Dirk Büche

Accelerating evolutionary algorithms with Gaussian process fitness function models

We present an overview of evolutionary algorithms that use empirical models of the fitness function to accelerate convergence, distinguishing between evolution control and the surrogate approach. We describe the Gaussian process model and propose using it as an inexpensive fitness function surrogate. Implementation issues such as efficient and numerically stable computation, exploration versus exploitation, local modeling, multiple objectives and constraints, and failed evaluations are addressed. Our resulting Gaussian process optimization procedure clearly outperforms other evolutionary strategies on standard test functions as well as on a real-world problem: the optimization of stationary gas turbine compressor profiles.

Multiobjective evolutionary algorithm for the optimization of noisy combustion processes

This work introduces a multiobjective evolutionary algorithm capable of handling noisy problems with a particular emphasis on robustness against unexpected measurements (outliers). The algorithm is based on the Strength Pareto evolutionary algorithm of Zitzler and Thiele and includes the new concepts of domination dependent lifetime, re-evaluation of solutions and modifications in the update of the archive population. Several tests on prototypical functions underline the improvements in convergence speed and robustness of the extended algorithm. The proposed algorithm is implemented to the Pareto optimization of the combustion process of a stationary gas turbine in an industrial setup. The Pareto front is constructed for the objectives of minimization of NO/sub x/ emissions and reduction of the pressure fluctuations (pulsation) of the flame. Both objectives are conflicting affecting the environment and the lifetime of the turbine, respectively. The optimization leads a Pareto front corresponding to reduced emissions and pulsation of the burner. The physical implications of the solutions are discussed and the algorithm is evaluated.

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.

Self-organizing Maps for Pareto Optimization of Airfoils

This work introduces a new recombination and a new mutation operator for an accelerated evolutionary algorithm in the context of Pareto optimization. Both operators are based on a self-organizing map, which is actively learning from the evolution in order to adapt the mutation step size and improve convergence speed. Standard selection operators can be used in conjunction with these operators.The new operators are applied to the Pareto optimization of an airfoil for minimizing the aerodynamic profile losses at the design operating point and maximizing the operating range. The profile performance is analyzed with a quasi 3D computational fluid dynamics (Q3D CFD) solver for the design condition and two off-design conditions (one positive and one negative incidence).The new concept is to define a free scaling factor, which is multiplied to the off-design incidences. The scaling factor is considered as an additional design variable and at the same time as objective function for indexing the operating range, which has to be maximized. We show that 2 off-design incidences are sufficient for the Pareto optimization and that the computation of a complete loss polar is not necessary. In addition, this approach answers the question of how to set the incidence values by defining them as design variables of the optimization.

Multi-Objective Evolutionary Algorithm for Optimization of Combustion Processes

This work introduces a multi-objective evolutionary algorithm capable of handling noisy problems like experimental setups with a particular emphasis on robustness against unexpected measurements (outliers). The algorithm is based on the Strength Pareto Evolutionary Algorithm (SPEA) of Zitzler and Thiele and includes the new concepts of domination dependent lifetime, re-evaluation of solutions and modifications in the update of the archive. Several tests on prototypical functions underline the improvements in convergence speed and robustness of the extended algorithm. The proposed algorithm is implemented to the Pareto optimization of the combustion process of a stationary gas turbine in an industrial setup. The free parameters of the optimization are the fuel injection rates through transverse jets. The Pareto front is constructed for the objectives of minimization of NO x emissions and reduction of the pressure fluctuations (pulsation) of the flame. Both objectives are conflicting affecting the environment and the lifetime of the turbine, respectively. The optimization leads a Pareto front corresponding to reduced emissions and pulsation of the burner. The physical implications of the solutions are discussed and the algorithm is evaluated.