3 Method

   
3.1 Genetic evolution

In terms of genetic programming the objective of AMORE is to determine the genome (i.e. the set of astrophysical parameters described in Sect. 2.10, see also Table 2) of a specified individual (i.e. the observed stellar population). Note that it is not possible to directly observe the genome. The genome is determined from the phenotype of each individual (i.e. the synthetic CMDs, see for example Fig. 6). The genetic information is located in the genes of one chromosome.

Figure 4: The filled circles in panels a)- f) display the values obtained for the parameters using the models in Table A.1. The solid line refers to the value set for the original population.

A guess of the genotype of the observed CMD is obtained through comparison with a synthetic CMD, which is generated via supervised evolution and breeding (PIKAIA together with POWELL). The stars in the synthetic CMD population with a particular genotype are raised to maturity (HRD-ZVAR and HRD-GST). A group of individuals is allowed to procreate (the chance of an individual procreating depends on its fitness and the selection pressure, see Charbonneau 1995 and Charbonneau & Knapp 1996) and the genetic information of the parents is passed on to their offspring (see Fig. 2). A fitness evaluation (a comparison between the observed and synthetic CMD) provides a ranking of the resulting group of individuals. If the individual has "good genes'' it survives, remains in the group and gets a chance of procreation.

The evolutionary process of breeding and fitness evaluation is repeated for a fixed number of generations. The gene pool of the resulting best individual at the end of the evolutionary run with AMORE hopefully represents a near-optimum representation of the unknown genome.

   
3.2 Running AMORE

Initially PIKAIA is in control (see Fig. 1) of the evolution for a fixed number of generations. Afterwards POWELL tries to improve the genome of the fittest individual communicated through PIKAIA. We then determine the uncertainty for each gene on the chromosome. Subsequently, we tighten the limits on the range of variation allowed for each gene and re-scale the parameters on the genetic print of the fittest individual accordingly. During the shrinkage of the parameter range we do not re-scale the genetic information of the remaining individuals, but preserve their former values as semi-random input for the continued optimization process. The latter addition to the hybrid scheme is most likely a significant driver in speeding up the search for a fitter individual.

After each optimization with POWELL a new cycle with PIKAIA is started with the current best parameter set as "educated next guess'' for AMORE's progressive evolution. The total number of PIKAIA cycles is user defined.

In Sect. 2.9 we argued that the parameters are on average about $\sqrt{F/{n}}~\sigma_k$ away from its optimum value. The convergence however is not governed by the average "distance'' that each parameters is away from its optimum setting. It is mainly determined from the ability to tune the parameter which has the largest offset from its optimum value.

In the AMORE training sessions it was noted that with $F\simeq\!3.0$ about three of the eight parameters are about 1em$\sigma_k$ ( $\simeq\sqrt{F/3}~\sigma_k$) away from their optimum value. AMORE has a built-in option to do a random variation from 0-3 $\sigma_k$ of two parameters (randomly selected) from the running best solution when the fitness is less than 0.30. Above this threshold we choose a new value for two parameters according $\pm\sqrt{F/\rho}~\sigma_k$, where $\rho$ can be any number between 1.0 and 4.0.