Building Performance Optimization of Net Zero-Energy Buildings - Modeling, Design, and Optimization of Net-Zero Energy Buildings - page 252

(5.1)
where x is the design variable vector x = ( x 1 , x 2 ,…, x N ) T in design space X
⊂ ; the objective or fitness function, f (), maps the set of design variables
onto an objective vector y = ( y 1 , y 2 ,…, y M ) T where f i ∈ , y i = f i (x), f i :
for i = 1, 2,…, M , describes the objective solution space Y ⊂ ; the
search for is subject to L constraints g i ( x ) ≤ 0 where i = 1, 2,…, L ;
feasible design vectorsset x | g i ( x )≤0formthefeasible design space X * ,and
corresponding objective vectors set y | x ∈ X * form feasible objective space
Y * ; for a minimization problem, a design vector a ∈ X * is Pareto optimum if
no design vector b ∈ X * exists such that y i ( b ) ≤ y i ( a ), i = 1, 2,…, M .
5.2.3 Review of Optimization Algorithms Applicable to BPS
In this section, suitable optimization approaches for building simulation
studiesarereviewed.Ageneraloverviewofseveralmethodsandalgorithms,
which have proven to be versatile in BPS applications, are presented. The
following approaches are discussed: (i) deterministic searches, (ii)
population-based searches, and (iii) hybrid search approaches.
A deterministic search attempts to operate on individual building
representations to identify optimal regions by changing the value of
variables using small increments or decrements. Although the goal of a
deterministic search is to identify global optimums, there is a risk of
preconverging to local optimums in multimodal problems. Two
deterministic searches are discussed: (i) hill-climbing search and (ii)
Hooke-Jeeves search. These searches are called deterministic, as a search
operation on a given individual will always result in the same outcome.
Hill-climbing searches are a simple deterministic search strategy. Building
design variables are incrementally changed to improve an objective
function. Typically, the order in which variables are searched and the
particular building design representation being searched will greatly affect
the search outcome. Renders (1994) recommended integrating a
hill-climbing search into the mutation operator of a genetic algorithm or
as a forked process interwoven into the search algorithm. Bucking et al.
(2010) compared the search performance of using hill-climbing searches at
the beginning and end of an Evolutionary Algorithm (EA). This research
demonstrated that performing a hill-climbing search on weakly interacting