ARTICLE IN PRESS
Building and Environment 40 (2005) 1512–1525
www.elsevier.com/locate/buildenv
Applying multi-objective genetic algorithms in green building
design optimization
Weimin Wanga, Radu Zmeureanua,, Hugues Rivardb
a
Department of Building, Civil and Environmental Engineering, Centre for Building Studies, Concordia University, Montreal, Canada
b
Department of Construction Engineering, École de Technologie Supérieure, Montreal, Canada
Received 2 December 2003; accepted 24 November 2004
Abstract
Since buildings have considerable impacts on the environment, it has become necessary to pay more attention to environmental
performance in building design. However, it is a difficult task to find better design alternatives satisfying several conflicting criteria,
especially, economical and environmental performance. This paper presents a multi-objective optimization model that could assist
designers in green building design. Variables in the model include those parameters that are usually determined at the conceptual
design stage and that have critical influence on building performance. Life cycle analysis methodology is employed to evaluate
design alternatives for both economical and environmental criteria. Life cycle environmental impacts are evaluated in terms of
expanded cumulative exergy consumption, which is the sum of exergy consumption due to resource inputs and abatement exergy
required to recover the negative impacts due to waste emissions. A multi-objective genetic algorithm is employed to find optimal
solutions. A case study is presented and the effectiveness of the approach is demonstrated for identifying a number of Pareto optimal
solutions for green building design.
r 2005 Elsevier Ltd. All rights reserved.
Keywords: Building design; Green building; Life cycle assessment; Life cycle cost; Multi-objective genetic algorithm
1. Introduction
Buildings are energy gluttons and have a large impact
on the global climate change and other energy-related
environmental issues. In Canada, residential and commercial/institutional buildings consume about 30 percent of the total secondary energy use [1]. As a direct
result, they are responsible for nearly 29 percent of CO2
equivalent greenhouse gas emissions. A similar situation
is also observed in the United States, where buildings
account for 39 percent of the total primary energy
consumption and 70 percent of the electricity consumption [2]. About 38 percent of CO2 emissions, 52 percent
Corresponding author. Tel.: +1 514 848 2424x3203;
fax: +1 514 848 7965.
E-mail address: [email protected] (R. Zmeureanu).
0360-1323/$ - see front matter r 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.buildenv.2004.11.017
of SO2, and 20 percent of NOx are produced in the US
because of building-related energy consumption.
As the environmental impacts of buildings are
acknowledged, it becomes important to consider the
environmental performance in building design. Green
building is a recent design philosophy which requires the
consideration of resources depletion and waste emissions during its whole life cycle [3]. A green building is
designed with strategies that conserve resources, reduce
waste, minimize the life cycle costs, and create healthy
environment for people to live and work.
The successful design of green buildings requires that
special attention be paid to the conceptual stage when
many potential design alternatives are generated and
roughly evaluated in order to obtain the most promising
solution. Decisions made in the conceptual stage have
considerable impacts on the building performance. For
example, simply making buildings the right shape and
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W. Wang et al. / Building and Environment 40 (2005) 1512–1525
the correct orientation can reduce energy consumption
by 30–40% with no extra cost [4]. Currently, designers
heavily rely on previous experience or building energy
simulation programs to determine appropriate values
for design parameters. However, the previous experience
might lead to incorrect conclusions because they cannot
cover every foreseeable circumstance and cannot reflect
the complicated interactions between various parameters. Although many sophisticated energy simulation
programs (e.g., DOE, Energy Plus) are valuable to study
the impacts of design parameters on building performance, the iterative trial-and-error process of searching
for a better design solution is time-consuming and
ineffective because of the inherent difficulty in exploring
a large design space.
This paper presents the use of an optimization
program coupled with an energy simulation program,
which allows the design space to be explored in the
search for an optimal or near optimal solution(s) for a
predefined problem.
The remainder of this paper is organized as follows.
Related studies are reviewed in the next section. It is
followed by a presentation of exergetic life cycle
assessment to evaluate environmental performance of
buildings. The optimization model is presented in the
fourth section, followed by a brief introduction to the
multi-objective genetic algorithm used to solve the
optimization problem. A case study is finally presented
to illustrate the application of the multi-objective genetic
algorithm in green building design.
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alternatives. A review of some optimization studies is
presented below.
End-use operating energy consumption is the optimization criterion in many studies [9–11]. Heating and
cooling energy are covered by Al-Homoud [9] and Coley
and Schukat [11] while Wetter [10] enlarged the scope
further to include lighting energy consumption into the
optimization model. If the operating energy consumption is considered as the only optimization criterion, the
proposed building is likely to have excessive amount of
insulation and would not be cost-effective. To overcome
this problem, life cycle cost has been used as the
performance criterion in several studies [12–14].
Since designers rarely consider only one criterion in
the decision-making process, multi-objective optimization models have been proposed. Radford and Gero [15]
applied dynamic programming in the multi-criteria
design optimization with the following four performance criteria: thermal load, daylight availability,
construction cost and usable area. Hauglustaine and
Azar [16] optimized the building envelope using genetic
algorithms. As many as 10 criteria related with code
compliance, energy consumption, and cost are considered. Wright et al. [17] applied a multi-objective genetic
algorithm to building thermal optimization with emphasis on mechanical system design. Operating energy
cost and occupant thermal comfort are the two
performance criteria used.
Although the above efforts in optimization studies are
significant to explore effective ways for better building
design, several limitations may undermine their application in practice. They are discussed below.
2. Previous related studies
Many efforts have been made to assist designers in
green building design. Integrated simulation environment provided by some tools (e.g., Building Design
Advisor [5]) can facilitate the comparison of several
design alternatives with respect to different performance
criteria, such as daylighting and thermal energy consumption. Some tools such as ATHENA [6] have been
developed to assess the environmental performance of a
building design by considering a number of environmental impact categories due to its construction.
Building performance rating systems such as GBTool
[7] can evaluate a broad range of green building related
issues and obtain an overall score after weighting
aggregation. Recognizing the disadvantage of trialand-error process to improve the design solution using
building simulations, Shaviv et al. [8] combined knowledge-based heuristics and procedural simulation to
support low-energy building design. Optimization is
another approach adopted in some studies to avoid the
trial-and-error problem. It has the distinctive advantage
of finding optimum or near optimum building design
2.1. Difficulty in making cost-effective decisions
accounting for environmental performance
Most previous studies deal with either economical or
environmental performance [9–12]. Two approaches
were followed in an effort to consider the two criteria
simultaneously: (1) one criterion is handled as a
constraint [13,14] or (2) the weighted sum technique is
used [16]. Both approaches require a priori information
from designers: boundary value for the constraint or
weights for the performance criteria. With little knowledge about the performance space of the problem in
advance, designers may find it difficult to set appropriate values for those required inputs. Furthermore,
only one optimal solution is obtained for each run if the
two performance criteria are treated separately or
coupled together into one meta-criterion. The designer
cannot learn about the impact of the marginal change of
one criterion on another just from a single optimal
solution. Therefore, it is difficult to make cost-effective
decisions without knowing the trade-off relationship
between economical and environmental performance.
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W. Wang et al. / Building and Environment 40 (2005) 1512–1525
2.2. Incomplete environmental performance criterion
The embodied energy and environmental impacts are
neglected in all previous studies. This may be due to the
following three reasons: it is difficult to obtain consistent
and accurate data about environmental impacts for all
building materials and components; few simulation
programs considering the life cycle environmental
impacts of a building [18] have been developed;
embodied energy and environmental impacts are not
directly related to building construction costs. However,
as indicated by Yohanis and Norton [19], increasing
operating energy efficiency in buildings makes it
important to consider embodied energy. Furthermore,
energy consumption is no longer a complete criterion to
evaluate environmental performance because many
environmental impacts associated with material production are not energy-related. Therefore, it is necessary to
incorporate other impact categories such as natural
resource depletion and global warming into the objective function.
2.3. Mismatch between optimization model and design
practice in terms of variables
The mismatch between optimization model and
design practice can be seen in two ways. In the first
case, the variable type is not properly defined. Many
parameters such as window types can only take discrete
values. However, they are often defined as continuous
variables because of the difficulty for numerical optimization methods to deal with discrete variables. For
example, Miller and Hittle [12] represented the window
type by its thermal resistance value. However, there may
be no windows available in the market having the
obtained optimal thermal resistance value. In the second
case, some variables in the model are not directly designoriented, but are intermediate results from other design
calculations. For example, Al-Homoud [9] gave an
optimal value for time lag of walls, for which designers
may find it difficult to map to a corresponding design
solution.
A new optimization model is proposed in this paper
that addresses the above limitations. One of the main
characteristics of the new model is that the environmental performance is evaluated through a life cycle
assessment methodology.
3. Exergetic life cycle assessment
Life cycle assessment (LCA) is a system analysis
method that is useful in understanding and evaluating
the resource consumption and waste emissions associated with products, processes and activities, across all
phases of their life cycle from materials acquisition to
Natural
resource
extraction
Building
material
production
Transportation
On-site
construction
Operation
Demolition
Maintenance
Transportation
Fig. 1. Building life cycle process.
final disposition [20]. The life cycle of buildings (Fig. 1)
covers all processes from natural resource extraction,
through material production, construction, and operation, until demolition. Maintenance is usually required
during the operation phase while transportation is an
activity associated with most other phases.
3.1. Scope definition
Some previous studies [21] have indicated that
material acquisition, production, on-site construction
and operation account for about 94% of an office
building’s life cycle energy consumption over its 50-year
life expectancy. Hence, the phases considered in this
study are limited to natural resource extraction, building
material production, on-site construction, operation,
and transportation associated with the above phases.
They are enclosed by a dashed line in Fig. 1.
Maintenance and demolition are not included because
the corresponding environmental impact data are
unavailable for many building materials or assemblies.
Although some life cycle assessment tools like ATHENA [6] have made some efforts in this respect, lack of
reliable data is still a serious problem.
According to Barnthouse et al. [20], global/continental, long-lasting impact categories (e.g., global warming)
usually have characteristics that can be dealt with by
LCA with acceptable theoretical accuracy, but there is
increasing loss of accuracy as more local and transient
impact categories (e.g., ecotoxicity) are considered in the
aggregated LCA indicators. Therefore, impact categories considered in this optimization study should
include natural resources consumption, global warming,
acidification, and ozone depletion, while other impacts
characterized as being local and transient such as
ecotoxicity and photochemical smog are not considered.
The emissions considered in this paper are restricted to
three major greenhouse gases (CO2, CH4, N2O) and two
major acidic gases (SOx and NOx). Ozone depletion
gases due to refrigerant leaks are not considered in this
study.
It is difficult, however, to characterize natural
resource depletion and to integrate various impact
categories with different units and magnitudes in the
context of life cycle optimization. Available approaches
for characterizing resource depletion in the context of
LCA are reviewed by Finnveden [22]. Some studies
focus on energy consumption only, while some others
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W. Wang et al. / Building and Environment 40 (2005) 1512–1525
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use depletion indices based on reserves and reserve-touse ratios to consider non-energy resources such as
mineral ore. For the latter case, normalization coefficients are required to aggregate depletion indices
together since they vary in the order of magnitudes.
However, it is not a simple task to set appropriate
normalization coefficients, because the difference of
magnitudes for depletion indices is problem dependent.
Once the whole impact profiles are defined, normalization and weighting are performed to get an overall
value for life cycle environmental impacts. The normalization is made by comparing the estimated impacts with
a reference situation, for instance, the estimated impact
scores evaluated at the world, country, or person level.
The weighting approaches usually employ weights or
monetary values to aggregate the normalized environmental impacts [20]. Although reference situation and
weights influence the results, there is no widely accepted
choice for both of them. The use of exergy can
potentially overcome the above two problems of
resource characterization and weigthing integration
[22,23].
the environmental impact potentials and the exergy of
waste emissions. Abatement exergy (AbatEx) is employed in this study to evaluate the required exergy to
remove or isolate the emissions from the environment.
As indicated by Cornelissen [23], it is feasible to
determine an average AbatEx for each emission based
on current available technologies.
Thus, by extending the cumulative exergy consumption
to include abatement exergy, the expanded cumulative
exergy consumption can consider both resource inputs
and waste emissions to the environment, across all life
cycle phases. It can be regarded as a unifying indicator to
evaluate life cycle environmental impacts. The main
advantages of using the expanded cumulative exergy
consumption for life cycle optimization with respect to
environmental performance can be summarized as
3.2. Exergy application in life cycle assessment
Exergy is ‘‘the maximum theoretical work that can be
extracted from a combined system consisting of the
system under study and the environment as the system
passes from a given state to equilibrium with the
environment—that is, passes to the dead state at which
the combined system possesses energy but no exergy’’
[24]. Unlike energy, exergy is always destroyed because
of the irreversible nature of the process. Exergy is an
extensive property whose value is fixed by the state of
the system once the environment has been specified.
Therefore, the evaluation of exergy depends on both the
state of a system under study and the conditions of the
reference environment. Most applications of exergy
analysis in the published literatures concentrate on
thermal system design [24], chemical and metallurgical
process analysis [25], and energy conversion system
design [26].
Exergy can be incorporated into LCA to address the
issues of natural resource depletion characterization and
valuation. Cumulative exergy consumption proposed by
Szargut et al. [25] expresses the sum of the exergy of all
natural resources consumed in all the steps of a
production process. Unlike cumulative energy consumption, it also takes into account the chemical exergy of the
nonfuel raw materials extracted from the environment.
Therefore, cumulative exergy consumption can be used
to measure natural resource depletion.
Exergy can also be a measure of waste emissions.
Because exergy can evaluate the degree of disequilibrium
between a substance and its environment, some rational
and meaningful relationships can be established between
It can combine resource depletion and waste emissions together, and therefore, the life cycle environmental impacts can be condensed into one single
objective function. Moreover, it can avoid the
subjectivity of weights setting in the evaluation of
environmental impacts.
It can combine fuel and nonfuel materials together to
characterize the resource depletion.
3.3. Life cycle environmental impact calculation and data
preparation
The expanded cumulative exergy consumption is
calculated as the sum of cumulative exergy consumption
and abatement exergy consumption. For the convenience of the following descriptions, the life cycle phases
are grouped into pre-operation phase (PP) and operation phase (OP). The pre-operation phase includes
natural resource extraction, building material production, on-site construction, and transportation associated
with the above phases.
Three methods can be used to calculate the cumulative exergy consumption [25]: process analysis; balance
equations of cumulative exergy consumption; extension
from cumulative energy consumption. The idea underlying the method of process analysis is to trace and
evaluate all the manufacturing processes of a product.
The method of balance equations of cumulative exergy
consumption uses a system of equations expressing the
cumulative exergy consumption of final products as a
sum of the cumulative exergy due to the intermediate
products and the natural resources extracted directly
from the environment. The last method, which is selected
to be employed in this study, calculates the cumulative
exergy consumption based on cumulative energy consumption, which can be obtained conveniently from some
available LCA tools such as ATHENA [6].
Cumulative exergy consumption is evaluated as the
sum of the exergy, from both nonenergetic resources
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W. Wang et al. / Building and Environment 40 (2005) 1512–1525
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(e.g., mineral ore) and energetic resources (fuel),
consumed in all the steps of a production process.
Nonfuel exergy can be calculated as the product of mass
and its chemical exergy. Fuel exergy can be obtained by
multiplying the amount of energy consumption with the
ratio a between the fuels exergy and its energy content.
Thus, the cumulative exergy consumption (CExC) can
be expressed as
CExC ¼ CExCPP
"
þ CExCOP ¼
"
þ n
X
j
X
j
#
aj
ONj
;
Zj
ðaj ENj Þ þ
X
#
where 0.86 is the transmission efficiency of electricity, 0.30
and 0.26 are the overall efficiency of the generation and
transmission of electricity if oil and nuclear are used [26].
The on-site annual energy consumption (ON) can be
obtained from an energy simulation program. Embodied energy (ENj) and the mass of nonfuel resources
(mk) for a building material or assembly can be obtained
from life cycle assessment programs. This study uses
ATHENA [6] because it has the following advantages:
ðek mk Þ
k
ð1Þ
where
CExCPP cumulative exergy consumption (MJ) due to
the pre-operation phase;
CExCOP cumulative exergy consumption (MJ) due to
the operation phase;
ENj
embodied energy (MJ) of fuel j consumed in
the pre-operation phase;
ONj
annual on-site operating energy (MJ) of fuel j;
ek
chemical exergy of nonfuel material k (MJ/kg);
mk
mass of nonfuel material k (kg);
n
life expectancy of building in years;
aj
ratio between exergy and energy content for
fuel j;
Zj
overall efficiency of production and delivery
for fuel j.
The value of a is taken from [25,27]. For instance, a is
equal to 1.07 and 1.04 for oil and natural gas,
respectively, and 1.0 for both nuclear energy and
electricity. In this paper, weighted sum of a according
to the national electricity mix is applied to the total
embodied energy for simplification. The national
electricity mix is used, because the related activities such
as manufacturing processes are not limited to the local
place. The overall efficiency Z is used to convert on-site
operating energy to primary sources, taking into
account the production and transportion losses. Its
values are taken from [26] with the following two
exceptions. First, generation loss is not considered for
hydro-electricity because it comes from a renewable
energy source. Second, the overall efficiency value of
electricity is calculated from the local electricity mix.
For example, given the electricity mix in Quebec,
Canada (96% from hydro, 2% from oil, and 2% from
nuclear), the Z value is calculated as
1
Z¼
1:0 0:96=0:86 þ 1:07 0:02=0:30 þ 1:0 0:02=0:26
¼ 0:79;
The ATHENA database covers typical materials or
assemblies for building structure and envelope and
contains updated data for North America.
The components of an assembly defined in ATHENA
are more construction-oriented than other LCA
programs because overlap, waste and other miscellaneous ancillary materials are considered in the
estimation of materials quantity.
It presents values for the natural resource consumption and waste emission in detail for a given assembly.
These values are essential to derive cumulative exergy
consumption and other environmental impacts.
AbatEx is calculated as the product of mass of waste
emissions and its unit abatement exergy. The unit
AbatEx is usually determined according to particular
processes used to remove or separate waste emissions
(e.g., decarbonization of flue gases after combustion). In
this paper, the values of unit AbatEx for CO2, SOx, and
NOx are taken as 5.86, 57, and 16 MJ/kg, respectively
[23]. Since the values of unit AbatEx for CH4 and N2O
have not been found in the literature, they are derived by
assuming that the AbatEx is proportional to the global
warming potential (GWP) index. Hence, they are
calculated by multiplying the GWP index (over a 100year period) by the unit AbatEx for CO2. However, they
could be easily updated when the actual values become
available. The mass of each waste emission generated in
the pre-operation phase is calculated by multiplying the
emission per unit area by the applicable envelope area.
The emissions per unit area for different materials
construction are stored in the program data files, which
are prepared in advance with the aid of the ATHENA
program. The mass of each waste emission generated in
the operating phase is calculated by multiplying the onsite operating energy consumption with an emission
factor. The emission factor of delivered electricity is
calculated from the electricity mix and the emission
coefficients due to electricity generation from different
fuel types [28].
4. Multi-objective optimization model
The components of the optimization model are
presented in the following order: variables, constraints,
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W. Wang et al. / Building and Environment 40 (2005) 1512–1525
and objective functions. The model concentrates on the
building envelope system because of its importance in
determining both environmental and economical performance of buildings. The same methodology could be
applied later to a large scope covering other building
systems such as heating, ventilation, and air conditioning system.
4.1. Variables
Two types of variables are used to define a building
design alternative: discrete and continuous. Some
variables such as window type can only be of discrete
type with a list of available types of windows. Some
variables can be either continuous or discrete. Orientation, for example, may assume any value between 01 and
901, or it may take one from a pre-set list such as 01, 151
or 301.
In this study, buildings are limited to a rectangular
shape with a known total floor area. Fig. 2 illustrates the
definition of some variables. The following variables
have been defined with their corresponding names in
parenthesis:
Building orientation (orientation) in degrees with
clockwise direction being positive.
Aspect ratio (aspectRatio) a/b of a building plan,
where a and b are defined as shown in Fig. 2.
Window type (winType) defines the window construction. An example is a double glazing window with 13
mm airspace in between.
Window-to-wall ratio (winRatio) for each building facade.
Wall type (wallType ) defines the wall configuration
with a sequence of layers. Masonry cavity wall,
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for example, consists of the following sequence of
layers from outside to inside: cladding, cavity,
insulation, vapor barrier, masonry structure,
and finish.
Each layer of wall (wallLayer) defines the actual
material selected. For example, the insulation layer in
a wall type can be 76.2 mm fiberglass batts or
101.6 mm mineral wool batts.
Roof type (roofType) defines the roof configuration
with a sequence of layers. For example, a compact
conventional roof type is composed of roofing
membrane, insulation, structure, and finish, presented
in order from outside to inside.
Each layer of roof (roofLayer) defines the actual
material selected.
4.2. Constraints
Two types of constraints are considered in this
optimization model. They are box constraints for
continuous variables and selection constraints for
discrete variables. Box constraints give the boundary
values of continuous variables. For example, if winRatio
is set as a continuous variable and the lower and upper
boundary values are 0.2 and 0.8, respectively, then the
corresponding box constraint is 0:2pwinRatiop0:8:
Selection constraints give a predefined set of alternatives
for discrete variables. For example, winType can be
limited to one of three available window types: double
clear glazing, triple clear glazing, and double glazing
with low-emissivity coating.
4.3. Objective functions
Since the purpose of this study is to assist designers in
achieving cost-effective green building design, both life
cycle cost (LCC) and life cycle environmental impact
(LCEI) are selected as the two objective functions to be
minimized using the optimization model. Let X denotes
a variable vector, the general expressions to calculate
LCC ($) and LCEI (MJ) are
a
LCCðXÞ ¼ ICðXÞ þ OCðXÞ;
(2)
LCEIðXÞ ¼ EEðXÞ þ OEðXÞ
¼ ½CExCPP ðXÞ þ AbatExPP ðXÞ
þ ½CExCOP ðXÞ þ AbatExOP ðXÞ;
b
Building North
ð3Þ
where
Orientation
True North
Fig. 2. Definition of orientation and aspect ratio.
IC
OC
initial construction cost of building envelope
including exterior walls, windows, roof, and
floor ($);
life cycle operating cost including both demand
and energy consumption costs ($);
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EE
environmental impacts due to the pre-operation
phase (MJ);
OE
environmental impacts due to the operation
phase (MJ);
AbatExPP abatement exergy consumption due to the
pre-operation phase (MJ);
AbatExOP abatement exergy consumption due to the
operation phase (MJ).
5. Multi-objective genetic algorithm
The selection of the optimization algorithm depends
on the particularities of a problem domain. The
optimization problem presented in the previous section
has the following characteristics:
Initial construction cost data are taken from the R.S.
Means cost databook [29]. The life cycle operating cost
is derived from the annual operating cost which is
discounted to the present worth considering the time
value of money [30]:
OCðXÞ ¼ ACðXÞ
1 ð1 þ aÞn
;
a
(4)
where,
AC
a
annual operating cost ($);
effective interest rate.
The effective interest rate is related with the discount
rate (i) and the rate of energy price escalation (r), both
of which have incorporated inflation rate. It can be
calculated as [30]:
a¼
ir
:
1þr
(5)
A simulation program based on the ASHRAE
toolkit for building load calculations [31] has been
developed to calculate both life cycle cost and life cycle
environmental impact. The simulation program uses the
variable values from the optimization module, and
prepares a text input file with the building description
required by the toolkit. Using the heat balance method,
the ASHRAE toolkit calculates hourly heating or
cooling loads of two typical days per month, which
correspond to (1) the average weather condition, for the
calculation of energy consumption; and (2) the extreme
weather condition, for peak load calculation. Based on
the hourly loads, the simulation program estimates the
operating energy consumption accounting for the
efficiency of heating and cooling system. The operating
energy consumption is then used to calculate the
environmental impacts due to the operation phase
(OE), and the operating cost (OC). The environmental
impacts due to the pre-operation phase (EE), and the
initial construction cost (IC) are derived directly from
the building description, construction cost and embodied impact data of building materials/products. The
simulation program is coupled with and called by an
optimization program which is described in the next
section.
It is a multi-objective optimization problem with
conflicting criteria. In contrast with single objective
optimization with one single solution, multi-objective
optimization aims at finding a set of Pareto solutions.
A solution is said to be Pareto optimal if and only if it
is not dominated by any other solution in the decision
variable space. If solution X1 dominates another
solution X2, it implies that X1 is non-inferior to X2 for
all the considered performance criteria but it is better
than X2 for at least one criterion. All the points in the
objective function space corresponding to Pareto
solutions form a Pareto front which is useful to
understand the trade-off relationship between the
performance criteria. Therefore, the goal of this study
is to identify the Pareto solutions to assist designers in
making cost-effective decisions for green building
design.
It is a hard combinatorial problem. To illustrate this
point, let us consider a simple design problem with the
following variables and corresponding number of
alternatives (the number in parenthesis): orientation(10), aspectRatio(10), winType(3), wallType(3),
roofType(3), winRatioi(10), each wallLayerj(5), each
roofLayerj(5), with i ¼ 4 for four fac- ades and j ¼ 5
for five layers; there are about 2.6 1010 possible
solutions to explore.
Variables are at different hierarchical levels. For
example, wall type and wall layers are variables at
different levels. The wall type determines the sequence
and the material types of all contained layers. If there
are several alternative wall types, only the layers
belonging to the active wall type should be used. For
instance, there are two types of walls: masonry cavity
wall using rigid insulation and steel-frame wall using
batt insulation. If the steel-frame wall is active, only
the batt insulation is considered. Thus, variables
located at lower hierarchical levels are affiliated to
and controlled by variables at higher levels.
Both continuous and discrete variables coexist in the
same optimization problem.
The above characteristics lead to genetic algorithm
(GA) as an appropriate optimization method to be used
in this study. GA is a population-based stochastic global
search technique inspired from the biological principles
of natural selection and genetic recombination [32]. A
notable characteristic distinguishing it from other
optimization methods is that it maintains and operates
not on a single solution, but on a population of
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W. Wang et al. / Building and Environment 40 (2005) 1512–1525
solutions, which are randomly generated for the first
generation. This characteristic of GA determines it to be
a suitable tool for multi-objective optimization problems because it can locate multiple Pareto optimal
solutions in a single run. Each individual in the
population, usually called chromosome, stands for a
potential solution in the problem space. The chromosome is usually represented as a binary string which can
capture both continuous and discrete variables. The
fitness of an individual is related with its objective
function values and it is used to determine the
probability of each individual to be selected for
reproduction. One of the commonly used selection
operators is the binary tournament selection which
works as follows: two individuals are randomly selected
from the current generation and the stronger one
survives to the next generation. Crossover and mutation
operations are then applied on the selected individuals
to form a new population. The crossover operator
exchanges some genetic materials between two chromosomes, while the mutation operator may flip the values
of some bits at random. The above procedure is
repeated until the maximum number of generations is
reached.
Many multi-objective GA have been proposed in the
literature [33]. All proposed algorithms have two distinct
goals [33]: to discover solutions as close to the true
Pareto optimal solutions as possible; and to find
solutions as diverse as possible in the obtained Pareto
front. The first goal is usually obtained by applying the
principle of dominance, which means non-dominated
solutions are assigned large fitness to survive selection
and have more chance for reproduction. The second
goal can be achieved by some techniques such as niche
sharing strategy, which requires that similar individuals
in the population be penalized by a reduction in fitness
in order to get a wide spread and even distribution along
the Pareto optimal front [33].
The multi-objective GA proposed by Fonseca
and Flemming [34] is employed in this study. This
algorithm uses a rank-based fitness assignment
strategy, where the rank of an individual is equal to
one plus the number of solutions in the current
population that dominate it. A linear function [33] is
used to map ranks to fitness values so that the individual
with the lowest rank has the maximum fitness value
and vice versa. Niche sharing carried out in the
performance space is applied to all individuals located
at the same rank. The radius parameter required by
niche sharing is calculated as 2=ðN 1Þ; where N is the
population size [33].
An improved version of the traditional GA called
‘‘structured GA’’, as proposed by Dasgupta and
McGregor [35], is employed here to represent the
chromosome as hierarchical genomic structures.
This means that dominant and recessive genes for
1519
low-level variables may coexist in a chromosome.
High-level genes will determine which low-level genes
are active.
Two supporting techniques were adopted to improve
the performance of this algorithm based on a series of
trial runs. These two techniques are
Mating restriction. Two individuals are permitted to
mate only if they are similar but not identical
according to some metrics. Normalized Euclidean
distance is used in this study to evaluate the
similarity between individuals. This means that two
different individuals will crossover if the normalized
Euclidean distance between them is less than the
mating radius, which is assigned the same value
as the niching radius. Since the mating restriction is
helpful to maintain local distributation but unfavorable for exploring search space, it is used only starting
with the second third of the total number of
generations.
Elitist strategy realized by using the external population. After each generation is produced, the nondominated individuals are copied to the external
population, while dominated individuals in the
external population are removed. This external
population has a predefined capacity. If it cannot
accommodate all the elites, the clustering technique
adopted by Zitzler and Thiele [36] is used to remove
some individuals located in crowded regions. In this
study, the external population is not used only for
storage, since some members are randomly chosen
and introduced into the original genetic population
before selection for each generation to accelerate
convergence.
6. Case study
6.1. Problem formulation
The design of a single-story office building located in
Montreal, Canada, is employed in this paper as a case
study. The building has a total above-basement floor
area of 1000 m2 with a 40-year life expectancy. The floor
type is an open web steel joists (OWSJ) on beam system
with concrete topping. The floor to roof height is 3.6 m.
The energy consumption due to lighting is kept constant
according to a given schedule. Only heating and cooling
energy consumption are considered in this case study.
Heating season is from November to March, and
cooling season from June to August. The indoor design
temperatures are 21 1C and 23 1C in the heating and
cooling season, respectively, without night setback or
setup. Rooftop units (coefficient of performance of 3.0)
are assumed to be used for cooling, and electric
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W. Wang et al. / Building and Environment 40 (2005) 1512–1525
baseboard heaters for heating. Internal loads and daily
operating schedule take the default values for office
buildings according to the Model National Energy Code
of Canada for buildings [30]. The discount rate and the
expected energy cost escalation rate (both including
general inflation) are 9% and 3%, respectively [30].
Local electricity rate structure is used: $11.97 per KW of
billing demand, $0.0372 per KWh for the first
2 10 000 KWh, $0.0242 per KWh for the remaining
electricity consumption.
The list of variables used in this study is given in
Table 1. The provincial energy code regulation [37] has
been used in the instantiation of insulation variables so
that all solutions satisfy mandatory requirements. Low-e
double glazing with 12.7 mm air space is the window
type selected for this building. There are two possible
wall types. The first wall type is a masonry cavity wall,
composed of the following layers in sequence from
outside to inside: clay brick cladding, air space, rigid
insulation, vapor barrier, masonry structure, and finish.
The second wall type is a steel-frame wall composed of
clay brick cladding, air space, air barrier, sheathing,
steel-stud with cavity insulation, vapor barrier, and
finish. Only one roof type is considered in this case
study: a compact conventional roof system composed of
ballast, roofing membrane, insulation, structure, and
finish. Two rigid insulation materials: expanded polystyrene (EPS) and extruded polystyrene (XPS), are used
in the masonry cavity wall and the roof. Two types of
insulation batts: fiberglass batts and rockwool batts, are
used in the steel-frame wall. Each insulation layer can
take one of six possible discrete values:
W1. Masonry cavity wall:
W1-1 102 mm EPS;
W1-2 127 mm EPS;
W1-3 152 mm EPS;
W1-4 102 mm XPS;
W1-5 127 mm XPS;
W1-6 152 mm XPS.
W2. Steel-frame wall:
W2-1 152 mm fiberglass;
W2-2 203 mm fiberglass;
W2-3 254 mm fiberglass;
W2-4 152 mm rockwool;
W2-5 203 mm rockwool;
W2-6 254 mm rockwool.
R1. Compact conventional roof:
R1-1 178 mm EPS;
R1-2 203 mm EPS;
R1-3 229 mm EPS;
R1-4 178 mm XPS;
Table 1
Variable instantiation
Variable name
Variable
type
Range or value
Orientation
Aspectratio
Wintype
Winratio1
Winratio2
Winratio3
WinRatio4
Walltype
Rooftype
Continuous
Continuous
Constant
Continuous
Continuous
Continuous
Continuous
Discrete
Constant
[0, 90]
[0.1, 1.0]
Double Low-e
[0.2, 0.8]
[0.2, 0.8]
[0.2, 0.8]
[0.2, 0.8]
(1, 2)
Compact
conventional
roof
Cladding
Other
Constant
Constant
Insulation
Membrane
Discrete
Constant
Structure
Constant
Finish
Constant
Brick veneer
20 mm air
space
(1, 2, 3, 4, 5, 6)
6 mil
polyethylene
100 mm
concrete block
back-up
12.7 mm
Gypsum
Cladding
Other
Constant
Constant
Membrane
Constant
Sheathing
Constant
Insulation
(stud)
Membrane
Discrete
Constant
Finish
Constant
Other
Membrane
Insulation
Structure
Constant
Constant
Discrete
Constant
Finish
Constant
Layer of wall Type1
Layer of wall Type2
Layer of roof Type
R1-5
R1-6
Brick veneer
20 mm air
space
Asphalt
sheathing
paper
12.7 mm
oriented strand
board
(1, 2, 3, 4, 5, 6)
6 mil
polyethylene
12.7 mm
Gypsum
Ballast
4-ply Built-up
(1, 2, 3, 4, 5, 6)
OWSJ and
steel decking
12.7 mm
Gypsum
203 mm XPS;
229 mm XPS.
For the structured multi-objective genetic algorithm
(MOGA) implementation, the following parameters are
specified: crossover
probability ¼ 0.9,
mutation
probability ¼ 0.02, maximum number of generations ¼ 200, population size ¼ 40, external population
capacity ¼ 30, the maximum number of elites
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W. Wang et al. / Building and Environment 40 (2005) 1512–1525
6.500
6.000
LCEI (107 MJ)
introduced from the external population to the original
population in each generation is 10, the selection
operator is the binary tournament selection.
For the above described problem, the design space
consists of 7.6 1012 possible solutions. The problem is
solved for two scenarios with different electricity mix for
building operation. One is a hypothetical case assuming
that electricity is totally generated from oil. The other is
the actual case in Quebec with the dominant share of
hydro-electricity.
1521
initial
final
external
5.500
5.000
zone A
4.500
4.000
zone C
6.2. Results and discussion
3.500
3.200
zone B
3.400
3.600
3.800
4.000
4.200
4.400
4.600
Due to the inherent randomness of GA, the program
is run three times for each scenario. Each run takes
approximately 30 h on a computer with Windows XP
system (3.06 GHz Pentium-IV processor, 512 MB
RAM). Because the first scenario is better to illustrate
the trade-off relationship between the two performance
criteria, the results from this scenario are presented and
discussed in detail while the results from the second
scenario are presented briefly at the end of this section.
For all three runs of the first scenario, the external
population has reached its predefined capacity before
the termination of the GA. If all external individuals
from the three runs are put together, the number of
nondominated solutions is 21, 26, and 29, for each of the
three runs. Results from the run with 29 nondominated
solutions are further analyzed below.
Individuals in the initial, final, and external population are distributed in the performance space as
illustrated in Fig. 3. It can be seen from this figure that
impact but large cost, and solutions in zone B have
intermediate values for both criteria.
Solutions for the 29 nondominated individuals and
the corresponding objective function values are listed in
Table 2, which is arranged in increasing order of the
LCC. Some abbreviations are used because of space
limitations. Because window-to-wall ratios on all the
four sides take the same value, it is indicated in the table
without distinction about fac- ade. The actual insulation
material presented in Table 2, was defined in Section 6.1.
One can notice the following:
The initial randomly produced individuals are widely
distributed, while the final population is clustered to
the lower left corner. The final population is close to
the external population. Both of the two observations
indicate that a good convergence has been achieved.
The role of optimization is noticeable. Every solution
in the initial population is dominated by some
solutions in the final external population. The
minimum values of the life cycle cost and the life
cycle environmental impact are $3.569 105 and
4.612 107 MJ in the initial population, while they
reached $3.352 105 and 3.819 107 MJ in the
external population after the optimization.
Since it is hard to obtain the actual global Pareto
front for most practical problems, the curve drawn from
individuals in a well-converged external population can
be regarded as the Pareto front with reasonable
accuracy. It can be seen from Fig. 3 that the Pareto
front is composed of three isolated regions which are
indicated as zones A, B, and C in the figure. Solutions in
Pareto zone A have low cost but large environmental
impact, solutions in zone C have low environmental
LCC (105 $)
Fig. 3. Distribution of initial, final and external population in
performance space (scenario 1).
The optimal wall type is the steel-frame wall for all the
solutions located in the Pareto zone A while it is the
masonry cavity wall for the other two Pareto zones.
This indicates that the light wall is more favorable for
economical performance. However, the heavy wall is
better in terms of environmental performance.
For all Pareto solutions, orientation converges to
zero; window ratio on each fac- ade converges to the
low bound value which is equal to 0.2 in this case
study. This indicates that orientation and window
ratio will converge to the same optimal point even if
the two objective functions are optimized separately.
Aspect ratio may take different values in the range
between 0.702 and 0.986 for different Pareto solutions. This indicates that the optimal values of aspect
ratio are different for LCC and life cycle environmental impact. For example, only the aspect ratio is
changed for solutions with ID between 26 and 29
(Table 2). A value close to 1 is favorable for cost
reduction because square shape has the minimum
exterior envelope surface. However, a rectangular
shape with long side towards south is helpful for
energy performance.
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1522
Table 2
Selected Pareto solutions in external population
Pareto Zone
ID
Orien.
Aspect Ratio
WinRatio
Wall Type
Wall Insu.
Roof Insu.
LCC ($105)
LCEI (107 MJ)
A
1
2
3
4
5
6
7
8
9
10
0
0
0
0
0
0
0
0
0
0
0.901
0.787
0.851
0.773
0.965
0.823
0.965
0.802
0.908
0.795
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
2
2
2
2
2
2
2
2
2
2
W2-1
W2-1
W2-1
W2-1
W2-1
W2-1
W2-3
W2-3
W2-3
W2-3
R1-1
R1-1
R1-2
R1-2
R1-3
R1-3
R1-2
R1-2
R1-3
R1-3
3.352
3.357
3.361
3.366
3.368
3.372
3.379
3.384
3.389
3.394
4.598
4.595
4.491
4.490
4.409
4.401
4.329
4.322
4.236
4.232
B
11
12
13
14
15
16
17
18
19
0
0
0
0
0
0
0
0
0
0.986
0.787
0.865
0.787
0.958
0.787
0.738
0.695
0.908
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
1
1
1
1
1
1
1
1
1
W1-3
W1-3
W1-3
W1-3
W1-3
W1-3
W1-3
W1-3
W1-6
R1-1
R1-1
R1-2
R1-2
R1-3
R1-3
R1-3
R1-3
R1-3
3.436
3.442
3.446
3.451
3.454
3.461
3.466
3.471
3.485
4.194
4.184
4.088
4.085
4.010
4.001
4.000
3.999
3.975
C
20
21
22
23
24
25
26
27
28
29
0
0
0
0
0
0
0
0
0
0
0.936
0.823
0.731
0.901
0.901
0.752
0.936
0.809
0.752
0.702
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
1
1
1
1
1
1
1
1
1
1
W1-3
W1-3
W1-3
W1-6
W1-3
W1-3
W1-6
W1-6
W1-6
W1-6
R1-5
R1-5
R1-5
R1-5
R1-6
R1-6
R1-6
R1-6
R1-6
R1-6
3.622
3.626
3.634
3.653
3.658
3.667
3.687
3.693
3.698
3.704
3.930
3.924
3.921
3.897
3.857
3.851
3.828
3.821
3.820
3.819
More insulation increases the initial cost, however, it
can reduce the operating energy consumption. The
situation of insulation changing with the two
performance criteria can be observed in each Pareto
zone and between Pareto zones. In Pareto zone A , for
example, the wall insulation changed from W2-1
(152 mm fiberglass) to W2-3 (254 mm fiberglass). The
fiberglass is preferred because it has much less
embodied environmental impacts than the rockwool,
at almost equivalent thermal properties and construction cost. From Pareto zone B to C , the insulation in
roof changed from EPS to XPS which has lower
thermal conductivity and higher density. In addition,
insulation thickness for most solutions in Pareto zone
C takes the maximum value available for this
material, that is, 229 mm XPS.
Some additional information can be obtained if the
detailed constituents of each criterion are investigated
for different Pareto zones. The median is used to
represent all individuals in a Pareto zone. For the three
selected median individuals, their detailed constituents
of each performance criterion are shown in Table 3,
where the percent is indicated in the parentheses. It can
be seen from this table that
The initial cost has a large portion of LCC. This is
due to several reasons. First, the electricity price is
low. Second, lighting is not covered in the operating
cost because it is regarded as a constant, and therefore
it does not affect the optimal solutions. Third, the
structural components for floor and roof have high
construction costs.
For the two components of operating cost, demand
cost is much higher than energy consumption cost.
For example, in Pareto zone B, demand cost
($4.68 104) accounts for about 62% of operating
cost ($7.53 104), while energy consumption cost
($2.85 104) contributes the remaining 38%. This
indicates that it is important to incorporate demand
cost whenever LCC is optimized.
The pre-operation phase contributes to about 12% of
the life cycle environmental impact, while the building
operation phase takes the remaining 88%.
As more insulation is used by design solutions from
Pareto zone A to C, the proportion of initial cost and
embodied environmental impact increased by about
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W. Wang et al. / Building and Environment 40 (2005) 1512–1525
1523
Table 3
Constituents of performance criteria for representative individuals
Pareto zone
LCC ($104)
IC
LCEI (106 MJ)
OC
Demand
A
33.70
25.36 (75%)
B
34.54
27.01 (78%)
C
36.62
29.45 (80%)
8.34 (25%)
5.16 (16%)
7.53 (22%)
4.68 (14%)
7.18 (20%)
4.50 (13%)
In the pursuit of a sustainable society, improvements
in the environmental performance of buildings have a
critical effect. It is essential to have suitable tools
44.05
4.33 (10%)
39.72 (90%)
40.10
4.51 (11%)
35.58 (89%)
38.54
5.02 (14%)
33.52 (86%)
3.18 (9%)
2.85 (8%)
2.68 (7%)
2.100
initial
final
external
2.000
LCEI (107 $)
1.900
7. Conclusions
OE
Consumption
5%. Accordingly, the proportion of operating cost
and operating environmental impact decreased by an
equivalent amount.
The Pareto front obtained from the multi-objective
GA is useful in decision-making process. It can be used
in a number of ways. First, it can be used to get
information about the best values for each criterion.
This information is useful to set a reasonable target or
constraint with respect to selected criterion in the
conceptual design stage. Second, with predefined constraints for one criterion, the Pareto front can be used to
determine the optimal value for the other criterion.
Third, the Pareto front can be used to investigate the
trade-off relationship between the two criteria.
In the case of the second scenario, due to the
dominant share of hydro-electricity, only two Pareto
zones A and B are observed (Fig. 4). The life cycle
environmental impact values are about 65% less than
those for the first scenario. The contribution of building
operation to the life cycle environmental impacts
decreases to 70% while the contribution of the preoperation phase increases to 30%. Since the same
electricity price is used for both scenarios, the LCC
values and their allocation between demand and energy
consumption for the Pareto solutions in zone A and B
are almost the same. The optimal solutions are similar as
those for the first scenario except that the wall insulation
for all the solutions in Pareto zone B converge to W1-3
(152 mm EPS in masonry cavity wall).
EE
1.800
1.700
zone A
1.600
1.500
1.400
zone B
1.300
3.200
3.400
3.600
3.800
4.000
4.200
4.400
4.600
LCC (105 $)
Fig. 4. Distribution of initial, final and external population in
performance space (scenario 2).
available at the conceptual design stage that can assist
designers in finding better design alternatives efficiently.
The multi-objective optimization model proposed in this
paper can be used to locate optimum or near optimum
green building designs for given conditions. Using
expanded cumulative exergy consumption as the indicator for life cycle environmental performance, the
optimization problem can be simplified by incorporating
all considered impact categories into one objective
function. The structured formulation between wall/roof
types and layer components make it possible to
simultaneously optimize variables at different hierarchical levels. The multi-objective genetic algorithm can
identify multiple Pareto solutions in a single run. The
obtained Pareto front is important in helping designers
to understand the trade-off relationship between the
economical and the environmental performance.
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W. Wang et al. / Building and Environment 40 (2005) 1512–1525
The case study has shown that the Pareto front
consists of discrete regions with different optimal
solutions. Some variables such as orientation and
window ratio on each fac- ade converge to the same
value for all Pareto solutions. However, optimal values
for some variables such as aspect ratio and insulation
materials vary with different Pareto solutions or Pareto
zones. The case study has demonstrated that the utility
structure has a large impact on the environmental
performance. If the energy source of electricity generation changes from oil to hydro, the life cycle environmental impacts can be reduced by about 65%, and the
contribution of building operation to the life cycle
environmental impacts decreases from 90% to 70%.
The current stage of this study, however, focuses on
building envelope only. More parameters can be
optimized if the scope is expanded to cover mechanical
systems and passive solar design strategies. In addition,
complex building shape should be considered. Multizone energy simulation program with daylighting
consideration will be employed in the future in order
to enlarge the application scope of the established
optimization model.
Acknowledgement
The authors would like to acknowledge the financial
support provided by the EJLB Foundation for the
‘‘Environmental Impact of Building Materials’’ project.
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