This blog post is a rough approximation of the lecture I gave at the AAG10 conference in Vienna on September 21st 2010. Naturally it will be quite a different experience as the medium is quite…
Added by David Rutten at 3:27pm on September 24, 2010
levator over the automobile, complex issues are at play in concentrating population and built infrastructure in contemporary high-rise cities. How do you meet the challenges of system design for high quality compact urban environments?
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DP ($$$ aside), GC, and Grasshopper. Arthur’s original question is very important
and the exact question (and hopefully answer) I was hoping to find on a
forum.
“How to take intelligent 3D parametric generative design models (scripting, etc.) into 2D documents?" Or, deliver the 3D design for evaluation, bid, construction, etc.
I am intrigued by Jon’s comments in the same thread and would like to know how I can learn more about the process (and
pitfalls) of turning over a 3D digital generative models to a contractor/fabricator.
Are there any industry guidelines established I could use as a reference to guide our firm through this type of uncharted territory?
Arthur’s question is very reminiscent of 10 years ago when I was frustrated with the amount of time spent on the development of a 3D model design (physical and/or virtual) only to have to wipe the table clean and start the process all over again in 2D in order to document the project for delivery. From this I jumped head first into BIM and Revit, vowing never to go back to unintelligent 2D line work. I am now working on Bentley software (v8i: Microstation and Bentley Architecture) with the access and desire to venture into Generative Components. I am very intrigued by Rhino/Grasshopper primarily with the apparent ease of use and available resources assisting in the learning process – something not really available with Bentley.
In hindsight, as I am doing my software research I think the current use of Revit and BA (Bentley Architecture) are more of a “bridge”
between the past (decades of digital 2D work, i.e. AutoCAD) and where hopefully
we all will be someday in the near future (100% 3D modeling, i.e. Digital
Project??). Without having the experience
it would appear that DP/CATIA (PLM software) are closer to this than any other
type of software. As complicated as the
industry standards are for the automobile and airline industry, I feel we
(architectural industry and others) are heading in a similar direction with
total understanding (PLM/ Evidence Based Design) of a design (a whole other topic). If anything I think the market will begin to
demand it sooner or later.
Gehry (DP) article NY Times:
http://www.nytimes.com/2009/02/11/business/11gehry.html
I know these type of broad discussions (software vs. software) can be blown out of proportion on forums, but I am would like to read
the pulse of those who are already in the trenches (using Grasshopper, CATIA, Digital Project, Generative Components, others??) and hear your thoughts. Just as valuable would be other threads,
industry articles/reviews of 3D parametric generative design software.
Thanks,
Boyd…
Crystallon is an open source project for creating lattice structures using Rhino and Grasshopper3D. The goal is to generate lattice structures within Rhino’s design environment without exporting t
lly it should not make much of a difference - random number generation is not affected, mutation also is not. crossover is a bit more tricky, I use Simulated Binary Crossover (SBX-20) which was introduced already in 1194:
Deb K., Agrawal R. B.: Simulated Binary Crossover for Continuous Search Space, inIITK/ME/SMD-94027, Convenor, Technical Reports, Indian Institue of Technology, Kanpur, India,November 1994
Abst ract. The success of binary-coded gene t ic algorithms (GA s) inproblems having discrete sear ch sp ace largely depends on the codingused to represent the prob lem variables and on the crossover ope ratorthat propagates buildin g blocks from pare nt strings to childrenst rings . In solving optimization problems having continuous searchspace, binary-co ded GAs discr et ize the search space by using a codingof the problem var iables in binary st rings. However , t he coding of realvaluedvari ables in finit e-length st rings causes a number of difficulties:inability to achieve arbit rary pr ecision in the obtained solution , fixedmapping of problem var iab les, inh eren t Hamming cliff problem associatedwit h binary coding, and processing of Holland 's schemata incont inuous search space. Although a number of real-coded GAs aredevelop ed to solve optimization problems having a cont inuous searchspace, the search powers of these crossover operators are not adequate .In t his paper , t he search power of a crossover operator is defined int erms of the probability of creating an arbitrary child solut ion froma given pair of parent solutions . Motivated by t he success of binarycodedGAs in discret e search space problems , we develop a real-codedcrossover (which we call the simulated binar y crossover , or SBX) operatorwhose search power is similar to that of the single-point crossoverused in binary-coded GAs . Simulation results on a number of realvaluedt est problems of varying difficulty and dimensionality suggestt hat the real-cod ed GAs with t he SBX operator ar e ab le to perform asgood or bet t er than binary-cod ed GAs wit h t he single-po int crossover.SBX is found to be particularly useful in problems having mult ip le optimalsolutions with a narrow global basin an d in prob lems where thelower and upper bo unds of the global optimum are not known a priori.Further , a simulation on a two-var iable blocked function showsthat the real-coded GA with SBX work s as suggested by Goldberg
and in most cases t he performance of real-coded GA with SBX is similarto that of binary GAs with a single-point crossover. Based onth ese encouraging results, this paper suggests a number of extensionsto the present study.
7. ConclusionsIn this paper, a real-coded crossover operator has been develop ed bas ed ont he search characte rist ics of a single-point crossover used in binary -codedGAs. In ord er to define the search power of a crossover operator, a spreadfactor has been introduced as the ratio of the absolute differences of thechildren points to that of the parent points. Thereaft er , the probabilityof creat ing a child point for two given parent points has been derived forthe single-point crossover. Motivat ed by the success of binary-coded GAsin problems wit h discrete sear ch space, a simul ated bin ary crossover (SBX)operator has been develop ed to solve problems having cont inuous searchspace. The SBX operator has search power similar to that of the single-po intcrossover.On a number of t est fun ctions, including De Jong's five te st fun ct ions, ithas been found that real-coded GAs with the SBX operator can overcome anumb er of difficult ies inherent with binary-coded GAs in solving cont inuoussearch space problems-Hamming cliff problem, arbitrary pr ecision problem,and fixed mapped coding problem. In the comparison of real-coded GAs wit ha SBX operator and binary-coded GAs with a single-point crossover ope rat or ,it has been observed that the performance of the former is better than thelatt er on continuous functions and the performance of the former is similarto the lat ter in solving discret e and difficult functions. In comparison withanother real-coded crossover operator (i.e. , BLX-0 .5) suggested elsewhere ,SBX performs better in difficult test functions. It has also been observedthat SBX is particularly useful in problems where the bounds of the optimum
point is not known a priori and wher e there are multi ple optima, of whichone is global.Real-coded GAs wit h t he SBX op erator have also been tried in solvinga two-variab le blocked function (the concept of blocked fun ctions was introducedin [10]). Blocked fun ct ions are difficult for real-coded GAs , becauselocal optimal points block t he progress of search to continue towards t heglobal optimal point . The simulat ion results on t he two-var iable blockedfunction have shown that in most occasions , the sea rch proceeds the way aspr edicted in [10]. Most importantly, it has been observed that the real-codedGAs wit h SBX work similar to that of t he binary-coded GAs wit h single-pointcrossover in overcoming t he barrier of the local peaks and converging to t heglobal bas in. However , it is premature to conclude whether real-coded GAswit h SBX op erator can overcome t he local barriers in higher-dimensionalblocked fun ct ions.These results are encour aging and suggest avenues for further research.Because the SBX ope rat or uses a probability distribut ion for choosing a childpo int , the real-coded GAs wit h SBX are one st ep ahead of the binary-codedGAs in te rms of ach ieving a convergence proof for GAs. With a direct probabilist ic relationship between children and parent points used in t his paper,cues from t he clas sical stochast ic optimization methods can be borrowed toachieve a convergence proof of GAs , or a much closer tie between the classicaloptimization methods and GAs is on t he horizon.
In short, according to the authors my SBX operator using real gene values is as good as older ones specially designed for discrete searches, and better in continuous searches. SBX as far as i know meanwhile is a standard general crossover operator.
But:
- there might be better ones out there i just havent seen yet. please tell me.
- besides tournament selection and mutation, crossover is just one part of the breeding pipeline. also there is the elite management for MOEA which is AT LEAST as important as the breeding itself.
- depending on the problem, there are almost always better specific ways of how to code the mutation and the crossover operators. but octopus is meant to keep it general for the moment - maybe there's a way for an interface to code those things yourself..!?
2) elite size = SPEA-2 archive size, yes. the rate depends on your convergence behaviour i would say. i usually start off with at least half the size of the population, but mostly the same size (as it is hard-coded in the new version, i just realize) is big enough.
4) the non-dominated front is always put into the archive first. if the archive size is exceeded, the least important individual (the significant strategy in SPEA-2) are truncated one by one until the size is reached. if it is smaller, the fittest dominated individuals are put into the elite. the latter happens in the beginning of the run, when the front wasn't discovered well yet.
3) yes it is. this is a custom implementation i figured out myself. however i'm close to have the HypE algorithm working in the new version, which natively has got the possibility to articulate perference relations on sets of solutions.
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