highest_concentration {spatialrisk}

Highest concentration risk

Description

Find the centre coordinates of a circle with a fixed radius that maximizes the coverage of total fire risk insured. 'highest_concentration()' returns the coordinates (lon/lat) and the corresponding concentration. The concentration is defined as the sum of all observations within a circle of a certain radius. See concentration for determining concentration for pre-defined coordinates.

Usage

highest_concentration(
  df,
  value,
  lon = lon,
  lat = lat,
  lowerbound = NULL,
  radius = 200,
  grid_distance = 25,
  gh_precision = 6,
  display_progress = TRUE
)

Arguments

df

data.frame of locations, should at least include column for longitude, latitude and sum insured

value

column name with value of interest to summarize (e.g. sum insured)

lon

column name with longitude (defaults to 'lon')

lat

column name with latitude (defaults to 'lat')

lowerbound

set lower bound for outcome (defaults to NULL)

radius

radius (in meters) (default is 200m)

grid_distance

distance (in meters) for precision of concentration risk (default is 25m). 'neighborhood_search()' can be used to search for coordinates with even higher concentrations in the neighborhood of the highest concentrations.

gh_precision

positive integer to define geohash precision. See details.

display_progress

show progress bar (TRUE/FALSE). Defaults to TRUE.

Details

A recently European Commission regulation requires insurance companies to determine the maximum value of insured fire risk policies of all buildings that are partly or fully located within circle of a radius of 200m (Commission Delegated Regulation (EU), 2015, Article 132). The problem can be stated as: "find the centre coordinates of a circle with a fixed radius that maximizes the coverage of total fire risk insured". This can be viewed as a particular instance of the Maximal Covering Location Problem (MCLP) with fixed radius. See Gomes (2018) for a solution to the maximum fire risk insured capital problem using a multi-start local search meta-heuristic. The computational performance of highest_concentration() is investigated to overcome the long times the MCLP algorithm is taking. highest_concentration() is written in C++, and for 500,000 buildings it needs about 5-10 seconds to determine the maximum value of insured fire risk policies that are partly or fully located within circle of a radius of 200m.

‘highest_concentration()' uses Gustavo Niemeyer’s wonderful and elegant geohash coordinate system. Niemeyer's Geohash method encodes latitude and longitude as binary string where each binary value derived from a decision as to where the point lies in a bisected region of latitude or longitudinal space. The first step is to convert all latitude/longitude coordinates into geohash-encoded strings.

The length of the geohash (‘gh_precision') controls the ’zoom level':

• precision 5 is 4.89 x 4.89km;

• precision 6 is 1.22km x 0.61km;

• precision 7 is 153m x 153m;

• precision 8 is 39m x 19m.

For a circle with a radius of 200m the precision of the geohash should be set equal to 6 (default). Then the 'value' column is aggregated (sum) per geohash (with a buffer of size 'radius' around each geohash, since the coordinates of the highest concentration can be near the edge of the geohash). The geohashes with a aggregated value below the lowerbound are removed, where the lowerbound is equal to the maximum of the 'value' column. Then a grid is created, with a distance of 'grid_distance' between the points. See example section for a illustration of the algorithm. As a last step for each grid point the concentration is calculated.

Value

data.frame with coordinates (lon/lat) with the highest concentrations

Author(s)

Martin Haringa

References

Commission Delegated Regulation (EU) (2015). Solvency II Delegated Act 2015/35. Official Journal of the European Union, 58:124.

Gomes M.I., Afonso L.B., Chibeles-Martins N., Fradinho J.M. (2018). Multi-start Local Search Procedure for the Maximum Fire Risk Insured Capital Problem. In: Lee J., Rinaldi G., Mahjoub A. (eds) Combinatorial Optimization. ISCO 2018. Lecture Notes in Computer Science, vol 10856. Springer, Cham. <doi:10.1007/978-3-319-96151-4_19>

Examples

 ## Not run: 
# Find highest concentration with a precision of a grid of 25 meters
hc1 <- highest_concentration(Groningen, amount, radius = 200,
 grid_distance = 25)

# Look for coordinates with even higher concentrations in the
# neighborhood of the coordinates with the highest concentration
hc1_nghb <- neighborhood_gh_search(hc1, max.call = 7000)
print(hc1_nghb)

# Create map with geohashes above the lowerbound
# The highest concentration lies in one of the geohashes
plot(hc1)

# Create map with highest concentration
plot(hc1_nghb)

## End(Not run)