Efficient Graph-based Genetic Programming Representation with Multiple Outputs

In this work, we explore and study the implication of having more than one output on a genetic programming （GP） graph-representation. This approach, called multiple interactive outputs in a single tree （MIOST）, is based on two ideas. First, we defined an approach, called interactivity within an individual （IWI）, which is based on a graph-GP representation. Second, we add to the individuals created with the IWI approach multiple outputs in their structures and as a result of this, we have MIOST. As a first step, we analyze the effects of IWI by using only mutations and analyze its implications （i.e., presence of neutrality）. Then, we continue testing the effectiveness of IWI by allowing mutations and the standard GP crossover in the evolutionary process. Finally, we tested the effectiveness of MIOST by using mutations and crossover and conducted extensive empirical results on different evolvable problems of different complexity taken from the literature. The results reported in this paper indicate that the proposed approach has a better overall performance in terms of consistency reaching feasible solutions.

Analysing the effect of stand density and site conditions on structure and growth of oak species using Nelder trials along an environmental gradient:experimental design,evaluation methods,and results

Background: Most current approaches in forest science and practice require information about structure and growth of individual trees rather than- or in addition to- sum and mean values of growth and yield at forest stand level as provided by classic experimental designs. By inventing the wheel design, Nelder provided the possibility to turn to the individual tree as basic information unit. Such trials provide valuable insights into the dependency of growth on stand density at particular sites.Methods: Here, we present an extension of the original design and evaluation by Nelder.(i) We established Nelder wheels along an environmental gradient through Europe in atlantic climate in Belgium and Germany, Mediterranean climate in Italy, continental climate in Hungary as well as on high land climate in Mexico. Such disjunct Nelder wheels along an environmental gradient can be regarded and analysed as a two-factor design with the factors of site condition and stand density.(ii) We present an advanced statistical approach to evaluate density dependent growth dynamics of trees planted in form of the Nelder design, which considers spatio-temporal autocorrelation.(iii)We prove the usefulness of the methods in improving ecological theory concerning density related productivity,trade-offs between facilitation and competition, and allometric relations between size variables.Results: First evaluations based on remeasured Nelder wheels in oak(Quercus robur L.) show a size growth differentiation during the first observation period. In particular, height growth is accelerated under higher competition indicating facilitation effects. We detect furthermore a high variability in allometric relations.Conclusions: The proposed design, methods, and results are discussed regarding their impact on forest practice,model building, and ecological theory. We conclude that the extended Nelder approach is highly efficient in providing currently lacking individual tree level information.