Building Performance Optimization of Net Zero-Energy Buildings - Modeling, Design, and Optimization of Net-Zero Energy Buildings - page 250

measures) is one of its most important applications in recent years. For
example, using optimization to evaluate the energy and cost-savings
potential from constructing more efficient new homes and net-zero energy
homes in the United States (Christensen, 2005). Also, this includes the call
of the European Commission for implementing a methodology to calculate
cost-optimal levels in the Energy Performance of Buildings Directive
(EPBD) framework. European Member States are required to define
cost-optimal levels of minimum energy performance according to their
specificities (Constantinescu, 2010).
5.2 Optimization Fundamentals
Applications of optimization are rapidly evolving for both building design
and operation. The most appropriate search algorithms and modeling
approaches vary depending on the application area including optimization
objectives.
5.2.1 BPO Objectives (Single-Objective and Multi-Objective
Functions)
Inmathematics,optimizationisthedisciplineconcernedwithfindinginputs
of a function that minimize or maximize its value, which may be subjected
to constraints (Pardalos and Resende, 2012). In the AEC community, most
BPO methods have focused on solving single-objective or multi-objective
functions (Caldas, 2001; Choudhary, 2004; Hamdy, 2012; Hopfe, 2009;
Nielsen, 2002; Pedersen, 2007; Verbeeck, 2007; Wang, 2005; Wetter,
2004).
In the case of single-objective functions, an optimum solution of the
problem is either its global maximum or minimum, depending on the
purpose. On the other hand, in multi-objective optimization problems, a
specific building variant is often not able to simultaneously minimize or
maximize each objective function. Instead, when searching for solutions,
one comes to limit variants such that a further improvement toward the
minimum value of one of the objective function causes the others to deviate
from the minima. Therefore, the aim of a multi-objective optimization
problem consists in finding such variants and possibly in quantifying the
trade-off in satisfying the individual objective functions. The role of the
optimization algorithm is to identify the solutions that lie on the trade-off
curve, known as the Pareto frontier (a set of optimal solutions plotted in