@inproceedings{46415, abstract = {{Noisy environments are a challenging task for multiobjective evolutionary algorithms. The algorithms may be trapped in local optima or even become a random search in the decision and objective space. In the course of the paper the classical definition of Pareto-dominance is enhanced subject to noisy objective functions in order to make the evolutionary search process more robust and to generate a reliable Pareto front. At each point in the decision space the objective functions are evaluated a fixed number of times and the convex hull of the objective function vectors is computed. Expectation is associated with the median of the objective function values while uncertainty is reflected by the average distance of the median in each dimension to the points defining the convex hull. By combining these two indicators a new concept of Pareto-dominance is set up. An implementation in NSGA-II and application to test problems show a gain in robustness and search quality.}}, author = {{Trautmann, Heike and Mehnen, Jorn and Naujoks, Boris}}, booktitle = {{2009 IEEE Congress on Evolutionary Computation}}, issn = {{1941-0026}}, pages = {{3119--3126}}, title = {{{Pareto-dominance in noisy environments}}}, doi = {{10.1109/CEC.2009.4983338}}, year = {{2009}}, } @inproceedings{46413, abstract = {{Industry applications of multiobjective optimization problems mostly are characterized by the demand for high quality solutions on the one hand. On the other hand an optimization result is desired which at any rate meets the time constraints for the evolutionary multiobjective algorithms (EMOA). The handling of this trade-off is a frequently discussed issue in multiobjective evolutionary optimization.}}, author = {{Naujoks, Boris and Trautmann, Heike}}, booktitle = {{2009 IEEE Congress on Evolutionary Computation}}, issn = {{1941-0026}}, pages = {{332--339}}, title = {{{Online convergence detection for multiobjective aerodynamic applications}}}, doi = {{10.1109/CEC.2009.4982966}}, year = {{2009}}, } @article{46416, author = {{Trautmann, Heike and Mehnen, J}}, journal = {{International Journal of Computational Intelligence Research}}, number = {{2}}, pages = {{72–78}}, title = {{{Statistical Methods for Improving Multi-objective Evolutionary Optimisation}}}, volume = {{5}}, year = {{2009}}, } @article{46417, abstract = {{ In this article a method for including a priori preferences of decision makers into multicriteria optimization problems is presented. A set of Pareto-optimal solutions is determined via desirability functions of the objectives which reveal experts’ preferences regarding different objective regions. An application to noisy objective functions is not straightforward but very relevant for practical applications. Two approaches are introduced in order to handle the respective uncertainties by means of the proposed preference-based Pareto optimization. By applying the methods to the original and uncertain Binh problem and a noisy single cut turning cost optimization problem, these approaches prove to be very effective in focusing on different parts of the Pareto front of the ori-ginal problem in both certain and noisy environments. }}, author = {{Trautmann, Heike and Mehnen, Jörn}}, journal = {{Engineering Optimization}}, number = {{1}}, pages = {{23--38}}, publisher = {{Taylor & Francis}}, title = {{{Preference-based Pareto optimization in certain and noisy environments}}}, doi = {{10.1080/03052150802347926}}, volume = {{41}}, year = {{2009}}, } @article{46418, abstract = {{In this paper, two approaches for estimating the generation in which a multi-objective evolutionary algorithm (MOEA) shows statistically significant signs of convergence are introduced. A set-based perspective is taken where convergence is measured by performance indicators. The proposed techniques fulfill the requirements of proper statistical assessment on the one hand and efficient optimisation for real-world problems on the other hand. The first approach accounts for the stochastic nature of the MOEA by repeating the optimisation runs for increasing generation numbers and analysing the performance indicators using statistical tools. This technique results in a very robust offline procedure. Moreover, an online convergence detection method is introduced as well. This method automatically stops the MOEA when either the variance of the performance indicators falls below a specified threshold or a stagnation of their overall trend is detected. Both methods are analysed and compared for two MOEA and on different classes of benchmark functions. It is shown that the methods successfully operate on all stated problems needing less function evaluations while preserving good approximation quality at the same time.}}, author = {{Trautmann, Heike and Wagner, T. and Naujoks, B. and Preuss, M. and Mehnen, J.}}, issn = {{1063-6560}}, journal = {{Evolutionary Computation}}, number = {{4}}, pages = {{493--509}}, title = {{{Statistical Methods for Convergence Detection of Multi-Objective Evolutionary Algorithms}}}, doi = {{10.1162/evco.2009.17.4.17403}}, volume = {{17}}, year = {{2009}}, } @inproceedings{46419, author = {{Mehnen, J and Trautmann, Heike}}, booktitle = {{Proceedings of the 6$^th$ CIRP International Seminar on Intelligent Computation in Manufacturing Engineering (CIRP ICME ’08)}}, editor = {{Teti, R}}, publisher = {{Copyright C.O.C. Com. org. Conv.}}, title = {{{Robust Multi-objective Optimisation of Weld Bead Geometry for Additive Manufacturing}}}, year = {{2008}}, } @inproceedings{46420, abstract = {{A systematic approach for determining the generation number at which a specific Multi-Objective Evolutionary Algorithm (MOEA) has converged for a given optimization problem is introduced. Convergence is measured by the performance indicators Generational Distance, Spread and Hypervolume. The stochastic nature of the MOEA is taken into account by repeated runs per generation number which results in a highly robust procedure. For each generation number the MOEA is repeated a fixed number of times, and the Kolmogorow-Smirnov-Test is used in order to decide if a significant change in performance is gained in comparison to preceding generations. A comparison of different MOEAs on a problem with respect to necessary generation numbers becomes possible, and the understanding of the algorithm’s behaviour is supported by analysing the development of the indicator values. The procedure is illustrated by means of standard test problems.}}, author = {{Trautmann, Heike and Ligges, Uwe and Mehnen, Jörn and Preuss, Mike}}, booktitle = {{Parallel Problem Solving from Nature – PPSN X}}, editor = {{Rudolph, Günter and Jansen, Thomas and Beume, Nicola and Lucas, Simon and Poloni, Carlo}}, isbn = {{978-3-540-87700-4}}, pages = {{825–836}}, publisher = {{Springer Berlin Heidelberg}}, title = {{{A Convergence Criterion for Multiobjective Evolutionary Algorithms Based on Systematic Statistical Testing}}}, year = {{2008}}, } @inproceedings{46421, abstract = {{Multi-objective evolutionary algorithms (MOEAs) are generally designed to find a well spread Pareto-front approximation. Often, only a small section of this front may be of practical interest. Desirability functions (DFs) are able to describe user preferences intuitively. Furthermore, DFs can be attached to any fitness function easily. This way, desirability functions can help in guiding MOEAs without introducing additional restrictions or changes to the algorithm. The application of noisy fitness functions is not straight forward but relevant to many real-world problems. Therefore, a variant of Harrington’s one-sided desirability function using expectations is introduced which takes noise into account. A deterministic strategy as well as the XSGA-II are used in combination with DF to solve a noisy Binh problem and a noisy cost estimation problem for turning processes.}}, author = {{Mehnen, Jorn and Trautmann, Heike and Tiwari, Ashutosh}}, booktitle = {{2007 IEEE Congress on Evolutionary Computation}}, issn = {{1941-0026}}, pages = {{2687--2694}}, title = {{{Introducing user preference using Desirability Functions in Multi-Objective Evolutionary Optimisation of noisy processes}}}, doi = {{10.1109/CEC.2007.4424810}}, year = {{2007}}, } @article{46423, abstract = {{The concept of desirability is a means for complexity reduction of multivariate quality optimization. This paper provides a theoretical breakthrough regarding desirability indices, which application fields were formerly limited primarily by the lack of its distribution. Focussed are the distributions of Harrington’s desirability functions and different types of the desirability index.}}, author = {{Trautmann, Heike and Weihs, C}}, journal = {{Metrika}}, number = {{2}}, pages = {{207–213}}, title = {{{On the Distribution of the Desirability Index using Harrington’s Desirability Function}}}, doi = {{10.1007/s00184-005-0012-0}}, volume = {{63}}, year = {{2006}}, } @inproceedings{46422, author = {{Mehnen, J and Trautmann, Heike}}, booktitle = {{CIRP ICME ’06) — Proceedings of the 5$^th$ CIRP International Seminar on Intelligent Computation in Manufacturing Engineering}}, editor = {{Teti, R}}, pages = {{293–298}}, publisher = {{C.O.C. Com. org. Conv. CIRP ICME ’06}}, title = {{{Integration of Expert’s Preferences in Pareto Optimization by Desirability Function Techniques}}}, year = {{2006}}, }