A Hierarchical Decomposition Approach for Multi-Level Building Design Optimization

With the advancement in and integration of building energy simulation and optimization tools, building design optimization considering different design objectives and involving multiple disciplines has become technically feasible. However, this multifaceted approach unavoidably increases the dimension of the problem and comes with a prohibitively high computational cost. Hierarchical decomposition divides an optimization problem into several interconnected subproblems, and each subproblem has its objectives and constraints. Therefore, a complex problem is represented by a series of manageable subproblems. However, solving subproblems may lead to the local optimal solutions of the original problem. This research proposes a hierarchical decomposition approach that can achieve global optimal solutions. The proposed approach is applied to a multi-objective optimization problem to minimize the carbon emission and operating cost of building. This problem is decomposed into two subproblems to be solved sequentially. The first subproblem is to minimize the energy consumptions of the building. The second subproblem has the same objectives as the original one, but the search space is the result of the first subproblem. The benefit of decomposing this problem is that only the second problem needs to be solved again when additional energy price and carbon emission scenarios to be considered. A mid-rise residential building is selected as a case study to demonstrate the approach. The results show that the decomposition approach can reduce the number of simulations while keeping the full set of solutions of the original problem. The application of the proposed approach is based on a fixed utility rate, and only two objectives are considered for each level of optimization. These limitations could be overcome by adjusting the way to apply this approach.