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NAVIGATING MULTI-DIMENSIONAL LANDSCAPES IN FOGGY

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David Rutten

on 6 August 2014

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Transcript of NAVIGATING MULTI-DIMENSIONAL LANDSCAPES IN FOGGY

Column Finder
example

Navigating multi-dimensional landscapes in foggy weather as an analogy for generic problem solving
Over-constrained fitness functions result in
gaps
in the landscape.
Landscape Geometry
Cliff faces
are manifestations of discontinuous fitness functions.
"High" dimensional landscapes
30 variables in the range 0.0 to 50.0,
with an accuracy of 3 decimal places:

50,000 ≈ 10 unique coordinates.

By comparison, the observable universe contains about 10 cubic nanometers.

This phase space is over 30 orders of magnitude larger than our universe...
Problems as Phase-Spaces
If a problem is semantically identical to 'hot-hot-cold', it can be solved by a
generic solver
.
David Rutten
Catenary & Box
examples
All possible answers, both good and bad

Hot

Warm

Cold

Colder

Freezing
Variable A

Variable B
Fitness landscapes are
extrusions
of phase
spaces, according
to a
fitness
function
.
Ridges
are manifestations of discontinuous fitness function
derivatives.
Plateaus
are manifestations of under-constrained fitness functions.
Landscape Topology
Other topological manifestations include:
Closedness
Discretisation
Variable dimensionality
Curve Intersections
example
140
30
107
Particle cloud
example
Fitness

Variable dimensional plateaus
Peaks
represent solutions.
Multiple peaks compete
with each other, in
accordance with
their
basins
.
Architecture & Urbanism


Software Development
[TUDelft; 1999 ~ 2005]
[Robert McNeel & Associates; 2005 ~ ...]
Conclusions
Generic Solvers are
Flexible
Widely applicable
Democratic
Easy to use
Generic Solvers are
not
Fast
Reliable
Landscapes are a versatile and apt analogy for phase-space and fitness-fields, suited to those who are not fluent in mathematics or algorithmics.
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