Evolutionary swarm design of architectural idea models
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 email@example.com firstname.lastname@example.orgABSTRACT 1. INTRODUCTIONIn this paper we present a swarm grammar system that Discoveries of intricate construction technologies appliedmakes use of bio-inspired mechanisms of reproduction, com- by ancient cultures are usually met with great surprise .munication and construction in order to build three-dimen- It is generally assumed that architectural freedom evolvessional structures. Ultimately, the created structures serve with scientiﬁc and technological progress . Accordingly,as idea models that lend themselves to inspirations for ar- the means to realize bold architectures have steadily grownchitectural designs. . Architects embrace the newly gained freedom — to im- Appealing design requires structural complexity. In or- plement almost anything conceivable — to devise innovativeder to computationally evolve swarm grammar conﬁgura- and compelling designs . Consequently, the search for in-tions that yield interesting architectural models, we observe triguing signature design ideas has shifted to the forefronttheir 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] wesure 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 . Traditionally these models are thesimulation 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 ourﬁtness function of a genetic algorithm. We show that the work in context in Section 2. In Section 3 we describeconducted measurements are useful to direct an evolutionary the swarm model that we have developed. In order to ﬁndsearch towards interesting yet well-constrained architectural swarm conﬁgurations that yield interesting architectural ideaidea 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 evolutionaryD.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]: Multiagentsystems, coherence and coordination; J.5 [Arts and Hu- 2. RELATED WORKmanities]: 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 . Lo- cal neighborhood information, consisting of ﬂock mates andGeneral Terms environmental stimuli (templates), trigger the individuals’ behaviors. Step by step, intricate architectural solutionsAlgorithms, 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 .Permission to make digital or hard copies of all or part of this work for Abstract constructive swarm models are utilized to createpersonal or classroom use is granted without fee provided that copies are traditional art , to craft virtual artistic sculptures ,not made or distributed for proﬁt or commercial advantage and that copies and for interactive art performances [18, 10]. Interactivelybear 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 forCopyright 2008 ACM 978-1-60558-131-6/08/07 ...$5.00. breeding aesthetically pleasing art works (e.g. [23, 24, 11]),
architectural designs quickly increase in complexity, thereby and robust buildings can emerge (see Section 2). Thus, wechallenging the breeder . 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 nowtationally as well as manually by a breeder. With the com- describe in more detail.putational means to determine and compare the complexityin architectural constructions, aesthetics could remain thesole 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. hierarchicalcomplexity) . Diﬀerent complexity measurements weretested on grammatical programs, respectively tree-like datastructures, whose interpretation leads to the creation of vir-tual artifacts . Under the assumption that a sound com-plexity measure scales with the size of the problem, it issuggested that the consideration of modularity, reuse andhierarchy yields reliable values of complexity. However, these characteristics cannot be easily identiﬁedin 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-. Swarms are non-determinstic systems in which local tion elements (boxes) are within the neighborhoodinteractions take place in parallel and create unforeseen in- perception of the blue swarm agent. This agent isterdependencies. 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 ﬂocking 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]. Wealso 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 0.5complexity by killing oﬀ ineﬃcient swarms that do not ter- </HEAD>minate within a ﬁxed time-frame. To keep the constructionof a swarm within well-deﬁned boundaries and to meet archi- <BODY>tecturally expected proportions, the approximation of pre- Construction Templatedeﬁned shapes is rewarded with an increase in evolutionaryﬁtness . 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  with the repro-duction abilities of a generative grammatical system, like Figure 2: The syntax of a behavioral rule, exemplaryL-systems . Hence, each swarm agent follows a set of for the encoding of the entire genotype.ﬂocking urges, e.g. alignment and separation, to constantlyadjust 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, thedetermines 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, allability 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 canhind 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 diethe reproduction of the swarm agents, resulting in plant-like, out. Third, the agent can place a construction element ororganic appearances. In a virtual creative system achieving a template in space. Templates, like pheromones, disappearan abundance of construction elements is inexpensive. We after a certain time and do not contribute to the outcomelearn from social insect swarms that when stigmergic inter- of the construction but help to coordinate the constructionplay directs the collective construction eﬀorts, sophisticated process. In our setup templates are evaluated qualitatively
by the agents: their mere existence can inﬂuence an agent’s duced population of successors. However, the population isbehavior . 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 . Figure 2 depicts the encoding of a rule taken ence the genetic operators can exercise due to incomputablefrom 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 EvaluationIn the following section we will reveal more details about an At the beginning of a simulation all N swarm agents2 ofagent’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-deﬁned4. 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 amodiﬁed 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 processlutionary 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 the4.1 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. Weswarm grammars over at least 30 generations. Each swarm will explore these constraints in more detail in the followinggrammar 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 geneticoperators we apply ﬁtness proportionate selection, elitism,mutation and crossover. How the two latter operate onthe swarm grammar genotypes is explained in the follow-ing paragraphs. The genotypes are encoded in tagged listsof key-value pairs, as illustrated in Figure 2. Only one fourth of the next generation is subjected tomutation which is applied with a 50% chance to each gene.Numerical values are changed in accordance with a normallydistributed maximal step size of 0.2. Hereby, the followingintervals 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 comparedvelocity and 30 for acceleration. Its perception extends at against this pre-deﬁned shape consisting of 103 smallmost to a 5.0 radians radius and reaches at most ten units. cubes.The separation urge impacts an agent’s acceleration only ifits neighbors are not further than 5.0 units . On muta-tion, rule conditions and actions are equally likely generatedanew, deleted, or inserted. In the generation of conditions 4.2.1 Preventing Escalationand 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. Inrective requires a parameter, it is chosen randomly as well. order to avoid such an excess of resource usage, a simulationFor instance, if ’Construction’ has been determined as new process taking longer than 100 real seconds is terminateddirective, ’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 thefrom recombination of the parents. Each behavioral rule one hand a certain degree of complexity in the emergingand the lists of ﬂocking parameters that appear in the geno- structures is desirable. On the other hand an outgrowth oftype 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 is50% 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 targettion. Elitism transfers the ﬁttest eighth of the parents to template are rewarded, whereas outgrowing the pre-deﬁnedthe next generation. limits is unproductive. Hereby, as in , the pre-deﬁned Individuals that are not assigned a ﬁtness value greater shape consists of smaller cubes with edge size 1.0 (Figurethan zero are considered extinct. If the parent population is 3(b)). We determine the ratio rp between the number ofdiminished, 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 2the agent’s orientation. For our experiments N=5.
Adding the ratio rp to a swam grammar’s ﬁtness valuerewards the swarm’s productivity but only within certainboundaries. 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 ofplaced construction elements nc can be utilized to furtherassess productivity and to limit the extent of constructionas well. Figure 4: Neighborhood perception rn during the4.2.2 Promoting Diversity construction process can sometimes be linked to the Since the construction patterns of individual swarm agents emerging structures. (a) A very compact structuremay vary, a wide diversity in constructions can be expected, emerges with rn = 0.87. (b) Swarm agents drift awaythat are built by a large number of diﬀerent swarm agents. from each other, which yields a low perception rateEven a homogeneous set of swarm agents can achieve greater rn = 0.08.diversity than a single swarm individual, as (1) the agentscan 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 + pavailable 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 availabletypes 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. RESULTSments, swarm agents may drop templates that do not con- A successful search for architectural idea models heavilytribute 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 resultingagents. We therefore also measure the ratio rt of created architectural constructions, before a variety of phenotypestemplates to those that actually trigger a behavioral rule. is presented and analyzed. Swarm interaction is based on each agent’s awareness ofother agents. Therefore, we compute the average ratio rn of 5.1 Fitness Evolution and Crossover Pointsagents 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 c1extreme 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 isclump as seen in Figure 4(a), whereas rn = 0.08 can be an considered for recombination (crossover operator c2). Theindication 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 of4.2.4 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 risesby 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. Thevariables to normalized values between 0.0 and 1.0 according tendency of avg c1 to stay considerably below avg c2 is notto their semantics: A neighborhood ratio not too close to a coincidence. If only agents of relatively successful swarm0.0 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 behavioralcontributing 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 workingarrive at the following ﬁtness function: on the building blocks of the agents’ genotypes. Especially
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 corresponding2.5 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 Architectures1.5 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 notFigure 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 nicethe 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 athemselves too frequently, the computing time rises and can pile of sheets, the second like a spiky armor and the thirdeasily exceed the maximum allowed timeframe. While the does not only mix cubic construction elements and elongatedaverage ﬁtness of the crossover on agents achieves a better rods, but also mixes two colors. The model in Fig. 6(b) candevelopment, the other crossover operator leads to a pop- also be divided into three parts. From the bottom-left ofulation of much greater diversity. On the one hand, the the image a lattice tail loosely connects to the main partrecombination possibilities are much greater when genetic of the model. From there on, rods are laid out horizontallyinformation on the agent behavior level is considered. On resembling stairs that lead to the top of an impenetrablethe 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-likeimpact on fSG and, consequently, on the evolutionary de- fashion around the model’s peak. Model Fig. 6(d) embodiesvelopment. 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 ofwhich did not contribute at all. Consequently, the following, dynamic parts. This vivid impression is supported by thesimpliﬁed 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 0.19variables seem too diﬃcult to be learned instantly, either Fig. 7(a) 0.30 0.28 Fig. 9(a) 0.81 0.35partial task fulﬁllment (e.g. ﬁrst, the placement of a tem- Fig. 7(b) 0.32 0.005 Fig. 9(b) 0.55 0.52plate and second, the response) should receive a reward. Fig. 7(c) 0.80 0.10 Fig. 9(c) 0.89 0.64Alternatively, the generation of behavioral rules could be Fig. 7(d) 0.75 0.16constrained, thereby reducing the search space for ‘useful‘rules. Table 1: Characteristic values of the presented5.2 Architectural Designs swarm grammar architectures. The outlined experimental setup results in a wide varietyof architectural designs, a selection of which is presented inthe following paragraphs. We diﬀerentiate between three 5.2.2 Body Architecturesstructure categories depending on the actual construction Figure 7 presents architectural idea models that are mainlyelements: rod, body or layer. This classiﬁcation schema assembled of (cubic) body construction elements. In fact,concurs with actual architectural categories . Addition- their share of all utilized construction elements varies be-
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 thebodies and rods on top of the bottom-up sequence of layered bent, the remaining 99.95% of the model consist of rodselements. The second example, Fig. 7(b), is distinct by its and body construction elements. Fig. 8(a) and (b) looksparse 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, resembledisplayed 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 isthe 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 numberin 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 resultsdiﬀerentiate upon sight of a body construction. The last in a rhythmic construction pattern that gains momentuminstance of body-based architectures is shown in Fig. 7(d). towards the model’s peak.Here, a dynamic character is introduced into the otherwiserather 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. In5.2.3 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
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 thethe 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 structureof 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 224play 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 Agentthat 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 0.5the 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 0.3hesion and alignment are forces to keep the agents orderly ﬂocking-center 0.6 Reproduction E ﬂocking-random 1.0together. When combined with a tendency for separation Reproduction A B ﬂocking-maxvelocity 0.5and randomness, the bulge formations can emerge. Fig. 9(c) ﬂocking-maxacceleration 1.7displays 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 isresponsible for the reproduction and diﬀerentiation — thecorresponding 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 skeletalfourth involved agent places a rod, a body and a layer all at structure in Figure 6(b). (b) The spawning rule toonce 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 toidea 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 perceivedby measuring neighborhood perception. Examples of suc- neighborhood ratio rn , where a series of cyclic or jumping
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