Building Performance Optimization of Net Zero-Energy Buildings - Modeling, Design, and Optimization of Net-Zero Energy Buildings - page 253

variables at the start of the hybrid algorithm and locking them inside an
EA improves algorithm performance and search resolution. Performing a
hill-climbing search after an EA was found to only marginally improve
search outcomes.
The Hooke-Jeeves (HJ) search (Hooke and Jeeves, 1961), a member of the
general pattern search family (Audet and Dennis, 2002), is a deterministic
search algorithm that explores defined step-sizes in each continuous design
variable coordinate. The algorithm selects the design variable, for a given
step-size, that best improves fitness. If fitness is not improved, then the
process is repeated to find the best step-size improvement in the other
design variable coordinates. When no further improvements are made, the
step-size is decreased, as previous step-sizes are assumed to be too large to
resolve local optimums. Decreasing step-sizes requires the algorithm to be
constantly converging. This feature can be overcome by combining the HJ
algorithm with other global searches, as demonstrated by Wetter and Polak
(2004).
Figure 5.5 illustrates a Hooke-Jeeves pattern search using a
two-dimensional test function. The cross with round circles represents the
search grid. The search grid has the same number of dimensions, as there
are optimization variables. Dots represent the selected direction of the next
search iteration. Note in the third iteration (3) that the fitness is not
improved so the algorithm halves the search grid size and continues from
the last known improvement. Step-sizes are decreased again in iterations 4,
5, and 6 until the global optimum is found and the search terminated.