Keywords: screw-type machine, multi-objective optimization, evolutionary algorithm, directed mutation, skew-normal distribution.

This paper presents a novel evolutionary optimization method applied to a real world scenario. The starting point is the well known evolution strategy optimization algorithm, here enhanced by the concept of directed mutation. Directed mutation has already been shown to improve the efficiency of evolutionary algorithms significantly for a broad spectrum of test problems. While the capability of directed mutation thus has been shown in the sandbox, in the case of real world applications it has not been done so far. The aim of this paper is to make up for this, considering a high dimensional problem with several constraints. Optimizing a screw-type machine, we will be concerned with a problem from mechanical engineering.

Designing any type of machine leads inevitably to the question of the optimized construction parameters. Mostly this can be estimated by the degree of performance with regard to the users demands. Thereby it appears the difficulty to define a capable performance degree and to evaluate a possible solution with a maintainable expense. Usually there are many different criteria to be considered. Thus an appropriate optimization method has to be able to either represent different criteria within one utility function or to treat several criteria in parallel. This problem will be investigated in this paper using a dry running twin-screw compressor [1] as an example. The most common form of screw-type machines are rotary compressors, especially the helical twin screw-type. Meshing male and female screw-rotors rotate inside a housing in opposite directions and thereby trapping air, reducing the volume of the air along the rotors to the air discharge point. Rotary screw-type compressors have low: initial cost, compact size, low weight, and are easy to maintain. A special topic during the construction of screw machines is to be seen in the design of the rotor geometry of an individual stage. One can differentiate between three-dimensional characteristics such as rotor length and wrap angle as well as two-dimensional characteristics such as rotor diameters, numbers of lobes and the lobe profile.

Tackled here is the parallel optimization of two criteria of the two-dimensional rotor profile by applying an evolution strategy with different mutation operators. Evolution strategies [2,3] are a set of optimization algorithms inspired by biology and especially by those processes that allow populations of organisms to adopt to their surrounding environment, namely the principles of variation and selection. Besides the conventional mutation operators (isotropic and scaled mutation) a novel variant, the directed mutation is proposed. Directed mutation [4,5] will impart true directionality to the search which means that for every problem dimension a tendency towards the positive or negative domain can be established by the mutation distribution. Thus, hopefully the mutation distribution will adapt favorable directions over the generations and sustain further advance into it.

It will turn out that with the directed mutation an operator is given that clearly outperforms the conventional mutation strategies for this high dimensional, constraint multi-objective real-world optimization problem. All results but one dominate all runs of the other strategies, i.e. are better in both criteria. Further, the resulting solutions form relatively sharp Pareto fronts and cover a good spectrum of the search space with respect to both criteria. Last, the directed mutation shows the greatest diversity under and within the different runs.

1

K. Kauder, B. Reusch, M. Helpertz, and S. Berlik, "Optimisation methods for rotors of twin-screw compressors". In VDI Berichte, volume 1715. VDI-Verlag, 2002.

2

I. Rechenberg, "Evolutionsstrategie '94", Frommann-Holzboog Verlag, Stuttgart, 1994.

3

H.-P. Schwefel, "Evolution and Optimum Seeking". John Wiley & Sons, New York, 1995.

4

S. Berlik, "Directed mutation by means of the skew-normal distribution". In Bernd Reusch, editor, Proc. of the Int. Conf. on Computational Intelligence, FUZZY DAYS, Sep. 29 - Oct. 1, 2004, Dortmund, Germany, Advances in Soft Computing, pages 35-50. Springer-Verlag Berlin Heidelberg, 2005. doi:10.1007/3-540-31182-3_4

5

S. Berlik and B. Reusch, "Directed mutation operators - an overview". In Rajiv Khosla, Robert J. Howlett, and Lakhmi C. Jain, editors, Proc. of the 9th Int. Conf. on Knowledge-Based & Intelligent Information & Engineering Systems, KES 2005, Sept. 14-16, 2005, Melbourne, Australia, volume 3683 of Lecture Notes in Computer Scienc, pages 1151-1159. Springer-Verlag Berlin Heidelberg, 2005.

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