Abstract-In many engineering optimization problems, the number of fitness function evaluations is limited by time and cost. These problems pose a special challenge to the field of evolutionary computation, since existing evolutionary methods require a very large number of problem function evaluations. One popular way to address this challenge is the application of approximation models as a surrogate of the real fitness function. We propose a model assisted Evolution Strategy, which uses a Gaussian Process approximation model to pre-select the most promising solutions. To refine the pre-selection process we determine the likelihood of each individual to improve the overall best found solution. Due to this, the new algorithm has a much better convergence behavior and achieves better results than standard evolutionary optimization approaches with less fitness evaluations. Numerical results from extensive simulations on several high dimensional test functions including multimodal functions are presented.

Abstract-In this paper we investigate the impact of different crossover operators for a real-valued Evolutionary Algorithm on the constrained portfolio selection problem based on the Markowitz mean-variance model. We also introduce an extension of a real-valued genotype, which increases the performance of the Evolutionary Algorithm significantly, independent of the crossover operator used. This extension is based on the effect that most efficient portfolios only consist of a selection of few assets. Therefore, the portfolio selection problem is actually a combination of a knapsack and continuous parameter problem. We also introduce a repair mechanism and examine the impact of Lamarckism on the performance of the Evolutionary Algorithm.

Abstract. While the unconstrained portfolio optimization problem can be solved efficiently by standard algorithms, this is not the case for the portfolio optimization problem with additional real world constraints like cardinality constraints, buy-in thresholds, roundlots etc. In this paper we investigate two extensions to Evolutionary Algorithms (EA) applied to the portfolio optimization problem. First, we introduce a problem specific EA representation and then we add a local search for feasible solutions to improve the performance of the EA. All algorithms are compared on the constrained and unconstrained portfolio optimization problem.

Abstract. In financial engineering the problem of portfolio selection has drawn much attention in the last decades. But still unsolved problems remain, while on the one hand the type of model to use is still debated, even the most common models cannot be solved efficiently, if real world constraints are added. This is not only because the portfolio selection problem is multi-objective, but also because constraints may turn a formerly continuous problem into a discrete one. Therefore, we suggest to use a Multi-Objective Evolutionary Algorithm and compare discrete and continuous representations. To meet constraints we apply a repair mechanism and examine the impact of Lamarckism and the Baldwin Effect on several instances of the portfolio selection problem.

Abstract. We propose a new niching method for Evolutionary Algorithms which is able to identify and track global and local optima in a multimodal search space. To prevent the loss of diversity we replace the global selection pressure within a single population by local selection of a multi-population strategy. The sub-populations representing species specialized on niches are dynamically identified using standard clustering algorithms on a primordial population. With this multi-population strategy we are able to preserve diversity within the population and to identify global/local optima directly without further post-processing.

Abstract. In this paper we address the problem of finding gene regulatory networks from experimental DNA microarray data. Different approaches to infer the dependencies of gene regulatory networks by identifying parameters of mathematical models like complex S-systems or simple Random Boolean Networks can be found in literature. Due to the complexity of the inference problem some researchers suggested Evolutionary Algorithms for this purpose. We introduce enhancements to the Evolutionary Algorithm optimization process to infer the parameters of the non-linear system given by the observed data more reliably and precisely. Due to the limited number of available data the inferring problem is under-determined and ambiguous. Further on, the problem often is multi-modal and therefore appropriate optimization strategies become necessary. We propose a new method, which evolves the topology as well as the parameters of the mathematical model to find the correct network.

Abstract. While Single-Objective Evolutionary Algorithms (EAs) parallelization schemes are both well established and easy to implement, this is not the case for Multi-Objective Evolutionary Algorithms (MOEAs). Nevertheless, the need for parallelizing MOEAs arises in many real-world applications, where fitness evaluations and the optimization process can be very time consuming. In this paper, we test the 'divide and conquer' approach to parallelize MOEAs, aimed at improving the speed of convergence beyond a parallel island MOEA with migration. We also suggest a clustering based parallelization scheme for MOEAs and compare it to several alternative MOEA parallelization schemes on multiple standard multi-objective test functions.

Abstract. In this paper we address the problem of finding gene regulatory networks from experimental DNA microarray data. We introduce enhancements to an Evolutionary Algorithm optimization process to infer the parameters of the non-linear system given by the observed data more reliably and precisely. Due to the limited number of available data the inferring problem is under-determined and ambiguous. Further on, the problem often is multi-modal and therefore appropriate optimization strategies become necessary. Therefore, we propose a new method, which will suggest necessary additional biological experiments to remove the ambiguities.