technique applied to the Method of Fundamental Solutions and Hadamard shape derivatives for the optimization of inner and outer boundaries.
The optimization approach uses a derivative variation method to efficiently identify the optimization range through analyzing the first order derivatives of the optimized quantity and the non-linear deviation profile of the derivative value.
Presented are the details on the development of the dimeric PTCs for the synthesis of optically active α-amino acid derivatives and the optimization of the reaction variables suitable for the dimeric PTCs.
The solution of this integrated optimization problem requires sensitivity analysis implying computing the derivatives of the constraints imposed on the optimization problem with respect to the design variables.
However, to the best of our knowledge, the derivatives are currently estimated numerically by finite difference approximation because it is very difficult to obtain the analytical derivatives of the object function for an implicit optimization problem.
Most optimization techniques require derivatives of the problem functions whereas in GA method only information related to each member is of prime importance.
We solve this optimization problem by obtaining the derivatives of the function of the total additional payment surplus.
· Optimization experiments without validation steps independent of the optimization runs.
In addition to this, the explicit partial derivatives of the cumomer network with respect to fluxes are obtainable, which is useful for gradient-based optimization algorithms.
This optimization problem has a special form that enables us to obtain analytic derivatives of the objective function.
