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 lowerbound.
- 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
set precision for geohash.
- 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.
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
if (FALSE) { # \dontrun{
# 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)
} # }