12 2. Backgroundrepresented by a set of coefficients for the corresponding functional forms. These co-efficients lead to another set of free parameters, and therefore a larger search-spacefor the Optimization Algorithms. Due to the increased search-space, more train-ing data in form of manual measurements are needed to offset for a phenomenoncommonly referred to as Curse of dimensionality. This phenomenon describes thestatistical problems that arise when the volume of the high-dimensional space in-creases so fast that the training samples become sparsely distributed. Therefore,this technique was not employed in this thesis for the sake of simplicity.2.1.2 Optimization with Genetic AlgorithmsBy using an Optimization Algorithm, it is possible to find a set of parameters for amodel that minimizes a given cost function. If the cost function evaluates the error orthe"quality" of the model, the found parameters are optimal with respect to the costfunction. A set of nfreeparameters can also be understood as an element of a nfree-dimensional search-space inR. The cost function that is given by a nfree-parametercontrolled raytracer run can be assumed to be non-linear and non-differentiable dueto the recursive nature of the involved algorithms. Furthermore, it can be safelyassumed, that the function is non-convex leading to multiple local optima.Of the three evaluated heuristics: Minimum Least Squares, Simulated Annealingand Genetic Algorithms , the last one was capable to generate the best results withrespect to the reached optimum. In a Genetic Algorithm a set of parameters is calleda candidate solution(in the search-space) or simply referred to as an organism. Thesearch for the best set of parameters, also referred to as the fittest organism, is aniterative procedure. The procedure starts with an initialization step where a prede-fined number of organisms are created randomly. Depending on prior informationit is sensible to seed organism in regions of the search-space where optima are moreprobable. In the context of the given optimization problem, it makes sense to useprior knowledge of the estimated power levels of common APs.After the initialization, the fitness of each organism of the population is evaluatedby calculating the result of the underlying cost function. In the present use casethis means a full raytracer run over all APs and the aggregation of the error at allmeasured locations. Then, the main iteration of the algorithm starts by choosing aproportion of the population for breeding by using the magnitude of the fitness of theorganisms as the selection criteria. Breeding leads to new organism and therefore tothe exploration of the search-space. New organism are breeded by choosing a pair ofparent organisms and crossing over their genes(the nfree-parameters) by selectinggenes randomly from each parent. Additionally to this random selection, a randommutation of the genes can also be applied to allow for a deeper exploration of thesearch-space.For each breeded organism the fitness will then be evaluated and used to select apredefined number of the fittest children as the new population for the next iterationstep. Different termination conditions can be chosen, like a maximum number ofgenerations/iterations or a minimum needed change toward a minimum cost target.Through this evolutionary inspired selection process the convergence to an, at leastlocal, optimum of the cost function is guaranteed.