Simulation-based building energy optimization
This dissertation presents computational techniques for simulation-based design optimization of buildings and heating, ventilation, air-conditioning and lighting systems in which the cost function is smooth. In such problems, the evaluation of the cost function involves the numerical solution of systems of differential algebraic equations (DAE). Since the termination criteria of the iterative solvers often depend on the design parameters, a computer code for solving such systems usually defines a numerical approximation to the cost function that is discontinuous in the design parameters. The discontinuities can be large in cost functions that are evaluated by commercial building energy simulation programs, and optimization algorithms that require smoothness frequently fail if used with such programs. Furthermore, controlling the numerical approximation error is often not possible with commercial building energy simulation programs.
In this dissertation, we present BuildOpt, a new detailed thermal building and daylighting simulation program. BuildOpt's simulation models dene a DAE system that is smooth in the state variables, in time and in the design parameters. This allows proving that the DAE system has a unique solution that is smooth in the design parameters, and it is required to compute high precision approximating cost functions that converge to a cost function that is smooth in the design parameters as the DAE solver tolerance is tightened.
For simulation programs that allow such a precision control, we constructed subprocedures for Generalized Pattern Search (GPS) optimization algorithms that adaptively control the precision of the cost function evaluations: coarse precision for the early iterations,with precision progressively increasing as a stationary point is approached. This scheme significantly reduces the computation time, and it allows to prove that the sequence of iterates contains stationary accumulation points. For optimization problems in which commercial building energy simulation programs are used to evaluate the cost function, we compared by numerical experiment several deterministic and probabilistic optimization algorithms.