Scientific Computing Seminar

Date:
Thursday, March 18, 2004
Time:
10:15am-11:15am
Location:
70-191
Seminar Speaker:
Michael Wetter
Lawrence Berkeley National Laboratory
Environmental Energy Technologies Division
Simulation Research Group
MWetter (at) lbl (dot) gov
Title:
Decreasing the computation time for Generalized Pattern Search optimization algorithms by using adaptive precision cost function evaluations
Abstract:
We are interested in solving optimization problems in which evaluating the cost function requires the numerical solution of a system of differential algebraic equations that needs to be solved using iterative solvers. We assume that the cost function is smooth in the design parameter, but that its numerical approximations, defined on the numerical solutions of the differential algebraic equations, are discontinuous in the design parameters. We show that this situation is typical for a large class of engineering optimization problems. For our problems, derivatives are not available, and using high-precision numerical solutions for all iterations is computationally too expensive for optimization to be applicable in the design process, while using low-precision numerical solutions can cause the optimization algorithm to fail at the discontinuities of the approximating cost function. For such problems, we developed subprocedures for Generalized Pattern Search (GPS) optimization algorithms that adaptively control the precision of the approximating cost functions in the course of the optimization. Our subprocedure reduces the computation time from five days to one day, making optimization fast enough to be applicable for the design of building envelope and energy systems.

We present our GPS algorithms with adaptive precision cost function evaluations. We show that our optimization algorithms provably construct sequences of iterates with stationary accumulation points. We present a new building energy simulation program that consists of 30,000 lines of code, which we were required to develop in order to compute numerical approximations to the cost functions that converge to a smooth function as the precision is increased. The simulation model contains smoothing methods that have not been used before in building energy simulation programs. We show that these smoothing methods were essential to compute high precision numerical solutions. We show numerical experiments of our adaptive simulation-precision control algorithms that yield a four to five times reduction in computation time.

Sponsor of Seminar:
Juan Meza
Scientific Computing

Contact Esmond G. Ng EGNg@lbl.gov