Knitectonics - Genetic Algorithm - Chapter VII

Knitectonics

Chapter VII

Genetic Algorithm

genetic algorithm

Basic Variables of the System

Number of Tracks: 7

Yarn:

1 6

2 6

3 6

4 6

5 6

6 6

7 6 Start Position: Track Bed Needle

Number of Yarns: 6

0

1

2

3

Yarn Properties: Strength Wheight Flexibility

4

5

6

0

1

2

Head Sequence: Continue Return Bridge

Number of Heads: 6

0

1

2

3

4

5

6

176

0

1

7

7

7

7

6

10

2

3

Knitectonics

The digital machinic system offers several ways to setup system in terms of the number of tracks, their design involves solving bridge what herbert simon terms anand ill-structured problem (simon, 1973). configuration, connections also number of yarn heads, An ill-structured problem is one that cannot be solved by a linear chain of reasoning detheir start point and the yarn type used. Along with the attachment, rived from the problem statement. Furthermore, it might not have a unique solution but a movement and solidification control and most importantly the semultiplicity of solutions. these design problem characteristics imply the need for many asquences prescribed to the yarn heads, the permutations and comsumptions within the design process that can only be verified after a solution is reached. binations possible are endless. For instance, with all other paramthis makes computational design systems a difficult area of study. Although recent eters constant justinby using permutations of three sequences possibilities provided by and advances computational power and new developments in perfor a single head, the number of iterations possible sixty four! formance analysis tools offer architects and engineers information that can is assist in deci1 introduction up the machine

sion making, insight gained through these tools remains limited. this is due to their inadequate of searching the design-space in addition, since these tools are Theability system provides multiplesatisfactorily. solutions with equal suitability

and

usually specific, they lack the ability to supply sufficient understanding of the not discipline a unique solution, thus making it impossible to solve in a linear

‘A generative multi-perfomance design system is composed of four main phases. Each phase is a clouster of modules’. Anas Alfaris & Riccardo Merello - ‘The Generative MultiPerformance Design System’.

possible tradeoffs the different disciplines. a creating effective computational de-could manner.

Webetween attempted at devising generative system that sign systems requires the development of new ways to represent designs and to evaluate

evaluate and choose, in order to locate appropriate architectural solutions.

their different disciplines performance collectively.

Generative synthesis models present a powerful formalism that can generate solutions

within the design space defined by the system’s design language. current design problems

understandand generative wetoreferred Anad Alfaris areTo multi-disciplinary, for architectssystems, and engineers adapt to ato highly competitive

and Riccardo Merello’s paper ‘The Generative Multi Performance Deglobal market, the need of integrating various performance criteria increases. sign System’, presented at the ACADIA 2008.and The paper proposes A design system that integrates generative synthesis models a range of performance analysis tools to andgenerate techniques issolutions required. this paper will presentspace a framework for a framework within design defined by building such a system, namely the Generative Multi-Performance Design System. the po- perthe system’s design language, with the integration of various tential of the design system will then be demonstrated through a pilot project application. formance criteria.

2 design models

The system is composed of four phases, namely, synthesis, analysis, evaluation and optimisation. Within these cycles modules store Asimow, 1962; cross, 1989; steadman, 1979). designs typically evolve through a cycle that parameters, and constraints. involves a synthesis constants mechanism and an analysis mechanism which is also known as the human problem solving including design is done using an iterative process (simon, 1973;

generate and test cycle (rowe, 1987).

Elaborating following phases: minsky suggeststhe the need for an additional mechanism which he terms the progress

principle (minsky, 1988). this is an optimization mechanism that guides the search rather than generate blindly possible solutions.

Progress extracts is easy to understand only one Synthesis: Inallthis phase, system design when intentions

and

objective is considered, but when there are many different or even conflicting formulates a collection of design parameters, rules orobjectives algorithms. progress becomes harder to define. An evaluation mechanism is needed to handle the de-

These provide for a generative mechanism, through parametric or algorithmic descriptions, such that variations are allowed. The defour mechanisms represent phases in a Synthesis, Analysis, Evaluation, and Optimization sign knowledge- form and performance – is embedded here, so cycle. as to provide restrictions such that the designs that do not comply to understand these design mechanisms we need to model them. models are an abwith constraints areworld discarded. stract description of the real that provides an approximate representation of more cision process and to manage the tradeoffs between the different objectives. together all

complex functions of physical systems (Papalambros, 2000). in this paper we are concerned with mathematical models. these are models that can be implemented in a com-

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puter environment. we aim at building a series of mathematical models that correspond to Synthesis, Analysis, Evaluation, and Optimization cycle.

genetic algorithm

Analysis: This phase infers the design solution characteristics relevant to a particular parameter or discipline.

Evaluation: Here the decision making tools are devised, which evaluate the quality of a design solution; not to achieve a single optimal solution, but a set of possible solutions.

Optimization: Lastly, the best solution within a domain of feasible solutions is chosen here. 1 In order to be able to compare different iterations and find the most optimum, we applied the same four phases to our digital machinic system.

Synthesis: We established the basic architectural parameters of structure and space as our design intentions. The synthesis could be further extended to other physical and performative parameters.

Analysis: Since the forces of gravity and pull on our knitting machine system control the fabric, the structure is characterised by the tension in the knots. The space is embodied in the dimension of the enclosure created.

Evaluation: We initiated by studying analogue models to understand the stretch in different regions and the cross- sectional changes in the knitted fabric along both axes.

‘Origin’ is a series of manipulated photo images which describes human evolution based on the imagination of artist David Lee. “I proposed that there were ten stages in human evolution, from the fish form (as Coelacanth) eventually transforming to reptiles, apes and humans.” O.K. Harris gallery, 1999 in New York City

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Knitectonics Evaluation System: Structure Analog Calibration Under stretched

Ideally stretched

Over stretched

Model Evaluation

Under streched Ideally streched

Over streched

Model: 7.0 Fitness Value: 2.1309524 Head sequence: 1,0,0,2,0,0

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genetic algorithm

Evaluation System: Space Formation

Sections Value: 0: 13.46048 1: 13.46048 2: 13.27084 3: 12.34016 4: 11.115439 5: 10.2026205 6: 9.087219 7: 7.1015997 8: 5.7774796 9: 4.90882

Model: 15.0 Model Fitness: 13.46048 Head sequence: 1,0,1,1,1,0

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Knitectonics Computationally, for structural evaluation the system measures the tensile forces (spring strength in comparison to the rest position strength) acting on each knot and categorises them to be: over stretched, under stretched and ideally stretched, on the basis of analogue calibration models. In our simulation, ideal stretch is typified with green colour, maximum under stretched with blue colour and the in between stretch situation with yellow. The red colour depicts maximum over stretch possible, beyond which the spring is at breaking point and hence unsuitable, shown in black.

From our analogue model we also concluded that a knitted fabric typically stretches up to a third of its original length. Considering the self organizing behaviour of knots, the implication of the increase in length is visible in the reduced cross section of the tube.

So for spatial evaluation we established the minimum dimensions for a habitable space based on the machine size and also the percentage decrease in cross section after stretching and evaluated the options against that minimum dimension, discarding infeasible options.

Optimization: Typically the most optimum solution could be chosen by comparing it against ‘predefined best solution’. But since in our system we do not have a preconceived ideal solution, the challenge was to locate the most optimum solutions. Referring back to the paper ‘The Generative Multi Performance Design System’, we saw the Genetic Algorithm as a potential optimization tool.

‘Evolution starts from a population of randomly generated design solutions to guide the evolution. The evolution happens in generations. For each generation, the fitness of every design solution in the population is evaluated. The purpose is not to produce a global optimum solution, but rather to direct the evolutionary process to produce populations of good solutions. The GA in the optimization cluster then evaluates the fitness of the design solutions in the population. Several solutions are chosen based on their fitness and undergo genetic transformations to form a new population. The GA runs until satisfactory fitness levels are reached.’2 This genetic or evolutionary algorithm can be decomposed into five stages: fitness function, selection mechanism, coupling, and mating and mutation introduction.3 Applying these principles to develop an optimisation tool for our system, we first set the constants or the chromosomes as: seven tracks in hexagonal packing with bridge connections between them and seven yarn heads starting at specific points on all tracks.

The first population of hundred iterations was generated by random combinations of sequences 0, 1, 2 and 3 (0 = continue, 1 = go back, 2 = bridge and 3 = cross bridge) which are comparable to the genes or the DNA in biological evolution.

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genetic algorithm

The iterations were evaluated against the parameters of structure and space and assigned a fitness value. For structural evaluation fitness is determined by the number of ideally stretched knots, with a positive weight value and the number of under and over stretched knots, with a negative weight value.

These are then averaged to get a fitness value. Similarly, for spatial evaluation the distance of ‘space cells’ on each segment of the surface from the central axis is measured against the ideal prescribed distance and then averaged across the entire envelope.

Of the hundred iterations, ten iterations with the highest combined structural and spatial fitness value are selected as the best. Each of these then mates with all the other ten iterations, to generate the offprings or the second generation. The process of selecting ten iterations with highest fitness values and then mating amongst is repeated for ten generations. Interestingly, the resulting ten iteration tend to become self similar by the sixth generation. So to interrupt the self similarity, we introduce a mutation in the genes i.e. few iterations are replaced with iterations with a random sequence, every now and then.

Evolutionary Optimisation System

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Knitectonics With the limitation of time, the genetic algorithm developed is our modest attempt to generate populations of valuable architectural solutions from our machinic system on the basis of structure and space. The procedure could be extended to other physical and performative parameters like openings, heights, surface resolution, layering, environmental, etc.

We see this as a possible future for our digital machinic system, as a tool to optimise architectural prequisites and to attempt achieving ‘economy of means’.

Notes for Chapter VII 1. Anas Alfaris & Riccardo Merello, ‘The Generative Multi Performance Design System’, ACADIA 2008, page 44.

2. Ibid, page 45.

3. David Rutten, ‘Evolutionary Principles applied to Problem Solving’, presented at AAG10 conference in Vienna on September 21st 2010, http://www.grasshopper3d.com/profiles/blogs/evolutionary-principles

Most optimun model after 10 generations

Generation: 1 Models Generated: 100 Head sequence randomly generated

10 most optimum models breed and produce offspring Generation: 2 to 10 Models Generated: 100 Head sequence is a breed result from previous generation

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Machinic Control 2.0 Design Research Lab v13 Archit ectural Association London Phase II Copyright Frozen Fibers 2011, otherwise indicated and used only for academic purposes.