An "ageing" operator and its use in the highly constrained topological optimization of HVAC system design.
ABSTRACT The synthesis of novel heating, ventilating, and airconditioning (HVAC), system configurations is a mixedinteger, nonlinear, highly constrained, multimodal, optimization problem, with many of the constraints being subject to timevarying boundary conditions on the system operation. It was observed that the highly constrained nature of the problem resulted in the dominance of the search by a single topology. This paper, introduces an new evolutionary algorithm operator that prevents topology dominance by penalizing solutions that have a dominant topology.The operator results in a range of dynamic behavior for the rates of growth in topology dominance. Similarly, the application of the ageing penalty can result in the attenuation of topology dominance, or more severely, the complete removal of a topology from the search. It was also observed that following the penalization of a dominant topology, the search was dynamically reseeded with both new and previously evaluated topologies. It is concluded that the operator prevents topology dominance and increases the exploratory power of the algorithm.The application of an evolutionary algorithm with ageing to the synthesis of HVAC system configurations resulted in a novel design solution having a 15% lower energy use than the best of conventional system designs.
 01/1994;

Conference Paper: Reducing energy use and operational cost of air conditioning systems with multiobjective evolutionary algorithms
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ABSTRACT: Air conditioning is responsible for around 60% of energy use in commercial buildings and is rapidly increasing in the residential sector. Although each system is individually small, the proliferation of air conditioning and the correlation of energy use with temperature is driving peak demand and the need for electricity distribution network upgrades. Energy retailers are now looking for ways to reduce this aggregate peak demand, leading to a tradeoff between peak demand, energy cost and the thermal comfort of building occupants. This paper presents a multiobjective evolutionary algorithm (MOEA) to quantify tradeoffs amongst these three competing goals. We study a scenario with 8 air conditioners (ACs) and compare our findings against the case of having all ACs working independently, irrespective of global goals. The results show that, with statistically significant certainty, any run of the MOEA outperforms any scenario where the ACs function independently to keep a given level of comfort on a typical hot day.Evolutionary Computation (CEC), 2010 IEEE Congress on; 08/2010  [Show abstract] [Hide abstract]
ABSTRACT: Poor indoor air quality (IAQ) may appear due to wrong choice of building materials, insufficient levels of ventilation, air filtering, and inadequate management of contaminant sources. The problems start with the lack of a decision mechanism besides the local or national standards when choosing a specific IAQ management option. Building industry is not thoroughly aware of the consequences of different IAQ management methods and decisions, yet they lack the resources to identify the "best" solutions to IAQ problems. These consequences may result in soft costs such as lost productivity as well as hard costs such as the conditioning of the incoming outdoor air. This paper proposes to combine these costs towards true costs and introduces a modeling methodology for optimizing IAQ in commercial buildings by mathematical programming. These analyses also explore the contradictions among IAQ and energy efficiency. This paper explores alternative IAQ control options in terms of improved ventilation and air cleaning and presents alternatives for decision variables, as well as the possible technical, financial, and legal constraints. Significance of the paper derives from introducing the idea of applying "Operations Research" to construction management and providing the conceptual background for formulating the optimization of IAQ in commercial buildings. (5931 Words)
Page 1
An “Ageing” Operator and Its Use in the Highly Constrained
Topological Optimization of HVAC System Design
Jonathan Wight, Yi Zhang
Department of Civil and Building Engineering, Loughborough University,
Loughborough, Leicestershire,
LE11 3TU, UK
Tel: +44(0)1509620365
J.A.Wright@lboro.ac.uk
ABSTRACT
The synthesis of novel heating, ventilating, and airconditioning
(HVAC), system configurations is a mixedinteger, nonlinear,
highly constrained, multimodal, optimization problem, with
many of the constraints being subject to timevarying boundary
conditions on the system operation. It was observed that the
highly constrained nature of the problem resulted in the
dominance of the search by a single topology. This paper,
introduces an new evolutionary algorithm operator that prevents
topology dominance by penalizing solutions that have a dominant
topology.
The operator results in a range of dynamic behavior for the rates
of growth in topology dominance. Similarly, the application of
the ageing penalty can result in the attenuation of topology
dominance, or more severely, the complete removal of a topology
from the search. It was also observed that following the
penalization of a dominant topology, the search was dynamically
reseeded with both new and previously evaluated topologies. It is
concluded that the operator prevents topology dominance and
increases the exploratory power of the algorithm.
The application of an evolutionary algorithm with ageing to the
synthesis of HVAC system configurations resulted in a novel
design solution having a 15% lower energy use than the best of
conventional system designs.
Categories and Subject Descriptors
I.2.8 [Artificial Intelligence]: Problem Solving, Control
Methods, and Search – heuristic methods.
J.6 [ComputerAided Engineering]: Computeraided Design
(CAD).
General Terms: Algorithms, Design.
Keywords: Evolutionary Algorithms, Topological
Optimization, HVAC, System Design.
1. INTRODUCTION
The temperature and humidity of the air in the occupied spaces of
commercial buildings, is maintained by “heating, ventilating and
air conditioning” (HVAC), systems. HVAC systems ventilate
buildings by taking in outside air and mixing it with air that has
been recirculated from within the building. The ventilation air is
further conditioned by heating, cooling, and humidifying
components. The ventilation air maintains the room temperature
and humidity by being supplied to the room at a condition that
offsets thermal loads on the room.
The air conditioning components can be connected together in a
number of ways to produce a viable system configuration. Over
the last 100 years, a number of recognized configurations have
evolved through the process of heuristic design [2]. The
alternative design solutions have been driven predominantly by
the need to limit the capital cost of the systems. This has led to
system configurations that are able to maintain the temperature
and humidity in more than one “control zone” (a control zone
being a collection of rooms that experience similar heat loads).
However, many of the established “multizone” systems have a
higher than necessary energy consumption (a “multizone” system
is one that simultaneously conditions more than one control
zone).
Concerns over climate change and associated energy use has
renewed interest in the design of HVAC systems for low energy
use. This paper describe an approach to the automatic synthesis of
HVAC system configurations for minimum energy use by an
evolutionary algorithm. A new algorithm operator which is
designed to maintain the power of the search in exploring
alternative system topologies is also described.
1.1 Problem Characteristics and
Optimization Approach
There are three elements to the design of an HVAC system,
1.
the selection of a component set (the choice of type and
number of components);
2.
given the component set, the design of the feasible
topology;
3.
optimization of the system operation (for several
different operating conditions).
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The selection of a feasible topology is dependent on the
component set and similarly, the optimization of system operation
Page 2
on the configuration. Hence, conventionally, the optimization of
such systems is conducted in a iterative manner, the iteration
sequence being first, the selection of a component set, followed
by the optimization of the system topology (with the evaluation of
each trail topology requiring the optimization of the system
operation). However, the need for repeated optimization of the
system topology and operation, results in the iteration being
computational intensive. Hence, the approach adopted here [1,7],
is that all three elements of the design problem are optimized
simultaneously. In the experiments described here, however, the
component set has been fixed so that the optimization is
concerned only with the choice of topology and system operation.
Note that HVAC systems are subject to time varying boundary
conditions (namely, the ambient climate and heat gains arising
inside the building), and that the system operation must be
optimized at each boundary condition. In the work reported here,
the system operation has optimized for 9 boundary conditions that
represent a period during the early morning, midday, and
afternoon, in each of three seasons (winter, spring or fall, and
summer).
The optimization problem can be described as a mixedinteger,
nonlinear programming problem, having nonlinear inequality
and equality constraints. The problem is also highly multimodal
in that there are many alternative system configurations, each
resulting in a local optimal solution for system operation. The
decision variables are derived from the representation of the
system topology, and the system operation (operation being
optimized for all 9 condition simultaneously). The problem
constraints maintain the feasibility of the topology and the system
operation. Finally, the objective function is formed from the
annual system energy use as estimated from the 9 operating
conditions.
The general approach to the problem formulation and solution has
been described previously [1,7], and is therefore only summarized
here.
1.1.1 Decision Variables and Encoding
There are two sets of decision variables, those relating to system
topology
, and those to the system operation,
decision variable
X , can be defined by:
(
XX
=
. The set of
d
X
c
X
)
cdX,
where:
nc
ncccc
nd
ndddd
RxxX
ZxxX
∈=
∈=
) ,....,(
) ,....,(
,,
,,
Each set of variables has been encoded in a separate chromosome,
the topology variables as an integer chromosome, and the system
operation variables as a real vector chromosome. The system
topology is represented by a modified adjacency matrix (system
graph), that has been designed to limit the duplicate
representation of topologies (although it does not eliminate this
effect completely). The topology chromosome has also been
designed to facilitate the implementation of problem specific
recombination and mutation operators [1,7].
The system operation variables are in two groups, those that
define the air–flow rate through the system and those that define
the thermal capacity (output) of the system components.
1.1.2 Objective Function
Formally, we seek to minimize the annual energy use of the
system
. The “annual energy use" is taken as a weighted
average of the system capacity at each of the 9 operating
conditions, the weights being applied in accordance with the
relative proportion of the prevailing climatic conditions. The
system capacity is a function of the capacity (thermal output), of
the air conditioning components, together with the fan power
required to move air through the duct system.
)(Xf
1.1.3 Constraint Functions and Infeasibility
Function
There are three sets of problem constraints, those concerned with
the viability of the system topology, those with the procedure for
evaluating the system performance and thirdly, those concerned
with the system operation. The topology constraints are concerned
with ensuring that that the system graph is connected in a manner
that enables feasible operation. Each topology constraint is
represented by an equality constraint (a binary constraint with a
value∈(0,1)). The aggregated value of topology constraint
violations
has been taken as the average of all topology
constraint violations (the aggregated value then being in the range
0.0 to 1.0).
)(
dtopXc
The system performance evaluation constraints are concerned
with identifying failure in the evaluation of system performance
(in effect, failure to solve the system algebraic equations). The
system operating constraints are concerned with ensuring that all
components operate within their performance limits and that the
system is able to maintain the desired zone conditions (the zone
constraints being on the amount of outside air entering the zone
and the zone temperature and humidity). The operation
constraints are in the form of both inequality and equality
constraints, although a reasonable engineering tolerance has been
applied to the equality constraints. As in the case of the topology
constraints, the constraints relating to the evaluation of system
performance and to system operation, have been aggregated to
have a value in the range 0.0 to 1.0 (0.0 indicating complete
feasibility).
Note that, although there are three groups of constraints (topology
constraints, performance evaluation constraints, system operation
constraints), the system performance can only be evaluated if a
feasible topology exists. Similarly, the system operation can only
be evaluated if the system performance evaluation has been
completed successfully. The constraint space is therefore
discontinuous; this has been reflected in the formulation of an
infeasibility function. If
aggregated constraint values for the topology, system
performance evaluation, and system operating constraints
respectively, then the system infeasibility
, and are the
, is given by:
)(
dtopXc
)(Xcev
)(Xcop
)(Xi
()
()
⎪
⎩
⎪
⎨
⎧
>+
c
>+
=
else),( 45. 0
0 . 0)( if else ),( 45
X
. 0 45. 0
0 . 0)( if),(1 . 0 9 . 0
)(XcXc
XcXc
Xi
op
evev
dtopdtop
This gives three bands of infeasibility, infeasible topologies result
in an infeasibility value in the range 0.9 to 1.0, failure to evaluate
the system performance, a value in the range 0.45 to 0.9, and
infeasible system operation in the range >0.0 to 0.45. The choice
Page 3
of banding is arbitrary and its impact on behavior of the
optimization has not been studied.
Note also, that the constraints on system performance evaluation
and system operation are a function of all variables (albeit an
implicit function of the topology variables), whereas the topology
constraints are only a function of the topology variables.
1.2 The Evolutionary Algorithm
The general form of the evolutionary algorithm used here has
been described previously [1,7]. In brief, a multichromosome
genetic algorithm has been developed to solve the topological
optimization problem, with each chromosome having its own
distinct recombination and mutation operators. Ten chromosomes
are active in the experiments reported here, one integer vector
chromosome representing the system topology (system graph),
and nine real vector chromosomes, one for each of the nine
system operating (boundary) conditions.
Several new recombination and mutation operators have been
developed for use with the topology chromosome, the goal of
these operators being to perform effective recombination and
mutation, while attempting to maintain the feasibility of the
system topology. The operators and their effectiveness have been
described previously [1]. In general, standard recombination and
mutation operators were adopted for use with the real vector
chromosomes, although some problem specific operators have
been developed for use in combination with a “hyperoperation”
(where the specific operator used at a given instance is decided
probabilistically) [7].
The fitness assignment is based on the stochastic ranking
algorithm [5], and selection by a binary tournament. A percentage
of the best solutions are treated as elite individuals and copied
directly to the next generation.
The algorithm control parameters used in the experiments
reported here are given in Table 1. The effect of the algorithm
control parameters on search performance has not been studied in
depth, although preliminary experiments where conducted to
confirm that the choice of parameters resulted in acceptable
performance of the algorithm. In particular, although it is
common to use high crossover rates in topological optimization
[3], a 100% probability of crossover for the topology chromosome
was found to be too disruptive, and resulted in a high probability
of generating infeasible topologies; the same behavior was
observed for the high mutation rates with the result that both the
crossover and mutation rates for the topology chromosome are
lower than used in solution of similar optimization problems. The
ageing control parameter relates to the new algorithm operator.
1.3 Topology Dominance
Previously reported results indicated that the evolutionary
algorithm had great potential to synthesize novel HVAC systems
[1]. An analysis of the performance of the approach was
subsequently extended to compare the energy use of the
synthesized systems against that of two conventional systems [7]
(referred to here as the “benchmark systems”). Many established
HVAC system configurations exist, with the choice of which
system is selected for a particular application depending on the
cost constraints on building construction and operation. In this
respect, the first of the benchmark systems is one with a moderate
capital cost, but potentially higher than necessary operating cost
Table 1. Algorithm Control Parameters
Operation Control Parameter Value
Population Size 1,000
Maximum Generations 10,000
Population
Elite Percentage 2%
Tournament
Selection
Number of Individuals 2
Topology
Chromosome
Probability
50%
Recombination
Operation
Chromosome
Probability
100%
Topology
Chromosome
Probability
2%
Mutation
Operation
Chromosome
Probability
10%
Stochastic Ranking
Probability of
Infeasible Solution
Ranking
45%
ageing
Maximum Evaluations
per Generation
20
(energy use); the second system has the higher capital cost, but
for the example building studied, has the lower operating cost
(energy use). In comparison to the performance of the two
benchmark systems, the evolutionary algorithm was able to
synthesize systems with an energy use in the range of the two
benchmark systems. Although this represents a significant
achievement in that the established systems are the result of over
a century of engineering research and development, a
thermodynamic analysis of the benchmark systems [7], suggested
that they were less than optimal in terms of their energy use.
An analysis of the algorithms behavior in respect to the
exploration of the topologies, indicated that at a single topology
could become dominant at an early stage in the search. Figure 1,
illustrates the lifespan of every topology synthesized during a
particular search. Each circle in the figure represents a unique
topology, with the horizontal axis indicating the generation in
which it was first synthesized. The vertical axis indicates the life
span of the topology in terms of the number of times it appeared
in any generation through the search (the total number of times it
was evaluated). Clearly, the search illustrated in Figure 1 has been
dominated by a single topology that first appeared at
(approximately) the 1200th generation, and was subsequently
evaluated more than 7x106 times throughout the duration of the
search. The dominance was further indicated by the topology
accounting for up to 80% of the individuals in a given generation.
It was also concluded that the reason for the dominance was the
implicit dependence of the system performance evaluation and
operating constraints on the system topology. For instance,
consider a solution which is completely feasible and therefore is
likely to have a reasonably high fitness. If the effect of a mutation
Page 4
operation on the topology is to move the position of one of the
components in the system, then it is highly likely that the solution
will become infeasible as the system operation will no longer be
valid (the change in position of the component would require a
change in the capacity of one or more components if the system
operation was to remain valid). In particular, the equality
constraints on the condition of the zone air have a high
probability of becoming infeasible when the system topology is
changed.
Figure 1. Topology Dominance
0 2000 40006000800010000
0
1
2
3
4
5
6
7
8x 10
6
Number of evaluations
Generation
Dominant topology
2. AN AGEING OPERATOR
The characteristic dominance of the search by a single topology
(Figure 1), is a clear indication that the exploratory power of the
search is limited. Such dominance can be addressed in several
ways; the population could be “partitioned” such that a number of
different topologies where forced to exist; or the spread of
topologies could be maintained by a sharing function with the
niche count derived from the topology chromosome only.
Partitioning the population is likely to have a limited effect as the
number of viable partitions and therefore alternative topologies is
restricted by the population size. Further, the notion of “distance”
between the different topologies as represented by the system
graph (topology chromosome), is not clearly defined and although
the topology chromosome has been designed to limit the duplicate
representation of alternative topologies by numerically different
chromosomes, the duplication is not guaranteed. As a result, a
new algorithm operator, known as “ageing”, was developed to
prevent the dominance of the search by any one topology.
The ageing concept is that any one topology has a maximum
number of evaluations, after which its fitness is reduced (as in real
life, fitness declines with age). The lifespan of the topology is
defined here in terms of the number of times the topology is
evaluated, rather than the number of generations that it has
survived. This allows a topology to survive many generations
provided that it does not dominate the population. The ageing
function is given by:
()
[] 0 . 1 , max)()(
'
ge
nqnXjXj
×−×=
where,
ageing,
, the maximum number of evaluations per generation allowed
for a given topology, and
(number of generations to date).
is the fitness of the individual,
the number of times the topology has been evaluated,
its fitness after
the current generation number
)(X
e n
j
)(
'Xj
q
g
n
The effect of the function is that provided the number of
evaluations to date (
), is less than the maximum allowed by
the current generation (
g
nq×
), the fitness remains unchanged. If
however, the number of evaluations exceeds the maximum
allowed, then the fitness function value is increased by a factor
equal to the number of evaluations in excess of the limit
(
ge
nqn
×−
). Note that in this formulation, the higher the fitness,
the lower the function value (
having a function value of 0.0. Since the best solution has a raw
fitness of 0.0, it is unaffected by the ageing operator, although any
other individual in the population having the same topology
would be subject to ageing. This acts to preserve at least one copy
of the current best topology, while limiting its dominance (the
best individual is preserved since we operate with a rank ordered
population, with the top 2% of individuals being copiedto the new
population).
e n
), with the best solution )(Xj
Figure 2, illustrates the effect of the ageing operator on limiting
topology dominance. As for Figure 1, the circles represent unique
topologies, the horizontal axis the generation in which they
appeared, and the vertical axis, the number of times a given
topology was evaluated over the search period. The dashed
diagonal line represents the ageing limit (in this case being 20
evaluations per generation, or 2% of the population per
generation). Topologies with evaluations above the line have been
subject to ageing, whereas those below survived without being
aged.
Figure 2. Effect of Ageing on Topology Dominance
5
0 20004000 6000800010000
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
x 10
Number of evaluations
Generation
Topology C (Optimum)
Topology B
Topology A
The three solid lines show the growth in number of evaluations
for three of the topologies (‘A’, ‘B’ and ‘C’). The point at which
the growth line crosses the ageing limit indicates the generation at
which ageing was applied to the particular topology. The three
example topologies exhibit very different behavior in this respect.
Page 5
Topology ‘A’ appeared early in the search and since the number
of duplicate topologies in any given population remained
relatively low, the topology survived many generations before
ageing was applied. Once aged, however, further growth in the
number of evaluations was highly attenuated (on the scale of
Figure 2, it would appear that there is no growth, although the
topology may in fact continue to survive with a few copies in
each subsequent generation).
Topology ‘B’ first appeared in midsearch, and remained
“dormant” for many generations, until it experienced a rapid
growth in the number of evaluations and subsequent application
of ageing. The behavior of topology ‘C’ is somewhat different to
that of topology ‘A’ and ‘B’, in that the rapid growth in number
of evaluations occurred soon after the topology first appeared.
Further, unlike topologies ‘A’ and ‘B’, topology ‘C’ remained
active after ageing, with the number of duplicate topologies
appearing in each subsequent generation being in the order of the
2% of the population (equivalent to the ageing limit).
Figure 2, therefore illustrates that the ageing operator allows a
topology to survive provided that it does not dominate the search,
and that the number of topologies having a significant impact on
the search has been increased (from 1 topology in Figure 1, to
many in Figure 2).
Figure 3. Dynamic Effect of Ageing on the Population
Diversity
60006500700075008000
0
100
200
300
400
500
600
700
800
900
1000
Topology count
Generation
All topologies
New topologies
Figure 3, illustrates the dynamic effect of ageing on the
population diversity (the vertical axis being the number of
different topologies in a given generation). Each increase in the
number of topologies corresponds to the application of the ageing
operator to a dominant topology. As the fitness of the dominant
topology is penalized, the diversity of the population grows both
in terms of new and previously evaluated topologies.
A detailed analysis of the effect of ageing on the behavior of the
search, or the effect of the ageing parameter
conducted, however, it can be concluded that, the ageing operator:
, has not been
q
•
prevents the long term dominance of the search by any one
topology;
•
allows topologies that have a low growth in number of
evaluations to survive for many generations, whereas
topologies that have a rapid increase in dominance of the
population are prevented from prolonged dominance;
•
and exhibits a dynamic behavior in the reseeding of the
population with new and previously searched topologies.
3. EXPERIMENTS
Two experiments have been conducted for the same example
problem, one experiment on the performance of the algorithm
without ageing, and second experiment with ageing.
3.1 Example Problem and Benchmark
Systems
The example HVAC optimization problem is for a two zone
building [7]. That is, the HVAC system is required to
simultaneously conditions two separate spaces in the building.
The level of difficultly associated with this “multizone” problem
is significantly greater than for the design of a system that serves
only one zone. The difficulty is associated with designing a
system that can condition zones that may be experiencing
different thermal loads and therefore have different conditioning
needs. For example, it is possible that one zone will require
cooling while a separate zone, conditioned by the same system,
may require heating. In the example developed here, the
operation of the system is optimized for 9 different boundary
(load) conditions, within which 5 different system operating
regimes occur (Table 2). As well as requiring the use of
mechanical heating and cooling, under some boundary conditions,
the system should be able to condition one or more zones through
the use of moderately cool outside air alone (which is referred to
as “free cooling” in Table 2).
Table 2. System Operating Regimes
Zone
East West
Heating Heating
Heating Cooling
Heating Free cooling
Free cooling Free cooling
Cooling Cooling
3.1.1 Problem Dimension
The component set selected for the experiments resulted in 21
discrete variables encoded in the integer topology chromosome
[7]. The number of alternative topologies resulting from the
chromosome structure is , which gives a search space of
5.1x10
duplication in the representation of the topologies and so the
number of unique topologies is <
) !(nO
20 topologies (although it is recognized that there is some
). ) !(nO
Each of the 9 boundary conditions results in 11 continuous
operational variables, which gives a total of 99 continuous
variables, encoded as 9 separate real chromosomes. Note that
separate recombination and mutation operators are applied to each
chromosome.
There are 10 equality constraints on the feasibility of the
topology; 1 equality and 9 inequality constraints on the evaluation