spsann - optimization of sample patterns using spatial simulated annealing

spsannoptimization 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

Session: Statistical, computational and visualization tools for assessing and communicating soil complexity and variabilityAbstract: spsann – optimization of sample patterns using spatial simulated annealingAuthors: Alessandro Samuel-Rosa, Gerard Heuvelink, Gustavos Vasques, Lúcia Anjos

Overview

● Motivation● Strategy● Features● Future


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


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


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)


Features – optimization problem (1)

● Multi-objective optimization problem

● Scaling– Upper-lower bound

● Pareto maximum and minimum● Numerical simulation

● Aggregation– Weighted sum method

f isc=

f i(x )−f io

f imax

−f io

U=∑i=1

k

w i f i(x )

f (x)=(f 1(x ) , f 2(x ) ,... , f k (x))


Features – optimization problem (2)

● Upper-lower bound with the Pareto maximum and minimum

ReferenceObjective 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-objectiveoptimization. Engineering Optimization, v. 37, p. 551-570, 2005. [link]

http://www.tandfonline.com/doi/abs/10.1080/03052150500114289


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


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


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


Features – graphical display (2)

Meuse data set from the -package sp; Function optimMSSD with 100 points


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++)

– ...


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

https://github.com/samuel-rosa

http://www.slideshare.net/alessandrosamuelrosa

spsann - optimization of sample patterns using spatial simulated annealing

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