## 7 Summary  
This paper presents a methodology for automating race strategy decisions in circuit motorsport. The focus is on the Formula 1 racing series and, thus, on the optimal determination of pit stops to replace worn-out tires. To be able to determine an initial estimate of the optimal race strategy, a quadratic optimization problem was set up that minimizes a driver's race duration, assuming a race without opponents. However, this estimate is not sufficient to be used in a race simulation or a real-world race, as it takes neither the opponent drivers nor the particular race situation into account. Therefore, we developed a virtual strategy engineer (VSE) based on two artificial neural networks. The first one decides in each respective lap whether the driver should make a pit stop. If it chooses to call for a pit stop, a second neural network determines which of the available tire compounds should be fitted to the car. Both neural networks were trained on Formula 1 timing data of the seasons from 2014 to 2019. The presented results of a race simulation, in which the VSE is used to make the race strategy decisions, indicate that the VSE makes reasonable decisions and is able to adapt its strategy to the particular race situation. Thus, the VSE improves a race simulation's realism and can support a real strategy engineer in his decisions.  
The entire Python code for the race simulation, including the trained VSE models, is available under an open-source license on GitHub ([[https://github.com/TUMFTM/race-simulation](https://github.com/TUMFTM/race-simulation)]([https://github.com/TUMFTM/race-simulation](https://github.com/TUMFTM/race-simulation))).  
The initial concept of automated decision-making based on neural networks was developed within the research project by [PERSON] under [PERSON]'s supervision in his semester thesis. As the first author, [PERSON] revised and extended the methodology. He reworked the feature selection and pre-processing, introduced the hybrid neural network, and integrated the approach into the race simulation. He also provided the following parts of the paper: database creation, formulation and implementation of the optimization problem, data analysis, and result evaluation. Moreover, he wrote most parts of the paper. After completing his semester thesis, [PERSON] started working on the reinforcement learning approach for his master's thesis within the research project. He wrote the outlook on this topic. As the mentor of the research project, [PERSON] critically scrutinized the approaches. [PERSON] and [PERSON] contributed to the conception of the research project and critically revised the paper. Conceptualization, A.H., A.T., M.G., J.B.; data curation, A.H.; formal analysis, A.H.; methodology, A.H., A.T.; software, A.H., A.T.; validation, A.H.; writing--original draft preparation, A.H., A.T.; writing--review and editing, A.H.; visualization, A.H.; supervision, M.G., J.B. All authors have read and agreed to the published version of the manuscript.  
Research was supported by the basic research fund of the Institute of Automotive Technology of the Technical University of Munich.  
The authors declare no conflict of interest.  
The following abbreviations are used in this manuscript:  
F1 FA Formula 1 World Championship  
FCY Full-Course Yellow  
FFNN Feed-Forward Neural Network  
LSTM Long Short-Term Memory  
MIQP Mixed-Integer Quadratic Programming  
ML Machine-Learning  
NN Neural Network  
RNN Recurrent Neural Network  
RS Race Simulation  
SC Safety Car  
VSC Virtual Safety Car  
VSE Virtual Strategy Engineer (combination of both NNs)