# MLP-Supported Mathematical Optimization of Simulation Models: Investigation into the Approximation of Black Box Functions of Any Simulation Model with MLPs with the Aim of Functional Analysis

### Bastian Stollfuss, Bastian Stollfuss, Michael Bacher

#### 2022

#### Abstract

This paper contains results from a feasibility study. The optimization of manufacturing processes is an elementary part of economic thinking and acting. In many cases, complex processes have unknown analytical and mathematical methods. If mathematical functions for the behaviour of a process are missing, one often tries to optimize the process according to the trial-and-error principle in combination with expertise. However, this method requires a lot of time, computational resources, and trained personnel to validate the results. The method developed below can significantly reduce these cost factors by mathematically optimizing the unknown functions of a complex system in an automatic process. This is accomplished with discrete performance and behaviour measurements. For this purpose, an approximate prediction function is modelled using a multi-layer perceptron (MLP). The resulting continuous function can now be analysed with mathematical optimization methods. After formulating the learned prediction function, it is examined for minima using Newton’s method. It is not necessary to know the exact mathematical and physical context of the system that needs improving. Calculating a precise interpolation also results in further optimization and visualization options for the production plant.

Download#### Paper Citation

#### in Harvard Style

Stollfuss B. and Bacher M. (2022). **MLP-Supported Mathematical Optimization of Simulation Models: Investigation into the Approximation of Black Box Functions of Any Simulation Model with MLPs with the Aim of Functional Analysis**. In *Proceedings of the 3rd International Conference on Innovative Intelligent Industrial Production and Logistics - Volume 1: IN4PL,* ISBN 978-989-758-612-5, pages 107-114. DOI: 10.5220/0011379800003329

#### in Bibtex Style

@conference{in4pl22,

author={Bastian Stollfuss and Michael Bacher},

title={MLP-Supported Mathematical Optimization of Simulation Models: Investigation into the Approximation of Black Box Functions of Any Simulation Model with MLPs with the Aim of Functional Analysis},

booktitle={Proceedings of the 3rd International Conference on Innovative Intelligent Industrial Production and Logistics - Volume 1: IN4PL,},

year={2022},

pages={107-114},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0011379800003329},

isbn={978-989-758-612-5},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 3rd International Conference on Innovative Intelligent Industrial Production and Logistics - Volume 1: IN4PL,

TI - MLP-Supported Mathematical Optimization of Simulation Models: Investigation into the Approximation of Black Box Functions of Any Simulation Model with MLPs with the Aim of Functional Analysis

SN - 978-989-758-612-5

AU - Stollfuss B.

AU - Bacher M.

PY - 2022

SP - 107

EP - 114

DO - 10.5220/0011379800003329