document: When we formulate the downscaling problem as a multi-objective optimization problem, we face, however, the following problems. Minimizing the sum of different objectives is problematic, since they may have different units and ranges. Even with an appropriate scaling procedure there is a risk of treating the objectives unequally or getting trapped in a local minimum. Firstly, we can never know, what is the minimum value of each objective that can be achieved by the regression. Thus, designing an appropriate scaling procedure is difficult and one would need to decide on the relative importance of the different objectives in advance. Secondly, adding multiple, conflicting objectives very likely results in a fitness function with multiple local minima, which makes optimization more difficult. To avoid these problems, we have implemented fitness calculation according to the Strength Pareto Evolutionary Algorithm (SPEA) by Zitzler and Thiele (1999), instead of using a single (weighted) fitness or cost function. Approaches for multi-objective optimization like SPEA are widely used in evolutionary computation. In SPEA the fitness calculation during the fitting procedure is based on an intercomparison of the different models. Further, a finite set of so called Pareto optimal models (downscaling rules) is returned.
doc_bio_tags: O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B I O O O B I I I B O O O O O O O O O O O O O O O O O O B O B O O O O B I O B O B I O O O O O O O O O O O O O O O O O O O O B I I B I O O
extractive_keyphrases: downscaling rules evolutionary computation fitness calculation optimization pareto optimal models regression scaling procedure spea strength pareto evolutionary algorithm
abstractive_keyphrases: multi-objective optimization using a single (weighted) fitness or cost function