Add a gap portfolio

Generate a portfolio of solutions for a conservation planning problem() by finding a certain number of solutions that are all within a pre-specified optimality gap. This method is useful for generating multiple solutions that can be used to calculate selection frequencies for moderate and large-sized problems (similar to Marxan).

add_gap_portfolio(x, number_solutions, pool_gap = 0.1)

Arguments

x	problem() (i.e. ConservationProblem) object.
number_solutions	integer number of solutions required.
pool_gap	numeric gap to optimality for solutions in the portfolio. This relative gap specifies a threshold worst-case performance for solutions in the portfolio. For example, value of 0.1 will result in the portfolio returning solutions that are within 10% of an optimal solution. Note that the gap specified in the solver (i.e. add_gurobi_solver() must be less than or equal to the gap specified to generate the portfolio. Defaults to 0.1.

Value

Object (i.e. ConservationProblem) with the portfolio added to it.

Details

This strategy for generating a portfolio requires problems to be solved using the Gurobi software suite (i.e. using add_gurobi_solver(). Specifically, version 9.0.0 (or greater) of the gurobi package must be installed. Note that the number of solutions returned may be less than the argument to number_solutions, if the total number of solutions that meet the optimality gap is less than the number of solutions requested. Also, note that this portfolio function only works with problems that have binary decisions (i.e. specified using add_binary_decisions()).

See also

portfolios.

Examples

# \dontrun{
# set seed for reproducibility
set.seed(600)

# load data
data(sim_pu_raster, sim_features)

# create minimal problem with a portfolio containing 10 solutions within 20%
# of optimality
p1 <- problem(sim_pu_raster, sim_features) %>%
      add_min_set_objective() %>%
      add_relative_targets(0.05) %>%
      add_gap_portfolio(number_solutions = 5, pool_gap = 0.2) %>%
      add_default_solver(gap = 0, verbose = FALSE)

# solve problem and generate portfolio
s1 <- solve(p1)
#> $LogToConsole
#> [1] 0
#> 
#> $LogFile
#> [1] ""
#> 
#> $Presolve
#> [1] 2
#> 
#> $MIPGap
#> [1] 0
#> 
#> $TimeLimit
#> [1] 2147483647
#> 
#> $Threads
#> [1] 1
#> 
#> $NumericFocus
#> [1] 0
#> 

# print number of solutions found
print(length(s1))
#> [1] 5

# plot solutions
plot(stack(s1), axes = FALSE, box = FALSE)

# create multi-zone  problem with a portfolio containing 10 solutions within
# 20% of optimality
p2 <- problem(sim_pu_zones_stack, sim_features_zones) %>%
      add_min_set_objective() %>%
      add_relative_targets(matrix(runif(15, 0.1, 0.2), nrow = 5,
                                  ncol = 3)) %>%
      add_gap_portfolio(number_solutions = 5, pool_gap = 0.2) %>%
      add_default_solver(gap = 0, verbose = FALSE)

# solve problem and generate portfolio
s2 <- solve(p2)
#> $LogToConsole
#> [1] 0
#> 
#> $LogFile
#> [1] ""
#> 
#> $Presolve
#> [1] 2
#> 
#> $MIPGap
#> [1] 0
#> 
#> $TimeLimit
#> [1] 2147483647
#> 
#> $Threads
#> [1] 1
#> 
#> $NumericFocus
#> [1] 0
#> 

# print number of solutions found
print(length(s2))
#> [1] 5

# plot solutions in portfolio
plot(stack(lapply(s2, category_layer)), main = "solution", axes = FALSE,
     box = FALSE)
# }