Presentation at the European Geosciences Union General Assembly 2015 (EGU2015), Soil System Sciences section 11.3 - Statistical, computational and visualization tools for assessing and communicating soil complexity and variability

1. spsann
optimization of sample patterns using
spatial simulated annealing
Alessandro Samuel-Rosa(1)
, Gerard Heuvelink(2)
,
Gustavo Vasques(3)
, Lúcia Anjos(1)
(1) Universidade Federal Rural do Rio de Janeiro, Seropédica, Brazil.
(2) ISRIC – World Soil Information, Wageningen, the Netherlands.
(3) Embrapa Solos, Rio de Janeiro, Brazil.
SSS11.3 – Statistical, computational and visualization tools for assessing and communicating soil complexity and variability

2. Session: Statistical, computational and visualization tools for assessing and communicating soil complexity and variability
Abstract: spsann – optimization of sample patterns using spatial simulated annealing
Authors: Alessandro Samuel-Rosa, Gerard Heuvelink, Gustavos Vasques, Lúcia Anjos
Overview
● Motivation
● Strategy
● Features
● Future

3. Session: Statistical, computational and visualization tools for assessing and communicating soil complexity and variability
Abstract: spsann – optimization of sample patterns using spatial simulated annealing
Authors: Alessandro Samuel-Rosa, Gerard Heuvelink, Gustavos Vasques, Lúcia Anjos
Motivation
● PhD study
– Sample for digital soil mapping in terra incognita
● Many private and public algorithms. A few only
in scientific articles and text books
– Reproducible research
● Wider adoption and further development is,
perhaps, being held back
– Access to scientific knowledge

4. Session: Statistical, computational and visualization tools for assessing and communicating soil complexity and variability
Abstract: spsann – optimization of sample patterns using spatial simulated annealing
Authors: Alessandro Samuel-Rosa, Gerard Heuvelink, Gustavos Vasques, Lúcia Anjos
Strategy
● Create an -package
– is FOSS, easy and popular
● Start from existing packages
– intamapInteractive (Edzer Pebesma, Jon
Skoien, et al.), and clhs (Pierre Roudier)
– Optimization using spatial simulated annealing
● Packaging tools
– RStudio + roxygen2 + Rcpp + GitHub

5. Session: Statistical, computational and visualization tools for assessing and communicating soil complexity and variability
Abstract: spsann – optimization of sample patterns using spatial simulated annealing
Authors: Alessandro Samuel-Rosa, Gerard Heuvelink, Gustavos Vasques, Lúcia Anjos
Features – objective functions
● Five single-objective functions
– Association/Correlation among covariates (optimCORR)
– Marginal distribution of the covariates (optimDIST)
– Mean squares shortest distance (optimMSSD)
– Mean/Maximum kriging variance (optimMKV)
– Number of unique points/pairs per lag (optimPPL)
● Two multi-objective functions
– CORR + DIST (optimACDC)
– ACDC + MSSD + PPL (optimPAN)

6. Session: Statistical, computational and visualization tools for assessing and communicating soil complexity and variability
Abstract: spsann – optimization of sample patterns using spatial simulated annealing
Authors: Alessandro Samuel-Rosa, Gerard Heuvelink, Gustavos Vasques, Lúcia Anjos
Features – optimization problem (1)
● Multi-objective optimization problem
● Scaling
– Upper-lower bound
● Pareto maximum and minimum
● Numerical simulation
● Aggregation
– Weighted sum method
f i
sc
=
f i(x)−f i
o
f i
max
−f i
o
U =∑
i=1
k
wi f i(x)
f(x)=(f 1(x),f 2(x),...,f k (x))

7. Session: Statistical, computational and visualization tools for assessing and communicating soil complexity and variability
Abstract: spsann – optimization of sample patterns using spatial simulated annealing
Authors: Alessandro Samuel-Rosa, Gerard Heuvelink, Gustavos Vasques, Lúcia Anjos
Features – optimization problem (2)
● Upper-lower bound with the Pareto maximum
and minimum
Reference
Objective function values
f1
f2
f3
At 0.1000 43.0336 20.0725
At 67.6807 0.0224 12.6562
At 32.0687 16.9994 11.2757
Maximum 84.2615 144.2401 37.7600
x1
∗
x2
∗
x3
∗
Source:
Marler, R. T. & Arora, J. S. Function-transformation methods for multi-objective
optimization. Engineering Optimization, v. 37, p. 551-570, 2005. [link]

8. Session: Statistical, computational and visualization tools for assessing and communicating soil complexity and variability
Abstract: spsann – optimization of sample patterns using spatial simulated annealing
Authors: Alessandro Samuel-Rosa, Gerard Heuvelink, Gustavos Vasques, Lúcia Anjos
Features – simulated annealing
● -package IntamapInteractive
● Search graph size
– Linear cooling schedule depending on the iterations
● Acceptance probability
– Exponential cooling schedule depending on the
iterations
● Starting system configuration
– Random points

9. Session: Statistical, computational and visualization tools for assessing and communicating soil complexity and variability
Abstract: spsann – optimization of sample patterns using spatial simulated annealing
Authors: Alessandro Samuel-Rosa, Gerard Heuvelink, Gustavos Vasques, Lúcia Anjos
Features – speeding up
● Bottlenecks implemented in C++
– -package Rcpp
– Parallel processing is of little help
● Use a finite set of candidate locations
● Data matrices
– Compute once and update at each iteration
● Function-specific solutions
– More work to maintain replicated source code

10. Session: Statistical, computational and visualization tools for assessing and communicating soil complexity and variability
Abstract: spsann – optimization of sample patterns using spatial simulated annealing
Authors: Alessandro Samuel-Rosa, Gerard Heuvelink, Gustavos Vasques, Lúcia Anjos
Features – graphical display (1)
● Evolution of the
energy state
● Evolution of the
acceptance
probability
● Initial and last best
energy state
● Evolution of the
search graph size
● Initial system
configuration
● Current system
configuration

11. Session: Statistical, computational and visualization tools for assessing and communicating soil complexity and variability
Abstract: spsann – optimization of sample patterns using spatial simulated annealing
Authors: Alessandro Samuel-Rosa, Gerard Heuvelink, Gustavos Vasques, Lúcia Anjos
Features – graphical display (2)
Meuse data set from the -package sp; Function optimMSSD with 100 points

12. Session: Statistical, computational and visualization tools for assessing and communicating soil complexity and variability
Abstract: spsann – optimization of sample patterns using spatial simulated annealing
Authors: Alessandro Samuel-Rosa, Gerard Heuvelink, Gustavos Vasques, Lúcia Anjos
Future – two ways
● Improve/Extend
– Find and correct bugs
– Use a cost surface
– Add more objective
functions
– Add/delete points
– C++
– ...
● Reformulate
– Simplify the structure
– Separate objective
functions from
simulated annealing
– Use a more efficient
language (C/C++)
– ...

13. Session: Statistical, computational and visualization tools for assessing and communicating soil complexity and variability
Abstract: spsann – optimization of sample patterns using spatial simulated annealing
Authors: Alessandro Samuel-Rosa, Gerard Heuvelink, Gustavos Vasques, Lúcia Anjos
Extra information
● This work was supported by the Brazilian government
– CAPES (Process BEX 11677/13-9)
– CNPq (Process 140720/2012-0)
● The source code of the -package spsann is freely
available at https://github.com/samuel-rosa
– Contributions are very welcome!
● This document is freely available at
http://www.slideshare.net/alessandrosamuelrosa