# Optimisation

Because of the lost of intermediates species, the reduced mechanisms obtained after the DRGEP and QSS simplifications do not predict well the trajectories of the detailed scheme. An optimisation step is then needed.

The optimisation algorithm performed in ORCh is the genetic algorithm [1] which apply the principles of natural selection and evolution, in order to look for the optimal solution of a problem initialised by a population of potential solutions.

In this case, we want to optimise the parameters of the Arrhenius law, describing the reaction rates. For example, the forward Arrhenius law for the reaction rate of the jth reaction reads :

${\displaystyle {\dot {Q}}_{j}=A_{j}T^{\beta _{j}}exp(-{\frac {E_{aj}}{RT}})[A]^{n_{Aj}}[B]^{n_{Bj}}}$

with ${\displaystyle A_{j}}$ the pre-exponential factor, ${\displaystyle E_{aj}}$ the activation energy, ${\displaystyle \beta _{j}}$ the temperature exponent, ${\displaystyle [A]}$ and ${\displaystyle [B]}$ the concentrations of the reactants involved and ${\displaystyle n_{Aj}}$ and ${\displaystyle n_{Bj}}$ the exponents of concentrations.

Given te high values of ${\displaystyle A_{j}}$, we prefer to work with ${\displaystyle a_{j}=log(A_{j})}$.

The parameters values to be optimised are then put in the form of a triplet (${\displaystyle a_{j}}$,${\displaystyle \beta _{j}}$,${\displaystyle E_{aj}}$) considered as a chromosome. A population will be composed of a set of chromosomes which will evolve and mutate until converging towards the best solution, i.e. the best chromosome.

The optimisation directory is organized as follows :

• CreateAnalyticDirectory :

Serves the coupling with Cantera : After the QSS step, the reduced scheme is composed of 2 files : a xml file which contain the transported species and an analytic routine which recalculate the reaction variables of the scheme. The CreateAnalyticDirectory file contains the method which calculate the analytic part of the scheme during the optimisation step.

• OptimScenario :

Contains all the inputs necessary to define the optimisation step like the population size, the crossover and mutation rates or the allowed variations of the parameters for example.

• Optimisation :

Contains the main methods of the optimisation step.

### Bibliography

1. J.H. Holland, Adaptation in natural and artificial systems, MIT press, Cambridge, MA, USA, 1992. ISBN 0-262-58111-6