Genetic Algorithm (GA)

The choice of using a GA to optimise the model is made because it has some advantages over the more traditional methods - it gives a more robust and global fit to the data and does not get stuck in the first local minimum it finds. The genetic algorithm can be broken down into the following stages:

Generate a set of random solutions, usually about 1000.
Calculate the goodness of each solution from their chi fit to the data and the regularisation term equation 1. Rank the solutions in order of their goodness.
Generate the next generation of solutions.
Repeat the last step until the goodness does not improve any further.

In producing the next generation of solutions, the genetic algorithm employs a type of natural selection where the solutions that were ranked best (according the the fitness function, equation 1) are more probable to breed the next generation. Formally, solutions are selected by using a stochastic exponential probability of the form

where S is the solution rank number after sorting and Npop is the size of each population. Cs is a scale parameter used to bias the selection criteria more to the best ranked solutions. INT is the INTEGER function and RND is a random number generator.

Eventually the improvement in goodness will start to level out and a more analytical approach is required to improve the fit further. For this we use the Powells method. (see numerical recipes)

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Stephen Potter
Thu Jul 31 14:44:15 BST 1997

larized light curves. The complete radiative transfer is not carried out.

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