Spotted: eVolo

eVolo Architecture holds the annual architectural competition for the skyscrapers of the future. You'll find some wild stuff there, just look at some of the entries: 1 2 3 4 5 etc.

Lessons in Genetic Algorithms

Easy in theory, hard in practice :-)

While Evolutionary Computing and it's most popular "flavour" - Genetic Algorithms - can be easily explained, it turns out that producing usable results with real-world problems can be a daunting task.

I quickly put together a light framework for the manipulation of populations, generations, subjects... and tested the system with kd-trees.

The aim was the optimization of 2d floor plans - for example, the fitness function would define whether more desirable subject would rather have rooms of equal size or maybe rooms of greater variety in size...

While the experiment moved in the right direction, it turned out that the problem of the local optimum quicky moves in place. After a plato in the population fitness is reached, the algorithm cannot find new ways to better subjects, if all new subjects are less fit than the "local optimum".

The local optimum problem is very well known and explored in the theory of Evolutionary Computing, so I wasn't very surprised that I encountered it in my first attempts.

Kd-trees and De Stijl

In the search for the vocabulary (the means of defining the genotype and rules of morphogenesis - growth of phenotype) for my genetic houses, I came across the kd-trees.

It's a method of space partitioning, or, as architects would say, "organizing the space". It can be applied in 2-d space (e.g. floorplans) or 3-d space (e.g. complex spatial plans).

Nice thing about kd-trees is that space is organized with a very simple set of input parameters - set of points. Each point divides the space (in witch it's put) in two partitions; then new points are put in those partitions and so on.

I don't know whether Piet Mondrian (one of the founders of De Stijl) was familiar with kd-trees, but, at least to me, it looks fishy! :-)

I'm a bit reluctant about using the kd-trees as a driving vechile for my genetic house. While the Gerrit Rietveld's Schroeder house certainly looks good, I'm afraid that all of my houses would look the same - infinity variety of cubic forms. Very far from examples from nature.

If I'm dealing with the evolutionary computing, it would be far more appropriate to explore more organic forms and not to limit myself by the cubic partitioning of space.

Evolutionary Computing Applications in Architecture design

While evolutionary computing (EC) is nothing more than a search for the optimum, so is every (and thus also architectural) design. How can EC be applied for usage in architecture?

As Vitruvius pointed out some two thousand years ago, a well designed architecture has to match three standards: firmness (structural integrity), commodity (functionality) and delight (aesthetic value).

So, in the search for optimal architecture, it is very logical to map each of the Vitruvius' standards to evolutionary computing's fitness function.

When asssessing the structural fitness of a subject (a building), the fittest are those capable of carrying more static stress (burden), preferably with less material used for the construction.

In a similar way, the functionality can be assessed based on the set of conditions. It is certanly better if the drawing room is bigger than the hall; and it's better that master bedrom is closer to the bathroom than to the kitchen.

The hardest thing to process for the computer is the aesthetic. While one could struggle to automate the aesthetic assessment process with certain mathematic rules (symetry, proportions, rythm....), I remain sceptic about such an approach - aesthetic is a highly subjective category.

But even if the fitness function for aesthetic cannot be calculated, that does not mean evolutionary computing cannot be applied in that field.

If aesthetic is a subjective quality, something in the eye of the beholder - the human being, then a real human being must perform the assessment of the subjects. Selection by fitness function still exists, but it is not automated nor calculated. A human being, artist/architect in our case, would make selections in the manner of a horse breeder. Some subjects in population would look better and would be favored for passing their properties to the next generations.

One might argue that human intervention would render EC unusable. Well, it might slow down the process (few seconds instead of few miliseconds - that's 1000x slower), but all the key elements of the EC remain. Only the fitness function for the aesthetic is admitted to be what it actually is - inevitably a human's judgement.

Evolutionary Computing (EC)

Evolutionary Computing (EC) is a method in the field of Artificial Intelligence. EC provides methods of search for the optimium by the means of randomization, mutation, recombination and selection. It mimics and learns from the biological evolution.

Similarities (compared to the biological evolution):

• each subject is defined by a highly abstract code (genotype),


• each subject is grown from genotype into phenotype (morphogenesis),


• the probability for each subject to survive depends on its fitness; environment plays a large role in that,


• the variety of the genetic pool of the population is ensured by recombination, providing offspring a new genotype, derived from genotypes of its ancestors,


• further variety is achieved by random mutation of genotype.

Differences (comapred to the biological evolution):

• generation turnover rate can be much higher - instead of hours, days or years, sequences of generations can be developed in miliseconds, evolution can run faster,


• flexibility in the rules of inheritance - for example, in nature a subject typically inherits genetic material from 2 ancestors; these limitations can be easily overcome (e.g. a subject can have 5 ancestors),
  
• it is not possible to simluate the complexity of natural systems in an artificial enviroment (for example, the human brain has at least 10-100 billion (short scale - 10⁹) neurons; each of them is capable of "parallel processing" and is connected to others through about 1.000-10.000 synapses; these estimates compute to 10¹³ to 10¹⁵ number of synapses...); and we're not talking just about data storing, but (parallel) information processing as well.

So, how to apply that stuff in architecture? The plan is to grow a population of "houses"; each house would be based on its encoded genotype (blueprint), from which a real house would be grown. The houses would mate and produce offspring, which would be assessed; the subject with the greatest fitness (most appropriate house) would survive and pass its genetic material to the next generation. After many generations, best designs should emerge. Huh. I admit it's a long shot, but certainly worth a try :-)

First steps

Before evolutionary computing can be applied, I have to develop a vocabulary for the representation and manipulation of three-dimensional forms. Such a vocabulary is needed for the construction of the genotype and growth of the fenotype.

Here I used the approach with "particle agents". Each particle/agent holds a set of properties - spatial position, direction, speed, color etc. When time passes, the properties are manipulated according to a set of simple rules. Changing the rules, you get something completely different each time the simluation is run.

Is it "just a random development"? Of course it is, but don't underestimate the power of "random". The eyes and brain you're using to read this are the result of random events, together with a little natrual selection, of course (we'll discuss the intelligent design hopefully some other time :-)).

Genetichouse

I decided to explore a field connecting two disciplines: architecture and evolutionary computing, specifically genetic algorithms.

This project - codenamed Genetichouse - is a part of completing my bachelor's degree in architecture at the University of Ljubljana under the mentorship of professor, Ph.D. Igor Kalčič.

The goal of the project is to devise new ways of designing architectural forms.