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.