Numerical Optimization – An Engineering Perspective on Computation Time and Uncertainties

Proceedings of 3rd International Conference on Applied Research in Science, Technology and Knowledge

Year: 2019

DOI: https://www.doi.org/10.33422/3rd.stkconf.2019.03.179

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Numerical Optimization – An Engineering Perspective on Computation Time and Uncertainties

Johannes Schmelcher, Patrick Treichel, Kai Kreisköther, Dieter Gerling and Achim Kampker

ABSTRACT: 

Numerical optimization is a vital element in all fields of engineering. Especially in present times, finding better solutions to given design problems is of eminent importance. Either to reduce material usage, find more cost-effective solutions or shorten times in production systems. All these design problems involve their respective description of the optimization problem and thus a specific solution approach. Common to all optimization problems in engineering is the treatment of the design optimization problem as a mathematical optimization problem. To address the different types of optimization problems, various approach to solve them have been developed. Some use surrogate models to approximate the optimization problem, other approaches employ the actual physical description in the solution process. In this case, typically either deterministic and stochastic methods are used. A characteristic feature of optimization problems in engineering is the conflict between the time to calculate the objective function and the accuracy of the function value. The scope of this paper is to assess, how different solution algorithms can cope with this conflict. For this purpose, representatives of deterministic and stochastic solution algorithms will be used to solve special test functions in order to mimic real-world optimization problems. The algorithms will be assessed regarding their ability to cope with increasing times to calculate the objective function and different levels of accuracy concerning the function values. Additionally, based on this assessment, a new hybrid algorithm will be outlined which will be able to combine the advantages and lessen the drawbacks of the respective algorithms.

Keywords: Numerical Optimization, Computation Time, Uncertainties, Stochastic Optimization, Deterministic Optimization.