# Solution Spaces

## Towards the theoretical limit of optimal requirement decomposition using solution spaces for complex systems design

### Keywords

Solution space engineering, requirement decomposition, complex systems design, optimization

### Problem

Separating a system into different, independent components is a development approach which can reduce the complexity of a given task and enable concurrent engineering of each part of the project. In this context, generating good component requirements, which guarantee that the overall system goal is reached when they are realized and are only as restrictive as necessary, is a crucial step in order to achieve a good design by the end of the process. However, it is still an open challenge to compute such requirements for complex, non-linear systems.

Current methods compute solution spaces that are Cartesian products of feasible regions for component properties, and procedures for non-linear systems are restricted to one-dimensional requirements, where each relevant property can be separately designed from each other. That, however, can be overly restrictive, as a given component may be composed of several properties, and thus independence from each other leads to unnecessary loss of solution space.

### Goal

The goal of this project is to develop a method to compute and maximize generalized component solution spaces, which are the largest permissible regions for all relevant properties of one component. The generated component requirements should allow for maximum design freedom while still satisfying all design objectives when realized.

### Approach

In order to achieve this, smaller, simpler problems will be analyzed in detail, and transfer methods to be compute solution spaces will be considered and tested in these problems. Methods will be developed and chosen based on their numerical performance and accuracy, and the selected ones will be integrated into a new optimization tool. This tool will then be used also for scaled-up problems and applications, and finally an analysis will be carried out to generalize the obtained results.

### Project Duration

January 2022 until January 2025

### Funding

DFG