# Multicriteria Optimisation

The project "Multicriteria Optimisation" considers mathematical questions and discrete problems within the CRC 1026 "Sustainable Manufacturing". The three sustainability dimensions "economic", "environmental" and "social", respectively, are considered as different objective functions by the project A5. Hence, discrete problems and mathematical questions are modelled by a feasible space of solutions and several objectives which have to be optimised simultaneously. In contrast to the single-criteria case, it is generally not possible to find a solution which optimises all considered objectives simultaneously. Instead one has to deal with trade-offs. For example, the cheapest way to manufacture a certain amount of bicycle frames might not be the environmentally friendliest. A solution that can be improved in at least one objective without getting worse off in the other is called *inefficient* and will generally be neglected by a decision maker. Hence, only the *efficient* solutions are interesting from a decision maker's point of view. Besides the mathematical questions about the existence and number of efficient solutions and the algorithmic approaches of how to compute them, the project A5 is also concerned with the modelling of quantitative problems within the CRC 1026. With respect to models the focus and expertise is on mixed integer programming.

We have developed PolySCIP, an open-source and freely available solver which aims at solving multicriteria mixed integer programs with an arbitrary number of objectives. With respect to scenario analysis two tools, tech-con and field-con, were implemented. Exemplary applications like the optimization of process chains for bicycle frame manufacturing, the selection of sustainable welding processes and design decision support are documented.

# Results from the first funding period

__PolySCIP__

Project A5 develops PolySCIP (link), a solver for multicriteria linear and multicriteria (mixed) integer problems.

__Scenario Tool__

Two software-tools for the creation of surrounding field scenarios on the one hand (Clustering with "FieldCon") and creation of technology scenarios (system creation with "TechCon") on the other hand can be downloaded. These tools have been developed in cooperation of the projects A1 and A5.

#### „FieldCon" for creation of surrounding field scenarios

** Surrounding field scenarios** are used to depict different future developments, the so called scenarios. For this purpose the approach of clustering of key factors of the surrounding field, which show a strong connection, is used.

#### „TechCon" for creation of technology scenarios

** Technology scenarios** are used to find useful and sustainable combinations of system elements to systems. This allows for example the technical reasonable and sustainable combination of alternative technologies.

# Team

Dipl.-Math. Sebastian Schenker

Prof. Dr. Ralf Borndörfer

Prof. Dr. Martin Skutella