Multivariate optimization of a solar water heating system using the Simplex method

Two Simplex computer library packages for multivariate optimization have been tested on an hour-by-hour simulation of a solar water heating system. The two packages are: MINUITS written at CERN (Geneva) , and the E04CCF routine which is part of the UK Numerical Algorithms Group Library. Technical and economic optima have been derived for three of the following variables simultaneously: collector area, tilt, azimuth, and store volume. The two packages give the same results. The meteorological data used were one (composite) year for Hamburg (Germany) and 1964 for Kew (UK). The Hamburg data were also condensed to form a year consisting of 60 averaged days. The optima derived with the 60-day year were very close to those obtained with the 365-day year. The Simplex method, which is a direct search method, is known to be very robust. It is particularly suited to hour-by-hour simulations of solar heating systems since the function being minimized is not monotonically decreasing towards the minimum in sufficient significant figures. For this reason, optimization methods which use derivatives are not appropriate unless the system performance is first expressed as a differentiable function. Because the Simplex method can be used directly on hour-by-hour simulations, it is extremely flexible and can be applied to a simulation of any system.