Optimization of Transformation Pathways for the Residential Building Sector

Transformation pathways provide information about which actions to take in which building and which year to transform and decarbonize residential building stocks. We define the problem of determining optimal transformation pathways of residential building stocks and introduce a MILP model for this problem. To accelerate the solving process, we propose different Benders decompositions of the original model. Further acceleration features include constraint modifications, valid inequalities, tailored Benders optimality cut strengthening, a primal construction heuristic, and an in-out method. The Benders cut separation process is embedded into the branch-and-cut algorithm of the MILP solver Gurobi. Based on the German Census 2011, we introduce instance sets to test the algorithmic implementations on which we heuristically refine solution strategies based on aforementioned features. For instances with 50 buildings, 20 years time horizon and a time limit of 30 h, the best-performing strategy yields relative MILP gaps of 5 % while Gurobi attains relative MILP gaps of 20 % and 10 % if performing a warm start with our construction heuristic.