Felix Streichert

Evolution strategies assisted by Gaussian processes with improved preselection criterion

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 preselect the most promising solutions. To refine the preselection 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.

Evolutionary Algorithms and the Cardinality Constrained Portfolio Optimization Problem

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.

Evaluating a hybrid encoding and three crossover operators on the constrained portfolio selection problem

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.

A Clustering Based Niching EA for Multimodal Search Spaces

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.

Optimizing Topology and Parameters of Gene Regulatory Network Models from Time-Series Experiments

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.

Comparing Discrete and Continuous Genotypes on the Constrained Portfolio Selection Problem

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.

Evolution strategies with controlled model assistance

Evolutionary algorithms (EA) are excellent optimization tools for complex high-dimensional multimodal problems. However, they require a very large number of problem function evaluations. In many engineering and design optimization problems a single fitness evaluation is very expensive or time consuming. Therefore, standard evolutionary computation methods are not practical for such applications. Applying models as a surrogate of the true fitness function is a quite popular approach to handle this restriction. It is straightforward that the success of this approach depends highly on the quality of the approximation model. We propose a controlled model assisted evolution strategy (C-MAES), which uses a support vector regression (SVR) approximation by preselecting the most promising individuals. The model assistance on the evolutionary optimization process is dynamically controlled by a model quality based on the number of correctly preselected individuals. Numerical results from extensive simulations on high dimensional test functions including noisy functions and noisy functions with changing noise level are presented. The proposed C-MAES algorithm with controlled model assistance has a much better convergence rate and achieves better results than the model assisted algorithms without model control.

The Effect of Local Search on the Constrained Portfolio Selection Problem

The portfolio selection problem is a prominent example for multi-objective optimization in financial engineering. While for some problem instances of the portfolio selection problem there are efficient optimization algorithms, other problem instances can only be addressed by means of meta-heuristics like evolutionary algorithms. These more complicated problem instances include portfolio selection with multiple quadratic objectives or with non-linear constraints, like cardinality constraints. Evolutionary algorithms allow hybridization with local search heuristics, resulting in so called memetic algorithms. Such memetic approaches to the portfolio selection problem seem to be an interesting alternative. Unfortunately, the interaction between the evolutionary global search and the local search heuristic is complicated and difficult to understand. In this paper we evaluate the hybridization of a multi-objective evolutionary algorithm and a quadratic programming local search on multiple instances of the constrained and unconstrained portfolio selection problem using a problem specific representation. This multi-objective memetic algorithm proves to be a two-edged approach: On the one hand it improves the convergence rate for some problem instances. While on other hand problem instances the local search causes a neutral search space and eventually premature convergence. This paper investigates this behavior more closely, offers a plausible explanation and also outlines a possible remedy.

A memetic inference method for gene regulatory networks based on S-Systems

In this paper, we address the problem of finding gene regulatory networks from experimental DNA microarray data. As underlying mathematical model we used S-Systems, a quantitative model, which recently has found increased attention in the literature. Due to the complexity of the inference problem some researchers suggested evolutionary algorithms for this purpose. We introduce enhancements to this optimization process to infer the parameters of sparsely connected non-linear systems 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. In this paper, we propose a new method, which evolves the topology as well as the parameters of the mathematical model to find the correct network. This method is compared to standard algorithms found in the literature.

Comparing Genetic Programming and Evolution Strategies on Inferring Gene Regulatory Networks

In recent years several strategies for inferring gene regulatory networks from observed time series data of gene expression have been suggested based on Evolutionary Algorithms. But often only few problem instances are investigated and the proposed strategies are rarely compared to alternative strategies. In this paper we compare Evolution Strategies and Genetic Programming with respect to their performance on multiple problem instances with varying parameters. We show that single problem instances are not sufficient to prove the effectiveness of a given strategy and that the Genetic Programming approach is less prone to varying instances than the Evolution Strategy.