  Optimizing a building's energy supply design is a task with multiple
competing criteria, where not only monetary but also, for example, an
environmental objective shall be taken into account. Moreover, when deciding
which storages and heating and cooling units to purchase
(here-and-now-decisions), there is uncertainty about future developments of
prices for energy, e.g. electricity and gas. This can be accounted for later by
operating the units accordingly (wait-and-see-decisions), once the uncertainty
revealed itself. Therefore, the problem can be modeled as an adjustable robust
optimization problem. We combine adjustable robustness and multicriteria
optimization for the case of building energy supply design and solve the
resulting problem using a column and constraint generation algorithm in
combination with an $\varepsilon$-constraint approach.
  In the multicriteria adjustable robust problem, we simultaneously minimize
worst-case cost regret and carbon emissions. We take into account future price
uncertainties and consider the results in the light of information gap decision
theory to find a trade-off between security against price fluctuations and
over-conservatism. We present the model, a solution strategy and discuss
different application scenarios for a case study building.
