Multicriteria Adjustable Regret Robust Optimization for Building Energy Supply Design

Optimizing a building’s energy supply design is a task with multiple com-peting criteria, where not only monetary but also, for example, an envi-ronmental objective shall be taken into account. Moreover, when decidingwhich storages and heating and cooling units to purchase (here-and-now-decisions), there is uncertainty about future developments of prices for en-ergy, e.g. electricity and gas. This can be accounted for later by operatingthe units accordingly (wait-and-see-decisions), once the uncertainty revealeditself. Therefore, the problem can be modeled as an adjustable robust opti-mization problem. We combine adjustable robustness and multicriteria opti-mization for the case of building energy supply design and solve the resultingproblem using a column and constraint generation algorithm in combinationwith an ε-constraint approach.In the multicriteria adjustable robust problem, we simultaneously min-imize worst-case cost regret and carbon emissions. We take into accountfuture price uncertainties and consider the results in the light of informationgap decision theory to find a trade-off between security against price fluctu-ations and over-conservatism. We present the model, a solution strategy and discuss different application scenarios for a case study building.