![Evolutionary Swarm Design of Architectural Idea Models
Sebastian von Mammen Christian Jacob
Department of Computer Science Department of Computer Science
University of Calgary University of Calgary
2500 University Drive NW 2500 University Drive NW
T2N 1N4 Calgary, Alberta, Canada T2N 1N4 Calgary, Alberta, Canada
s.vonmammen@ucalgary.ca cjacob@ucalgary.ca
ABSTRACT 1. INTRODUCTION
In this paper we present a swarm grammar system that Discoveries of intricate construction technologies applied
makes use of bio-inspired mechanisms of reproduction, com- by ancient cultures are usually met with great surprise [9].
munication and construction in order to build three-dimen- It is generally assumed that architectural freedom evolves
sional structures. Ultimately, the created structures serve with scientific and technological progress [5]. Accordingly,
as idea models that lend themselves to inspirations for ar- the means to realize bold architectures have steadily grown
chitectural designs. [4]. Architects embrace the newly gained freedom — to im-
Appealing design requires structural complexity. In or- plement almost anything conceivable — to devise innovative
der to computationally evolve swarm grammar configura- and compelling designs [5]. Consequently, the search for in-
tions that yield interesting architectural models, we observe triguing signature design ideas has shifted to the forefront
their productivity, coordination, efficiency, and their unfold- of architectural work.
ing diversity during the simulations. In particular, we mea- Inspired by building processes of social insects [7, 2] we
sure the numbers of collaborators in each swarm individual’s have developed a computer-based, evolutionary swarm sys-
neighborhood, and we count the types of expressed swarm tem to create 3D structures that lend themselves to archi-
agents and built construction elements. At the end of the tectural idea models [13]. Traditionally these models are the
simulation the computation time is saved and the created first three-dimensional realization of an architectural idea,
structures are rated with respect to their approximation of still omitting details of its actual construction.
pre-defined shapes. These ratings are incorporated into the We have organized our paper as follows. We place our
fitness function of a genetic algorithm. We show that the work in context in Section 2. In Section 3 we describe
conducted measurements are useful to direct an evolutionary the swarm model that we have developed. In order to find
search towards interesting yet well-constrained architectural swarm configurations that yield interesting architectural idea
idea models. models we apply evolutionary computation. The interplay of
genotype representation, phenotype simulation, their eval-
Categories and Subject Descriptors uation and deployed evolutionary operators is described in
Section 4. Section 5 presents results of our evolutionary
D.2.8 [Software Engineering]: Metrics—complexity mea- runs, followed by a summary and an outlook on future work.
sures, performance measures; I.2.6 [Learning]: Induction;
I.2.11 [Distributed Artificial Intelligence]: Multiagent
systems, coherence and coordination; J.5 [Arts and Hu- 2. RELATED WORK
manities]: Architecture; J.6 [Computer-aided Engineer- Wasp nests, ant galleries and termite mounds are exam-
ing]: Computer-aided design (CAD) ples of the construction abilities of natural swarms [7]. Lo-
cal neighborhood information, consisting of flock mates and
General Terms environmental stimuli (templates), trigger the individuals’
behaviors. Step by step, intricate architectural solutions
Algorithms, Design emerge while individuals transport construction elements,
place pheromones and react to traces left by their mates.
Keywords This stigmergic approach of nest constructions of social in-
Swarm grammar, constructive swarm, generative represen- sects has been reproduced in computational simulations [2,
tation, swarm model, stigmergy, boids, complexity 19]. Refined simulations showed that even the consideration
of physical constraints (like wind) do not negatively affect
the modeled decentralized swarm construction of termites
[15].
Permission to make digital or hard copies of all or part of this work for Abstract constructive swarm models are utilized to create
personal or classroom use is granted without fee provided that copies are traditional art [3], to craft virtual artistic sculptures [11],
not made or distributed for profit or commercial advantage and that copies and for interactive art performances [18, 10]. Interactively
bear this notice and the full citation on the first page. To copy otherwise, to trained rule-based lattice swarms have been used to repro-
republish, to post on servers or to redistribute to lists, requires prior specific duce human-like architectural construction [28, 29].
permission and/or a fee.
GECCO’08, July 12–16, 2008, Atlanta, Georgia, USA. While interactive evolution has proven most adequate for
Copyright 2008 ACM 978-1-60558-131-6/08/07 ...$5.00. breeding aesthetically pleasing art works (e.g. [23, 24, 11]),](https://image.slidesharecdn.com/evolutionaryswarmdesignofarchitecturalideamodels-111020172043-phpapp01/85/Evolutionary-swarm-design-of-architectural-idea-models-1-320.jpg)
![architectural designs quickly increase in complexity, thereby and robust buildings can emerge (see Section 2). Thus, we
challenging the breeder [1]. In a semi-interactive evolution- have extended previous swarm grammar systems by event-
ary system the fitness of an individual is evaluated compu- based construction and reproduction rules, which we now
tationally as well as manually by a breeder. With the com- describe in more detail.
putational means to determine and compare the complexity
in architectural constructions, aesthetics could remain the
sole role of the breeder [17, 16].
Complexity can incorporate different aspects, such as: eco-
logical diversity, complexity of construction (functionality),
or internal complexity (also logical depth, e.g. hierarchical
complexity) [22]. Different complexity measurements were
tested on grammatical programs, respectively tree-like data
structures, whose interpretation leads to the creation of vir-
tual artifacts [8]. Under the assumption that a sound com-
plexity measure scales with the size of the problem, it is
suggested that the consideration of modularity, reuse and
hierarchy yields reliable values of complexity.
However, these characteristics cannot be easily identified
in constructive swarm systems which do not offer a one-
to-one mapping from an encoding to the resulting artifact,
unlike other generative representations such as L-systems Figure 1: The green agents (polygons) and construc-
[20]. Swarms are non-determinstic systems in which local tion elements (boxes) are within the neighborhood
interactions take place in parallel and create unforeseen in- perception of the blue swarm agent. This agent is
terdependencies. Therefore, we need to analyze the swarm urged to align with the perceived agents’ orienta-
configuration, but we especially have to observe the result- tions (upper arrow) and to separate from its flock
ing construction process to estimate the unfolding system mates (lower arrow) at the same time.
complexity. For this purpose we measure the average num-
ber of flock mates within each individual’s neighborhood,
similar to the analysis of complex networks [12, 6]. We
also observe the diversity of the expressed swarms (num- <RULE>
ber of swarm agent types) and consider the number of types
<HEAD>
of construction elements used in the construction process.
Furthermore, we prevent an outgrowth of (computational) Probability 0.5
complexity by killing off inefficient swarms that do not ter-
</HEAD>
minate within a fixed time-frame. To keep the construction
of a swarm within well-defined boundaries and to meet archi- <BODY>
tecturally expected proportions, the approximation of pre-
Construction Template
defined shapes is rewarded with an increase in evolutionary
fitness [26]. Construction Body dynamic
</BODY>
3. SWARM GRAMMAR MODEL
</RULE>
Swarm grammars [25, 11, 27] are a very expressive ar-
tificial swarm model. They merge the interaction dynam-
ics of boid, i.e. agent-based, swarms [21] with the repro-
duction abilities of a generative grammatical system, like Figure 2: The syntax of a behavioral rule, exemplary
L-systems [20]. Hence, each swarm agent follows a set of for the encoding of the entire genotype.
flocking urges, e.g. alignment and separation, to constantly
adjust its acceleration in accordance with its local neighbor-
hood (Figure 10), while a grammatical production system The activation of a rule can be triggered by timers, the
determines the individual’s transformation over time. Thus, perception of a specific construction element or a pheromone,
a swarm grammar system comprises (1) a set of agent con- or plain chance. Empty rule heads result in the uncondi-
figurations, and (2) a set of production rules. Additionally, tional application of the rule body, whereas several con-
most swarm grammar models incorporate their individuals’ ditions are interpreted conjunctively. Correspondingly, all
ability to build structures by leaving construction elements directives listed in a rule’s body are executed successively.
in virtual space. The swarm agent can change its focus (world center [21, 14])
In preceding swarm grammar models the agents leave be- to a nearby agent, construction element or template. It can
hind steady traces of construction elements in space [25, 11]. apply a grammatical substitution, thereby reproduce itself,
As a result, many emerging structures branch according to differentiate into one or several different agent types, or die
the reproduction of the swarm agents, resulting in plant-like, out. Third, the agent can place a construction element or
organic appearances. In a virtual creative system achieving a template in space. Templates, like pheromones, disappear
an abundance of construction elements is inexpensive. We after a certain time and do not contribute to the outcome
learn from social insect swarms that when stigmergic inter- of the construction but help to coordinate the construction
play directs the collective construction efforts, sophisticated process. In our setup templates are evaluated qualitatively](https://image.slidesharecdn.com/evolutionaryswarmdesignofarchitecturalideamodels-111020172043-phpapp01/85/Evolutionary-swarm-design-of-architectural-idea-models-2-320.jpg)
![by the agents: their mere existence can influence an agent’s duced population of successors. However, the population is
behavior [2]. For construction, we provide the three basic automatically filled up with newly generated swarm gram-
elements that are common in architecture: rods, bodies and mars. This mechanism counterbalances the negative influ-
layers [13]. Figure 2 depicts the encoding of a rule taken ence the genetic operators can exercise due to incomputable
from an evolved swarm agent presented in Section 5: With rule sets.
a probability p = 0.5 the agent places a template and a cu-
bic body construction element in space at each time step1 . 4.2 Fitness Evaluation
In the following section we will reveal more details about an At the beginning of a simulation all N swarm agents2 of
agent’s genotype. a swarm grammar are expressed and initialized around the
center of the virtual space (up to 10 units in x and y di-
rection). Close by, at the bottom center of the pre-defined
4. EVOLUTIONARY SETUP shape, at coordinates (5, 5, 0)T , a template appears hint-
First, we describe how swarm grammars are encoded and ing at an ideal spot for construction (Figure 3(a)). For a
modified during the evolutionary process. Second, we ex- specified time period of ∆t = 8sec the swarm agents coor-
plain the process of fitness evaluation that directs the evo- dinate, build and reproduce. Then the construction process
lutionary search for architectural idea models. is stopped, all data is written into a file and the next swarm
grammar is evaluated. The fitness is evaluated based on the
4.1 Genotype and GA goals to limit computational and constructional outgrowth
In our breeding experiments we evolved populations of 20 and to promote production, diversity and collaboration. We
swarm grammars over at least 30 generations. Each swarm will explore these constraints in more detail in the following
grammar comprises 5 swarm agent types which are described sections and then propose a fitness function that incorpo-
by their flocking parameters [21, 14] and by sets of at most rates these aspects.
10 behavioral rules as described in Section 3. As genetic
operators we apply fitness proportionate selection, elitism,
mutation and crossover. How the two latter operate on
the swarm grammar genotypes is explained in the follow-
ing paragraphs. The genotypes are encoded in tagged lists
of key-value pairs, as illustrated in Figure 2.
Only one fourth of the next generation is subjected to
mutation which is applied with a 50% chance to each gene.
Numerical values are changed in accordance with a normally
distributed maximal step size of 0.2. Hereby, the following
intervals are considered: The flocking weights for cohesion,
alignment, separation, for the world center urge and for the Figure 3: (a) Initial simulation state: 5 agents (poly-
random urge are normalized to values between 0.0 and 1.0. gons) are randomly placed in the vicinity of a tem-
An agent’s mobility is limited to the absolute values 15 for plate (cube). (b) Emerging structures are compared
velocity and 30 for acceleration. Its perception extends at against this pre-defined shape consisting of 103 small
most to a 5.0 radians radius and reaches at most ten units. cubes.
The separation urge impacts an agent’s acceleration only if
its neighbors are not further than 5.0 units [14]. On muta-
tion, rule conditions and actions are equally likely generated
anew, deleted, or inserted. In the generation of conditions
4.2.1 Preventing Escalation
and actions each available directive, e.g. ’Change focus’ or Uncontrolled agent reproduction can quickly lead to an
’Reproduce’, are chosen with the same probability. If a di- exponentially growing demand for computing resources. In
rective requires a parameter, it is chosen randomly as well. order to avoid such an excess of resource usage, a simulation
For instance, if ’Construction’ has been determined as new process taking longer than 100 real seconds is terminated
directive, ’Rod’, ’Body’, ’Layer’ and ’Template’ are equally and is not considered for further evolution. Additionally,
likely chosen as its parameter. the computing time t for a swarm grammar is stored as a
5/8th of the next generation of swarm grammars result variable in order to determine a specimen’s fitness. On the
from recombination of the parents. Each behavioral rule one hand a certain degree of complexity in the emerging
and the lists of flocking parameters that appear in the geno- structures is desirable. On the other hand an outgrowth of
type of a swarm grammar are used for recombination. Here, (computational) complexity has to be avoided.
too, we apply the operation on each considered gene with a The same idea is realized when the swarm construction is
50% chance. An alternative crossover implementation con- compared against a pre-defined shape at the end of the sim-
siders only the agents of a swarm grammar for recombina- ulation: constructions within a certain range of the target
tion. Elitism transfers the fittest eighth of the parents to template are rewarded, whereas outgrowing the pre-defined
the next generation. limits is unproductive. Hereby, as in [26], the pre-defined
Individuals that are not assigned a fitness value greater shape consists of smaller cubes with edge size 1.0 (Figure
than zero are considered extinct. If the parent population is 3(b)). We determine the ratio rp between the number of
diminished, the genetic algorithm generates an equally re- these cubes that are penetrated by construction elements
versus the total number of cubes comprised by the pre-
1
The keyword dynamic that occurs in the rule in Figure 2 defined shape.
means that the body construction is rotated according to
2
the agent’s orientation. For our experiments N=5.](https://image.slidesharecdn.com/evolutionaryswarmdesignofarchitecturalideamodels-111020172043-phpapp01/85/Evolutionary-swarm-design-of-architectural-idea-models-3-320.jpg)
![f ally, we introduce a category for swirly architectural idea
3
models.
The discussion of the examples underlines that the map-
max_c2 ping from a swarm grammar genotype to the corresponding
2.5 structure is not trivial. The provided characteristic mea-
max_c1
sures drive the evolutionary process, yet one can hardly in-
fer specific architectural categories from these measures, as
2 we will demonstrate.
avg_c2
5.2.1 Rod Architectures
1.5
Figure 6 shows four examples of constructions in which
rods dominate their visual character. In fact, the structure
avg_c1 depicted in Fig. 6(c) only comprises about 60 rods, a mere
1 3% of the employed construction elements. The remaining
generation
three architectures, Fig. 6 (a), (b) and (d), however, are
0 10 20 30 40
based on 50% to 60% rods. Investigation of the genotypes
reveals that the rod-architecture swarms’ behaviors are not
Figure 5: Fitness evolution in two experiments im-
synchronized through timer conditions. In general however,
plementing different crossover operators. The upper
they exhibit rule conditions similar to those of the follow-
graphs represent the maximal fitnesses achieved in
ing examples (44% unconditional, 18% probabilistic, 15%
each generation, whereas the lower graphs depict
on template sight, 14% on agent sight, and 10% timers).
the average fitnesses of each generation.
The presented swarm grammars’ tracing success value rp
and neighborhood perception rn are listed in Table 1.
The four phenotypes displayed in Figure 6 show a nice
the exchange of behavioral rules can lead to a swarm gram- diversity. Fig. 6(a) exhibits three completely different seg-
mar’s quick extinction. As soon as the agents reproduce ments, arranged from left to right. The first looks like a
themselves too frequently, the computing time rises and can pile of sheets, the second like a spiky armor and the third
easily exceed the maximum allowed timeframe. While the does not only mix cubic construction elements and elongated
average fitness of the crossover on agents achieves a better rods, but also mixes two colors. The model in Fig. 6(b) can
development, the other crossover operator leads to a pop- also be divided into three parts. From the bottom-left of
ulation of much greater diversity. On the one hand, the the image a lattice tail loosely connects to the main part
recombination possibilities are much greater when genetic of the model. From there on, rods are laid out horizontally
information on the agent behavior level is considered. On resembling stairs that lead to the top of an impenetrable
the other hand, the high extinction rate allows new geno- spherical heap of rods. Fig. 6(c) shows a multifarious con-
types to enrich the gene pool. struction. Cubic elements are arranged at the bottom and
In our experiments certain fitness properties were obtained the top. They are interconnected with a densely packed,
faster than others. rp , gn , gc and ga had fast and great dynamically shaped hose. Rods are floating in a wave-like
impact on fSG and, consequently, on the evolutionary de- fashion around the model’s peak. Model Fig. 6(d) embodies
velopment. We were not able to promote rising values for the swarm dynamics of the construction process. The move-
ra , and rc which mostly exhibited erratic changes, or for rt ments of the flocks of swarm agents create the impression of
which did not contribute at all. Consequently, the following, dynamic parts. This vivid impression is supported by the
simplified fitness function might have sufficed to breed the rough looking combination of layers and rod elements.
presented examples.
Model rp rn Model rp rn
simple gc + ga
fSG = rp + gn + p Fig. 6(a) 0.89 0.16 Fig. 8(a) 0.77 0.51
max(t, 1) Fig. 6(b) 0.59 0.50 Fig. 8(b) 0.71 0.30
Fig. 6(c) 0.98 0.41 Fig. 8(c) 0.85 0.54
Also, since the ‘tasks‘ that correspond to the ineffective Fig. 6(d) 0.19 0.43 Fig. 8(d) 0.53 0.19
variables seem too difficult to be learned instantly, either Fig. 7(a) 0.30 0.28 Fig. 9(a) 0.81 0.35
partial task fulfillment (e.g. first, the placement of a tem- Fig. 7(b) 0.32 0.005 Fig. 9(b) 0.55 0.52
plate and second, the response) should receive a reward. Fig. 7(c) 0.80 0.10 Fig. 9(c) 0.89 0.64
Alternatively, the generation of behavioral rules could be Fig. 7(d) 0.75 0.16
constrained, thereby reducing the search space for ‘useful‘
rules.
Table 1: Characteristic values of the presented
5.2 Architectural Designs swarm grammar architectures.
The outlined experimental setup results in a wide variety
of architectural designs, a selection of which is presented in
the following paragraphs. We differentiate between three 5.2.2 Body Architectures
structure categories depending on the actual construction Figure 7 presents architectural idea models that are mainly
elements: rod, body or layer. This classification schema assembled of (cubic) body construction elements. In fact,
concurs with actual architectural categories [13]. Addition- their share of all utilized construction elements varies be-](https://image.slidesharecdn.com/evolutionaryswarmdesignofarchitecturalideamodels-111020172043-phpapp01/85/Evolutionary-swarm-design-of-architectural-idea-models-5-320.jpg)
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Evolutionary swarm design of architectural idea models
- 1. Evolutionary Swarm Design of Architectural Idea Models Sebastian von Mammen Christian Jacob Department of Computer Science Department of Computer Science University of Calgary University of Calgary 2500 University Drive NW 2500 University Drive NW T2N 1N4 Calgary, Alberta, Canada T2N 1N4 Calgary, Alberta, Canada s.vonmammen@ucalgary.ca cjacob@ucalgary.ca ABSTRACT 1. INTRODUCTION In this paper we present a swarm grammar system that Discoveries of intricate construction technologies applied makes use of bio-inspired mechanisms of reproduction, com- by ancient cultures are usually met with great surprise [9]. munication and construction in order to build three-dimen- It is generally assumed that architectural freedom evolves sional structures. Ultimately, the created structures serve with scientific and technological progress [5]. Accordingly, as idea models that lend themselves to inspirations for ar- the means to realize bold architectures have steadily grown chitectural designs. [4]. Architects embrace the newly gained freedom — to im- Appealing design requires structural complexity. In or- plement almost anything conceivable — to devise innovative der to computationally evolve swarm grammar configura- and compelling designs [5]. Consequently, the search for in- tions that yield interesting architectural models, we observe triguing signature design ideas has shifted to the forefront their productivity, coordination, efficiency, and their unfold- of architectural work. ing diversity during the simulations. In particular, we mea- Inspired by building processes of social insects [7, 2] we sure the numbers of collaborators in each swarm individual’s have developed a computer-based, evolutionary swarm sys- neighborhood, and we count the types of expressed swarm tem to create 3D structures that lend themselves to archi- agents and built construction elements. At the end of the tectural idea models [13]. Traditionally these models are the simulation the computation time is saved and the created first three-dimensional realization of an architectural idea, structures are rated with respect to their approximation of still omitting details of its actual construction. pre-defined shapes. These ratings are incorporated into the We have organized our paper as follows. We place our fitness function of a genetic algorithm. We show that the work in context in Section 2. In Section 3 we describe conducted measurements are useful to direct an evolutionary the swarm model that we have developed. In order to find search towards interesting yet well-constrained architectural swarm configurations that yield interesting architectural idea idea models. models we apply evolutionary computation. The interplay of genotype representation, phenotype simulation, their eval- Categories and Subject Descriptors uation and deployed evolutionary operators is described in Section 4. Section 5 presents results of our evolutionary D.2.8 [Software Engineering]: Metrics—complexity mea- runs, followed by a summary and an outlook on future work. sures, performance measures; I.2.6 [Learning]: Induction; I.2.11 [Distributed Artificial Intelligence]: Multiagent systems, coherence and coordination; J.5 [Arts and Hu- 2. RELATED WORK manities]: Architecture; J.6 [Computer-aided Engineer- Wasp nests, ant galleries and termite mounds are exam- ing]: Computer-aided design (CAD) ples of the construction abilities of natural swarms [7]. Lo- cal neighborhood information, consisting of flock mates and General Terms environmental stimuli (templates), trigger the individuals’ behaviors. Step by step, intricate architectural solutions Algorithms, Design emerge while individuals transport construction elements, place pheromones and react to traces left by their mates. Keywords This stigmergic approach of nest constructions of social in- Swarm grammar, constructive swarm, generative represen- sects has been reproduced in computational simulations [2, tation, swarm model, stigmergy, boids, complexity 19]. Refined simulations showed that even the consideration of physical constraints (like wind) do not negatively affect the modeled decentralized swarm construction of termites [15]. Permission to make digital or hard copies of all or part of this work for Abstract constructive swarm models are utilized to create personal or classroom use is granted without fee provided that copies are traditional art [3], to craft virtual artistic sculptures [11], not made or distributed for profit or commercial advantage and that copies and for interactive art performances [18, 10]. Interactively bear this notice and the full citation on the first page. To copy otherwise, to trained rule-based lattice swarms have been used to repro- republish, to post on servers or to redistribute to lists, requires prior specific duce human-like architectural construction [28, 29]. permission and/or a fee. GECCO’08, July 12–16, 2008, Atlanta, Georgia, USA. While interactive evolution has proven most adequate for Copyright 2008 ACM 978-1-60558-131-6/08/07 ...$5.00. breeding aesthetically pleasing art works (e.g. [23, 24, 11]),
- 2. architectural designs quickly increase in complexity, thereby and robust buildings can emerge (see Section 2). Thus, we challenging the breeder [1]. In a semi-interactive evolution- have extended previous swarm grammar systems by event- ary system the fitness of an individual is evaluated compu- based construction and reproduction rules, which we now tationally as well as manually by a breeder. With the com- describe in more detail. putational means to determine and compare the complexity in architectural constructions, aesthetics could remain the sole role of the breeder [17, 16]. Complexity can incorporate different aspects, such as: eco- logical diversity, complexity of construction (functionality), or internal complexity (also logical depth, e.g. hierarchical complexity) [22]. Different complexity measurements were tested on grammatical programs, respectively tree-like data structures, whose interpretation leads to the creation of vir- tual artifacts [8]. Under the assumption that a sound com- plexity measure scales with the size of the problem, it is suggested that the consideration of modularity, reuse and hierarchy yields reliable values of complexity. However, these characteristics cannot be easily identified in constructive swarm systems which do not offer a one- to-one mapping from an encoding to the resulting artifact, unlike other generative representations such as L-systems Figure 1: The green agents (polygons) and construc- [20]. Swarms are non-determinstic systems in which local tion elements (boxes) are within the neighborhood interactions take place in parallel and create unforeseen in- perception of the blue swarm agent. This agent is terdependencies. Therefore, we need to analyze the swarm urged to align with the perceived agents’ orienta- configuration, but we especially have to observe the result- tions (upper arrow) and to separate from its flock ing construction process to estimate the unfolding system mates (lower arrow) at the same time. complexity. For this purpose we measure the average num- ber of flock mates within each individual’s neighborhood, similar to the analysis of complex networks [12, 6]. We also observe the diversity of the expressed swarms (num- <RULE> ber of swarm agent types) and consider the number of types <HEAD> of construction elements used in the construction process. Furthermore, we prevent an outgrowth of (computational) Probability 0.5 complexity by killing off inefficient swarms that do not ter- </HEAD> minate within a fixed time-frame. To keep the construction of a swarm within well-defined boundaries and to meet archi- <BODY> tecturally expected proportions, the approximation of pre- Construction Template defined shapes is rewarded with an increase in evolutionary fitness [26]. Construction Body dynamic </BODY> 3. SWARM GRAMMAR MODEL </RULE> Swarm grammars [25, 11, 27] are a very expressive ar- tificial swarm model. They merge the interaction dynam- ics of boid, i.e. agent-based, swarms [21] with the repro- duction abilities of a generative grammatical system, like Figure 2: The syntax of a behavioral rule, exemplary L-systems [20]. Hence, each swarm agent follows a set of for the encoding of the entire genotype. flocking urges, e.g. alignment and separation, to constantly adjust its acceleration in accordance with its local neighbor- hood (Figure 10), while a grammatical production system The activation of a rule can be triggered by timers, the determines the individual’s transformation over time. Thus, perception of a specific construction element or a pheromone, a swarm grammar system comprises (1) a set of agent con- or plain chance. Empty rule heads result in the uncondi- figurations, and (2) a set of production rules. Additionally, tional application of the rule body, whereas several con- most swarm grammar models incorporate their individuals’ ditions are interpreted conjunctively. Correspondingly, all ability to build structures by leaving construction elements directives listed in a rule’s body are executed successively. in virtual space. The swarm agent can change its focus (world center [21, 14]) In preceding swarm grammar models the agents leave be- to a nearby agent, construction element or template. It can hind steady traces of construction elements in space [25, 11]. apply a grammatical substitution, thereby reproduce itself, As a result, many emerging structures branch according to differentiate into one or several different agent types, or die the reproduction of the swarm agents, resulting in plant-like, out. Third, the agent can place a construction element or organic appearances. In a virtual creative system achieving a template in space. Templates, like pheromones, disappear an abundance of construction elements is inexpensive. We after a certain time and do not contribute to the outcome learn from social insect swarms that when stigmergic inter- of the construction but help to coordinate the construction play directs the collective construction efforts, sophisticated process. In our setup templates are evaluated qualitatively
- 3. by the agents: their mere existence can influence an agent’s duced population of successors. However, the population is behavior [2]. For construction, we provide the three basic automatically filled up with newly generated swarm gram- elements that are common in architecture: rods, bodies and mars. This mechanism counterbalances the negative influ- layers [13]. Figure 2 depicts the encoding of a rule taken ence the genetic operators can exercise due to incomputable from an evolved swarm agent presented in Section 5: With rule sets. a probability p = 0.5 the agent places a template and a cu- bic body construction element in space at each time step1 . 4.2 Fitness Evaluation In the following section we will reveal more details about an At the beginning of a simulation all N swarm agents2 of agent’s genotype. a swarm grammar are expressed and initialized around the center of the virtual space (up to 10 units in x and y di- rection). Close by, at the bottom center of the pre-defined 4. EVOLUTIONARY SETUP shape, at coordinates (5, 5, 0)T , a template appears hint- First, we describe how swarm grammars are encoded and ing at an ideal spot for construction (Figure 3(a)). For a modified during the evolutionary process. Second, we ex- specified time period of ∆t = 8sec the swarm agents coor- plain the process of fitness evaluation that directs the evo- dinate, build and reproduce. Then the construction process lutionary search for architectural idea models. is stopped, all data is written into a file and the next swarm grammar is evaluated. The fitness is evaluated based on the 4.1 Genotype and GA goals to limit computational and constructional outgrowth In our breeding experiments we evolved populations of 20 and to promote production, diversity and collaboration. We swarm grammars over at least 30 generations. Each swarm will explore these constraints in more detail in the following grammar comprises 5 swarm agent types which are described sections and then propose a fitness function that incorpo- by their flocking parameters [21, 14] and by sets of at most rates these aspects. 10 behavioral rules as described in Section 3. As genetic operators we apply fitness proportionate selection, elitism, mutation and crossover. How the two latter operate on the swarm grammar genotypes is explained in the follow- ing paragraphs. The genotypes are encoded in tagged lists of key-value pairs, as illustrated in Figure 2. Only one fourth of the next generation is subjected to mutation which is applied with a 50% chance to each gene. Numerical values are changed in accordance with a normally distributed maximal step size of 0.2. Hereby, the following intervals are considered: The flocking weights for cohesion, alignment, separation, for the world center urge and for the Figure 3: (a) Initial simulation state: 5 agents (poly- random urge are normalized to values between 0.0 and 1.0. gons) are randomly placed in the vicinity of a tem- An agent’s mobility is limited to the absolute values 15 for plate (cube). (b) Emerging structures are compared velocity and 30 for acceleration. Its perception extends at against this pre-defined shape consisting of 103 small most to a 5.0 radians radius and reaches at most ten units. cubes. The separation urge impacts an agent’s acceleration only if its neighbors are not further than 5.0 units [14]. On muta- tion, rule conditions and actions are equally likely generated anew, deleted, or inserted. In the generation of conditions 4.2.1 Preventing Escalation and actions each available directive, e.g. ’Change focus’ or Uncontrolled agent reproduction can quickly lead to an ’Reproduce’, are chosen with the same probability. If a di- exponentially growing demand for computing resources. In rective requires a parameter, it is chosen randomly as well. order to avoid such an excess of resource usage, a simulation For instance, if ’Construction’ has been determined as new process taking longer than 100 real seconds is terminated directive, ’Rod’, ’Body’, ’Layer’ and ’Template’ are equally and is not considered for further evolution. Additionally, likely chosen as its parameter. the computing time t for a swarm grammar is stored as a 5/8th of the next generation of swarm grammars result variable in order to determine a specimen’s fitness. On the from recombination of the parents. Each behavioral rule one hand a certain degree of complexity in the emerging and the lists of flocking parameters that appear in the geno- structures is desirable. On the other hand an outgrowth of type of a swarm grammar are used for recombination. Here, (computational) complexity has to be avoided. too, we apply the operation on each considered gene with a The same idea is realized when the swarm construction is 50% chance. An alternative crossover implementation con- compared against a pre-defined shape at the end of the sim- siders only the agents of a swarm grammar for recombina- ulation: constructions within a certain range of the target tion. Elitism transfers the fittest eighth of the parents to template are rewarded, whereas outgrowing the pre-defined the next generation. limits is unproductive. Hereby, as in [26], the pre-defined Individuals that are not assigned a fitness value greater shape consists of smaller cubes with edge size 1.0 (Figure than zero are considered extinct. If the parent population is 3(b)). We determine the ratio rp between the number of diminished, the genetic algorithm generates an equally re- these cubes that are penetrated by construction elements versus the total number of cubes comprised by the pre- 1 The keyword dynamic that occurs in the rule in Figure 2 defined shape. means that the body construction is rotated according to 2 the agent’s orientation. For our experiments N=5.
- 4. Adding the ratio rp to a swam grammar’s fitness value rewards the swarm’s productivity but only within certain boundaries. From a different perspective, it promotes con- structions that retrace the provided pre-defined shape. In- dependently of the pre-defined shape, the total number of placed construction elements nc can be utilized to further assess productivity and to limit the extent of construction as well. Figure 4: Neighborhood perception rn during the 4.2.2 Promoting Diversity construction process can sometimes be linked to the Since the construction patterns of individual swarm agents emerging structures. (a) A very compact structure may vary, a wide diversity in constructions can be expected, emerges with rn = 0.87. (b) Swarm agents drift away that are built by a large number of different swarm agents. from each other, which yields a low perception rate Even a homogeneous set of swarm agents can achieve greater rn = 0.08. diversity than a single swarm individual, as (1) the agents can influence each other’s behavior, and (2) the same con- struction processes can be conducted in parallel. We ex- press these observations numerically by ra , the ratio of ac- tive agent types during a simulation to the total number of gc + ga fSG = rp + ra + rc + rt + gn + p available agent genotypes, and by na , the total number of max(t, 1) expressed agents. gn = sin(π ∗ rn ) Whenever different types of construction elements (rods, layers, bodies) are employed, an increase in structural di- gc = sin(π ∗ 0.005 ∗ min(nc , 200)) versity can be expected. As a consequence, the ratio rc of ga = sin(π ∗ 0.005 ∗ min(na , 200)) employed construction elements to the number of available types is also considered for fitness computation. This fitness evaluation is used in our experiments, which we describe in the following section. 4.2.3 Fostering Collaboration As an alternative to the deployment of construction ele- 5. RESULTS ments, swarm agents may drop templates that do not con- A successful search for architectural idea models heavily tribute to the construction and last for a short period of time depends on the effectiveness of the genetic algorithm, espe- only (for 20 iterations in the presented simulations). Con- cially on the crossover operator and on the fitness evalua- sequently, time-critical signals can be propagated through tion. Therefore, we first discuss our findings about the in- templates, thus promoting collaboration among the swarm fluence of the operator and fitness function on the resulting agents. We therefore also measure the ratio rt of created architectural constructions, before a variety of phenotypes templates to those that actually trigger a behavioral rule. is presented and analyzed. Swarm interaction is based on each agent’s awareness of other agents. Therefore, we compute the average ratio rn of 5.1 Fitness Evolution and Crossover Points agents that see each other to the total number of agents. For Figure 5 depicts representative graphs of the fitness evo- larger rn the swarm agents stick together, whereas smaller lution in two independent experiments. rn values reveal a very loose flight pattern — both of these In the first experiment we apply a crossover operator c1 extreme situations render collaboration difficult. For in- on rules and sets of flocking parameters only. In the sec- stance, a swarm grammar with rn = 0.87 might form a ond experiment each of the swarm grammars’ N agents is clump as seen in Figure 4(a), whereas rn = 0.08 can be an considered for recombination (crossover operator c2). The indication for uncoordinated growth as seen in Figure 4(b). average and the maximum fitness values of each generation are shown in the graphs avg c1 and max c1 in regards to c1, and in avg c2 and max c2 in regards to c2, respectively. Elitism ensures that the best individuals are transfered unchanged into the next generation. Noise in the sequence of 4.2.4 Proposed Fitness Function maximum fitness values (max c1 and max c2) is due to ran- The factors explained above are taken into consideration domness in the simulations. As shown, max c1 usually rises by the following scalar fitness function for a swarm grammar, slower but does not differ much from max c2. The develop- fSG . The terms gn , gc and ga transform the corresponding ment of average fitness values is of particular interest. The variables to normalized values between 0.0 and 1.0 according tendency of avg c1 to stay considerably below avg c2 is not to their semantics: A neighborhood ratio not too close to a coincidence. If only agents of relatively successful swarm 0.0 or 1.0 is presumably beneficial. Reasonable amounts grammars are exchanged, the offspring’s success mainly de- of expressed agents and placed construction elements are pends on the agent interaction encoded in their behavioral contributing to the fitness as well, especially, if these efforts rules. Underachievement and thereby extinction can hap- do not overly extend the computation time t. We therefore pen, but is less frequent than with recombination working arrive at the following fitness function: on the building blocks of the agents’ genotypes. Especially
- 5. f ally, we introduce a category for swirly architectural idea 3 models. The discussion of the examples underlines that the map- max_c2 ping from a swarm grammar genotype to the corresponding 2.5 structure is not trivial. The provided characteristic mea- max_c1 sures drive the evolutionary process, yet one can hardly in- fer specific architectural categories from these measures, as 2 we will demonstrate. avg_c2 5.2.1 Rod Architectures 1.5 Figure 6 shows four examples of constructions in which rods dominate their visual character. In fact, the structure avg_c1 depicted in Fig. 6(c) only comprises about 60 rods, a mere 1 3% of the employed construction elements. The remaining generation three architectures, Fig. 6 (a), (b) and (d), however, are 0 10 20 30 40 based on 50% to 60% rods. Investigation of the genotypes reveals that the rod-architecture swarms’ behaviors are not Figure 5: Fitness evolution in two experiments im- synchronized through timer conditions. In general however, plementing different crossover operators. The upper they exhibit rule conditions similar to those of the follow- graphs represent the maximal fitnesses achieved in ing examples (44% unconditional, 18% probabilistic, 15% each generation, whereas the lower graphs depict on template sight, 14% on agent sight, and 10% timers). the average fitnesses of each generation. The presented swarm grammars’ tracing success value rp and neighborhood perception rn are listed in Table 1. The four phenotypes displayed in Figure 6 show a nice the exchange of behavioral rules can lead to a swarm gram- diversity. Fig. 6(a) exhibits three completely different seg- mar’s quick extinction. As soon as the agents reproduce ments, arranged from left to right. The first looks like a themselves too frequently, the computing time rises and can pile of sheets, the second like a spiky armor and the third easily exceed the maximum allowed timeframe. While the does not only mix cubic construction elements and elongated average fitness of the crossover on agents achieves a better rods, but also mixes two colors. The model in Fig. 6(b) can development, the other crossover operator leads to a pop- also be divided into three parts. From the bottom-left of ulation of much greater diversity. On the one hand, the the image a lattice tail loosely connects to the main part recombination possibilities are much greater when genetic of the model. From there on, rods are laid out horizontally information on the agent behavior level is considered. On resembling stairs that lead to the top of an impenetrable the other hand, the high extinction rate allows new geno- spherical heap of rods. Fig. 6(c) shows a multifarious con- types to enrich the gene pool. struction. Cubic elements are arranged at the bottom and In our experiments certain fitness properties were obtained the top. They are interconnected with a densely packed, faster than others. rp , gn , gc and ga had fast and great dynamically shaped hose. Rods are floating in a wave-like impact on fSG and, consequently, on the evolutionary de- fashion around the model’s peak. Model Fig. 6(d) embodies velopment. We were not able to promote rising values for the swarm dynamics of the construction process. The move- ra , and rc which mostly exhibited erratic changes, or for rt ments of the flocks of swarm agents create the impression of which did not contribute at all. Consequently, the following, dynamic parts. This vivid impression is supported by the simplified fitness function might have sufficed to breed the rough looking combination of layers and rod elements. presented examples. Model rp rn Model rp rn simple gc + ga fSG = rp + gn + p Fig. 6(a) 0.89 0.16 Fig. 8(a) 0.77 0.51 max(t, 1) Fig. 6(b) 0.59 0.50 Fig. 8(b) 0.71 0.30 Fig. 6(c) 0.98 0.41 Fig. 8(c) 0.85 0.54 Also, since the ‘tasks‘ that correspond to the ineffective Fig. 6(d) 0.19 0.43 Fig. 8(d) 0.53 0.19 variables seem too difficult to be learned instantly, either Fig. 7(a) 0.30 0.28 Fig. 9(a) 0.81 0.35 partial task fulfillment (e.g. first, the placement of a tem- Fig. 7(b) 0.32 0.005 Fig. 9(b) 0.55 0.52 plate and second, the response) should receive a reward. Fig. 7(c) 0.80 0.10 Fig. 9(c) 0.89 0.64 Alternatively, the generation of behavioral rules could be Fig. 7(d) 0.75 0.16 constrained, thereby reducing the search space for ‘useful‘ rules. Table 1: Characteristic values of the presented 5.2 Architectural Designs swarm grammar architectures. The outlined experimental setup results in a wide variety of architectural designs, a selection of which is presented in the following paragraphs. We differentiate between three 5.2.2 Body Architectures structure categories depending on the actual construction Figure 7 presents architectural idea models that are mainly elements: rod, body or layer. This classification schema assembled of (cubic) body construction elements. In fact, concurs with actual architectural categories [13]. Addition- their share of all utilized construction elements varies be-
- 6. Figure 6: Rod-based architectural idea models. Figure 7: (Cubic) bodies coin the character of these architectural idea models. tween 30% and 50%. Simple as it might appear, the con- struction in Fig. 7(a) achieves a very good approximation of by the employment of layer construction elements. In fact, the pre-defined shape (Table 1) and grows an extended set of Fig. 8(c) only utilizes 5 layers that can be spotted at the bodies and rods on top of the bottom-up sequence of layered bent, the remaining 99.95% of the model consist of rods elements. The second example, Fig. 7(b), is distinct by its and body construction elements. Fig. 8(a) and (b) look sparse use of different construction elements. An interplay very similar. Yet, they originated from completely indepen- of flocking swarm agents is obviously not required for the dent experiments. Their characteristic values, too, resemble displayed model, as an extremely short perception radius of each other, except for the neighborhood ratio rn (Table 1). 0.6 units (maximally 10.0) keeps the swarm agents’ neigh- Figures 8(a) and (b) consist of 25% and 17% layers, respec- borhood perception very low (Table 1). Fig. 7(c) presents tively. During both construction processes, agents trans- a futuristic design that emerges through three interwoven form/reproduce 15 times. Their visual resemblance is strik- construction mechanisms. (1) Cubic body elements form ing: From the bottom a rather rigid and straight stem is the main part of the model. (2) Layers flank the main part drawn upwards for about 3/4th of the total height. Then, along the entire edge length. (3) Both layers and cubic body body construction elements rise to a podium that is orna- parts are rising in tandem to complete the construction with mented by several rods. During the construction of Fig. an elevated, inclined platform. The construction rule shown 8(d), agents reproduce 76 times. The increasing number in Figure 2 belongs to an agent involved in the construction of identical agents steadily widens the diameter of the con- of Fig. 7(c). In fact, another rule makes the same agent struction (67% layers). The interplay of the swarms results differentiate upon sight of a body construction. The last in a rhythmic construction pattern that gains momentum instance of body-based architectures is shown in Fig. 7(d). towards the model’s peak. Here, a dynamic character is introduced into the otherwise rather strict body architectures as seen in Fig. 7(a), (b) and 5.2.4 Swirly Architectures (c). Figure 9 presents three architectures that embody the ac- tual swarm dynamics during the construction processes. In 5.2.3 Layer Architectures Fig. 9(a) a homogeneous set of five agents swirls around a Figure 8 displays four tower constructions that are coined rising path while dropping layers and rods. The resulting
- 7. Figure 8: These tower architectures are mainly as- sembled of layer construction elements. construction receives good credit for the approximation of Figure 9: The displayed architectures emphasize the the pre-defined shape and proves that a relatively low neigh- swarm dynamics of the construction process. borhood ratio rn = 0.35 may very well lead to an intriguing, vivid swarm architecture (Table 1). The skeletal structure of Fig. 9(b) is assembled of rods and body construction el- < CONFIGURATION > ements. Several swarm agents wrap around and cement the <RULE> inner construction with waves of rods. Crucial for this inter- timers 24 70 98 247 224 play is the probability-driven reproduction of the ‘foremen‘ construction-color 0.4 0.4 0.3 <HEAD> and their differentiation into mere operative swarm agents flocking-neighborhoodradius 5.4 Agent that do nothing but place construction elements. The emer- flocking-neighborhoodangle 2.0 flocking-neighborhoodmindist 2.5 </HEAD> gence of a tight flocking pattern also strongly influenced flocking-alignment 0.5 the outcome. Figure 10(a) depicts the whole set of flocking flocking-cohesion 0.5 <BODY> parameters that determine the operative agent’s flight. Co- flocking-separation 0.3 hesion and alignment are forces to keep the agents orderly flocking-center 0.6 Reproduction E flocking-random 1.0 together. When combined with a tendency for separation Reproduction A B flocking-maxvelocity 0.5 and randomness, the bulge formations can emerge. Fig. 9(c) flocking-maxacceleration 1.7 displays a very complex swarm grammar: During the con- </BODY> struction process agents spawn 725 times which might have < /CONFIGURATION > </RULE> led to the long computation time of t = 63.3sec. During (b) (a) the interplay of the expressed swarm agents, one of them is responsible for the reproduction and differentiation — the corresponding behavioral rule is displayed in Figure 10(b). Figure 10: (a) The flocking parameters of the op- One agent only places rods, another one only layers. The erative agent that wraps rods around the skeletal fourth involved agent places a rod, a body and a layer all at structure in Figure 6(b). (b) The spawning rule to once but with a very low probability p = 0.2. delegate construction, employed in Figure 6(c). 6. SUMMARY AND FUTURE WORK We have presented an extended swarm grammar model cessfully bred swarm architectures are presented and dis- that is capable of stigmergic construction of architectural cussed. Although the introduced measures are efficient to idea models. In order to guide the evolutionary search we guide the evolutionary search for innovative architectures, prevent structural and computational outgrowth by reward- they cannot be directly linked to the architecture’s proper- ing the approximation of a pre-defined shape and fast com- ties. putation. Productivity, diversity and collaboration are fur- For future work we consider the following steps. (1) In- thered by counting events of construction, reproduction and vestigation of the temporal development of the perceived by measuring neighborhood perception. Examples of suc- neighborhood ratio rn , where a series of cyclic or jumping
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