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SWARMBESO: MULTI-AGENT AND EVOLUTIONARY
COMPUTATIONAL DESIGN BASED ON THE PRINCIPLES OF
STRUCTURAL PERFORMANCE
DING WEN BAO1, XIN YAN2, ROLAND SNOOKS3and
YI MIN XIE4
1School of Architecture & Urban Design, RMIT Architecture | Tectonic
Formation Lab and Centre for Innovative Structures and Materials,
School of Engineering, STEM College, RMIT University
1nic.bao@rmit.edu.au
2Center of Architecture Research and Design, University of Chinese
Academy of Sciences and Centre for Innovative Structures and
Materials, School of Engineering, RMIT University
2yanxin13@mails.ucas.ac.cn
3School of Architecture & Urban Design and RMIT Architecture |
Tectonic Formation Lab, RMIT University
3roland.snooks@rmit.edu.au
4Centre for Innovative Structures and Materials, School of
Engineering, STEM College, RMIT University
4mike.xie@rmit.edu.au
Abstract. This paper posits a design approach that integrates
multi-agent generative algorithms and structural topology optimisation
to design intricate, structurally efficient forms. The research proposes
a connection between two dichotomous principles: architectural
complexity and structural efficiency. Both multi-agent algorithms and
Bi-directional evolutionary structural optimisation (BESO) (Huang and
Xie 2010), are emerging techniques that have significant potential in
the design of form and structure.This research proposes a structural
behaviour feedback loop through encoding BESO structural rules within
the logic of multi-agent algorithms. This hybridisation of topology
optimisation and swarm intelligence, described here as SwarmBESO,
is demonstrated through two simple structural models. The paper
concludes by speculating on the potential of this approach for the design
of intricate, complex structures and their potential realisation through
additive manufacturing.
Keywords. Swarm Intelligence; Multi-agent; BESO (bi-directional
evolutionary structural optimisation); Intricate Architectural Form;
Efficient Structure.
1. Introduction
This research posits an innovative design methodology that establishes a
complementary relationship between topological optimisation and behavioural
PROJECTIONS, Proceedings of the 26th International Conference of the Association for Computer-Aided
Architectural Design Research in Asia (CAADRIA) 2021, Volume 1, 241-250. © 2021 and published by the
Association for Computer-Aided Architectural Design Research in Asia (CAADRIA), Hong Kong.
242 D.W. BAO ET AL.
generative design algorithms. The research explores and evaluates the application
of topology optimisation and multi-agent algorithms in a form-finding design
process. It demonstrates the process of integrating these two algorithms to
establish a real-time structural feedback loop in the process of designing intricate
forms. It describes a hybrid of architectural and structural behaviours through the
integration of swarm systems and BESO methods.
This approach, termed swarmBESO (see figure 1), creates a negotiation
between concerns of architectural design and structural engineering in a
simultaneous generative approach. This is a fundamental shift from the normative
sequential workflows that either inform generative approaches with structural
analysis or operate sequentially to optimise the structure of complex geometries
already created within generative processes. The swarmBESO algorithm is
demonstrated here through two- and three-dimensional cantilevered structure
examples.
The future application of swarmBESO to architectural design will enable the
creation of complex, the expressive architectural form which is highly efficient
in terms of material and structural performance. The complexity and intricacy of
the geometry generated through this process are expected to become increasingly
feasible through the rapid development of building-scale additive manufacturing
approaches.
Figure 1. SwarmBESO.
2. Swarm Intelligence and Behavioral Formation
Swarm intelligence examines the emergent behavior of systems that self-organise
through the interaction of autonomous agents. This behavior is evident within the
natural world through systems such as flocks of birds, schooling of fish, and social
insects’ interaction.
The phenomena of swarm intelligence can be simulated and generated through
multi-agent algorithms - a computational logic that dates to John von Neumann’s
work with cellular automata in the 1940s. Multi-agent algorithms operate through
SWARMBESO: MULTI-AGENT AND EVOLUTIONARY
COMPUTATIONAL DESIGN BASED ON THE PRINCIPLES OF
STRUCTURAL PERFORMANCE
243
the local interaction of computational agents. This interaction of agents creates a
self-organising behavior at the meta, or global, scale. These algorithms establish
a non-linear relationship where each agent responds to the neighbouring agents
without hierarchical, or top-down, control.
The development of generative design processes based on multi-agent
algorithms has been emerging for twenty years within experimental architectural
practices and academia. One pioneering approach, Behavioral Formation, has
been developed by Roland Snooks that builds on the computational boids research
of Craig Reynolds. (Reynolds 1987).
Behavioral Formation is a generative design approach that draws from swarm
intelligence logic and operates through a multi-agent algorithmic process (Snooks
2014). Through this approach, the architectural intention is encoded within
computation agents. The interaction of which creates a self-organised design
intention and generates emergent proto-architectural form.
Figure 2. Composite wing by Studio Roland Snooks.
The exclusively local interaction of multi-agent systems creates self-organising
behaviour at the expense of global, or meta, awareness. This global ignorance
limits the capacity of multi-agent design strategies to respond to global conditions
such as topology, enclosure and structure. A strategy has previously been
proposed by Roland Snooks in response to this, termed agency of structure, which
operates through a heuristic approach to local structural behaviors that respond
to global structural analysis. Agency of structure “operates by iteratively testing
agent-based geometry, such as a network of members or bundle of strands, using
a finite element structural method. Finite element methods analyse the entire
structural topology and return information pertaining to each individual node or
agent (see figure 2). The agent adapts its behavior in response to this information
based on heuristic structural rules designed to resist the load. Through this
strategy, agents respond to the local implication of global conditions and, in doing
so, re-form the global conditions, setting up a continuous feedback loop.” (Snooks
2014, p131-132)
3. Bi-directional Evolutionary Structural Optimisation Method
Topology optimisation techniques have been widely used in structural fields.
Conventional optimisation methods are always aimed at achieving the single
purpose of maximising the structural performance. Due to the potentials for
244 D.W. BAO ET AL.
generating elegant and light-weight structures with high structural performance,
topology optimisation has gained extensive attention and experienced considerable
progress over the three decades. Topology optimisation aims to find an initial
structural configuration which meets a predefined criterion, and occasionally
it gives a design that can be completely new and innovative. Several
notable topology optimisation methods have been widely developed in topology
optimisation field, e.g. the homogenisation method (Bendsoe 1989; Bendsoe
and Kikuchi 1988), the solid isotropic material with penalisation (SIMP) method
(Bendsoe and Sigmund 1999; Bendsoe and Sigmund 2004), the evolutionary
structural optimisation (ESO) (Xie and Steven 1993; Xie and Steven 1994), the
bi-directional evolutionary structural optimisation (BESO) (Huang et al. 2007;
Huang and Xie 2007) (see figure 3) and the level-set method (LSM) (Wang et al.
2003; Allaire et al. 2004). Among others, BESO method has been proved to be
a reliable optimisation technique, which has been successfully applied in many
engineering and architectural design (Zhao et al. 2018; Yan et al. 2019; Burry et
al. 2005).
Figure 3. Bi-directional Evolutionary Structural Optimisation (BESO).
Although most topology optimisation techniques aim at achieving the
most optimised solution, the structural layout with the highest performance
may contradict the functional requirements and aesthetic designing concepts
in real problematic practices. Therefore, some modification methods based
on conventional topology optimisation are explored widely to solve specific
application problems. In 1992, Mike Xie and Grant Steven proposed a
numerical method for topology optimisation Evolutionary Structural Optimisation
(ESO) (Xie and Steven 1993; Xie and Steven 1994), and later Mike Xie
and Xiaodong Huang developed the Bi-directional Evolutionary Structural
Optimisation (BESO). BESO method allows the material to be removed and
added simultaneously. In BESO method algorithm, The initial research on
BESO was conducted by (Yang et al. 1999) for stiffness optimisation. “In their
study, the sensitivity numbers of the void elements are estimated through a linear
extrapolation of the displacement field after the finite element analysis. Then, the
solid elements with the lowest sensitivity numbers are removed from the structure,
and the void elements with the highest sensitivity numbers are changed into solid
elements.” (Huang and Xie 2010, p17). Two unrelated parameters determine the
numbers of removed and added elements in each iteration: the rejection ratio (RR)
and the inclusion ratio (IR), respectively. “In their BESO algorithm, elements with
the lowest von Mises stresses are removed, and void elements near the highest von
Mises stress regions are switched on as solid elements. Similarly, the numbers of
SWARMBESO: MULTI-AGENT AND EVOLUTIONARY
COMPUTATIONAL DESIGN BASED ON THE PRINCIPLES OF
STRUCTURAL PERFORMANCE
245
elements to be removed and added are treated separately with a rejection ratio and
an inclusion ratio, respectively.” (Huang and Xie 2010, p17).
4. SwarmBESO Methodology: BESO Logical Multi-agent System
Figure 4. Flowchart of the SwarmBESO method.
The swarmBESO approach involves iterative feedback where the results of an
FEA analysis drive structural behaviour within a multi-agent generative algorithm,
which in turn re-forms a structural mass. Each step of the agent triggers this
recursive process such that a constantly updating structural model drives every
step. The multi-agent generative algorithm negotiates between these structurally
driven behaviours and non-structural design behaviours, to create forms that are
generated by architectural design intention while being near-optimal structural
solutions (see figure 4).
246 D.W. BAO ET AL.
Figure 5. The logic of SwarmBESO method.
The agent number in each FEA element is connected with the relevant element
material property, which means the element will be given a softer material with
less Young’s modulus value in the next iteration if it has fewer agents inside. As
the diagram shows (see figure 5), a strain energy field is generated based on the
whole structure FEA result in each iteration. Every agent can be assigned an
initial velocity according to the strain energy field, and this velocity represents
the structurally driven behaviour. Furthermore, some essential swarm-rule-based
modifications, such as separation, alignment and cohesion, are introduced to
modify the initial agent velocity. As a result, with the modified velocities, agents
will make movements inside the FEA mesh and change the next FEA process’s
material properties.
4.1. 2D CANTILEVER
Figure 6. 2D Cantilever in FEA platform (left) and initial generated velocity field (right).
SWARMBESO: MULTI-AGENT AND EVOLUTIONARY
COMPUTATIONAL DESIGN BASED ON THE PRINCIPLES OF
STRUCTURAL PERFORMANCE
247
The 2D cantilever model is a classic analysis model in structural optimisation. The
plate model is fixed around the left side and subjected to a concentrated load at the
middle point on the right side (see left in figure 6). With swarmBESO method,
the strain energy field and initial structurally driven velocity field are generated
like the illustration (see right in figure 6). After several iterations, the agent can
be re-located as the diagram shows (see figure 7), and this result is similar to the
conventional topology optimised result.
Figure 7. 2D evolutionary result.
The new method has also been tested on the 2D long beam structure (see
figure 8). The colourful cloud pictures are the visualization result of analysed
data in finite element method. The green figures are the normal BESO result. The
multi-agent figures are the swarmBESO result, they are respectively iteration 10
(see left in figure 8) and iteration 35 (see right in figure 8). In comparison, the
swarmBESO results both achieve structural performance and have more complex
& diverse forms.
Figure 8. BESO and swarmBESO result comparison.
However, because of the single element layer, the 2D model may be faced with
some local blocking during the evolution process. In the 3D model, the situation
248 D.W. BAO ET AL.
will be averted as there are multi-movement strategies for an agent to bypass the
local obstacles.
4.2. 3D CANTILEVER
Figure 9. The 3D cantilever in FEA platform.
Initially, a simple 3D cantilever (solid element) is tested for swarmBESO
algorithm in the FEA platform Abaqus (see figure 9). After setting up the boundary
conditions, the finite element method analyses the entire structural surface, and
return the information of the field of stress and strain energy density (SED) among
the whole structure. A certain number of agents are uniformly distributed over the
entire structure to represent the material distribution.
Figure 10. Real-time SED information feedback and iterations.
Based on the returned information of the field of stress and SED, the initial
vector will be applied to each agent. At the same time, three basic swarm rules are
applied to the agents (see figure 10).
The agent adapts its new modified behaviour in response to this integrated
information of vector and starts to move to a new position. Based on the logic of
BESO (Huang and Xie 2010), the material distribution will be kept updating in
each loop iteration until it reaches a certain volume fraction.
SWARMBESO: MULTI-AGENT AND EVOLUTIONARY
COMPUTATIONAL DESIGN BASED ON THE PRINCIPLES OF
STRUCTURAL PERFORMANCE
249
Figure 11. 3D evolutionary process.
In each step of the iteration, the information of structural performance will be
returned and reviewed. The information can be analysed by checking the strain
energy density distribution. Thus, the structural logic-based swarm evolutionary
method is applied and tested. From the above diagram (see figure 11), it is evident
that the swarmBESO generations are less than conventional topology optimisation
methods. In swarmBESO, all the agents are motivated based on local rules at
the same time rather than just some certain areas are changed in other traditional
methods. As a result, it may be difficult for swarmBESO to find the globally
optimised structure, but it can generate diverse results with similar structural
performance.
5. Conclusions
The integration of multi-agent generative algorithms and structural topology
optimisation creates a simultaneous process of architectural and structural
generation. This approach has the potential to develop a closer working
collaboration between architects and structural engineers in the early stages of
design and to avoid the structural rationalisation of unfeasible architectural forms.
The next steps in this research are to demonstrate the capacity of this algorithmic
tool through the design of several prototypical projects and to embed the logic
of additive manufacturing techniques within the swarmBESO algorithm. While
the simple cantilever examples illustrated here to demonstrate the operation of
swarmBESO, the real potential in this approach lies in the capacity of this
algorithm to create highly complex and intricate architectural tectonics that are
structurally efficient.
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