Optimization and Modeling Techniques for Food Service Appliances

In the last couple of years food service sector is embracing the fourth industrial revolution. Electrolux Professional, as a leader in this sector, is continuously searching for smart functionalities and intelligent products to improve the design process or directly the final products. This thesis, funded by Electrolux Professional, starts the analysis in food service sector of the emerging type of systems called Cyber Physical Systems, i.e. systems where computational and dynamical/physical capabilities as deeply intertwined. We present four different analyses focusing on optimization problems and reachability analyses. These two aspects even overlap in one case study. We start proposing a new functionality for professional ovens able to sort a list of cooking recipes in order to minimize the total energy consumption. Then a multi-objective optimization problem to select the complex parameters for a thawing system. For this second project we propose two approaches: a multi-objective analysis using a genetic algorithm and a reformulation of the optimization problem as a reachability analysis over a hybrid system. With this second study we build a bridge between the optimization field and the tools used for verification analysis. We open here the second topic of this thesis and the next two projects deal with reachability analysis. We select a specific reachability tool based on the Bernstein approximation for polynomial functions. We apply the Bernstein theory to the trajectories of a robot arm in order to check the collision with an obstacle or to prevent the collision applying a set of constraints in the joint domain. Finally, the last analysis touches another important trend of these years: Neural Networks (NN). We focus on the verification of neural net control systems (NNCS), i.e. systems where the NN are used to control the physical process. The challenge here is to be able to estimate and bound the behavior of the neural net. We propose a method, to this end, using rational and polynomial approximations for activation functions in order to bound the output image of each layer using the Bernstein expansion.