Sibylle D. Müller

Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES)

This paper presents a novel evolutionary optimization strategy based on the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). This new approach is intended to reduce the number of generations required for convergence to the optimum. Reducing the number of generations, i.e., the time complexity of the algorithm, is important if a large population size is desired: (1) to reduce the effect of noise; (2) to improve global search properties; and (3) to implement the algorithm on (highly) parallel machines. Our method results in a highly parallel algorithm which scales favorably with large numbers of processors. This is accomplished by efficiently incorporating the available information from a large population, thus significantly reducing the number of generations needed to adapt the covariance matrix. The original version of the CMA-ES was designed to reliably adapt the covariance matrix in small populations but it cannot exploit large populations efficiently. Our modifications scale up the efficiency to population sizes of up to 10n, where n is the problem dimension. This method has been applied to a large number of test problems, demonstrating that in many cases the CMA-ES can be advanced from quadratic to linear time complexity.

Step size adaptation in evolution strategies using reinforcement learning

We discuss the implementation of a learning algorithm for determining adaptation parameters in evolution strategies. As an initial test case, we consider the application of reinforcement learning for determining the relationship between success rates and the adaptation of step sizes in the (1+1)-evolution strategy. The results from the new adaptive scheme when applied to several test functions are compared with those obtained from the (1+1)-evolution strategy with a priori selected parameters. Our results indicate that assigning good reward measures seems to be crucial to the performance of the combined strategy.

Self-adaptation for multi-objective evolutionary algorithms

Evolutionary Algorithms are a standard tool for multi-objective optimization that are able to approximate the Pareto front in a single optimization run. However, for some selection operators, the algorithm stagnates at a certain distance from the Pareto front without convergence for further iterations. We analyze this observation for different multi-objective selection operators. We derive a simple analytical estimate of the stagnation distance for several selection operators, that use the dominance criterion for the fitness assignment. Two of the examined operators are shown to converge with arbitrary precision to the Pareto front. We exploit this property and propose a novel algorithm to increase their convergence speed by introducing suitable self-adaptive mutation. This adaptive mutation takes into account the distance to the Pareto front. All algorithms are analyzed on a 2- and 3-objective test function.

Increasing the Serial and the Parallel Performance of the CMA-Evolution Strategy with Large Populations

The derandomized evolution strategy (ES) with covariance matrix adaptation (CMA), is modified with the goal to speed up the algorithm in terms of needed number of generations. The idea of the modification of the algorithm is to adapt the covariance matrix in a faster way than in the original version by using a larger amount of the information contained in large populations. The original version of the CMA was designed to reliably adapt the covariance matrix in small populations and turned out to be highly efficient in this case. The modification scales up the efficiency to population sizes of up to 10n, where n ist the problem dimension. If enough processors are available, the use of large populations and thus of evaluating a large number of search points per generation is not a problem since the algorithm can be easily parallelized.

Microchannel Optimization Using Multiobjective Evolution Strategies

We implement multiobjective evolutionary algorithms for the optimization of micro-fluidic devices. In this work we discuss the development of multimembered evolution strategies with step size adaptation in conjunction with the Strength Pareto Approach. In order to support targeting, an extension of the Strength Pareto Evolutionary Algorithm is proposed. The results suggest a novel design for micro-fluidic devices used for DNA sequencing.

Evolution strategies for the optimization of microdevices

Single- and multicriteria evolution strategies are implemented to optimize micro-fluidic devices, namely the shape of a microchannel used for bioanalysls and the mixing rate in a micromixer used for medical applications. First, multimembered evolution strategies employing mutative step size adaptation are combined with the Strength Pareto approach. In order to support targetting, an extension of the Strength Pareto evolutionary algorithm is proposed. Applied on the optimization of the microchannel, these algorithms suggest a novel design with improved properties over traditional designs. A comparison with a gradient method is presented. Second, an evolution strategy with derandomized self-adaptation of the mutation distribution is used to optimize the micromixer. The results agree well with dynamical systems theory.

Flow optimization using stochastic algorithms

We present a set of stochastic optimization strategies and we discuss their applications to fluid mechanics problems. The optimization strategies are based on state-of-the-art stochastic algorithms and are extended for the application on fluid dynamics problems. The extensions address the question of parallelization, strategy parameter adaptation, robustness to noise, multiple objective optimization, and the use of empirical models. The applications range from burner design for gas turbines, cylinder drag minimization, aerodynamic profile design, micromixer, microchannel, jet mixing to aircraft trailing vortex destruction.

Control of Micromixers, Jets, and Turbine Cooling using Evolution Strategies

We present a class of evolution strategies and we discuss three engineering applications in the fields of mixing control and turbomachinery: (i) flow in micromixers, (ii) jet flow, and (iii) turbine cooling. Evolution strategies are chosen as optimization method as they are capable of handling noisy and multimodal functions, inherent to these applications, in an automated fashion.