Solution portfolios

Conservation planners often desire a portfolio of solutions to present to decision makers. This is because conservation planners often do not have access to "perfect" information, such as cost data that accurately reflects stakeholder preferences, and so having multiple near-optimal solutions can be a useful.

Details

All methods for generating portfolios will return solutions that are within the specified optimality gap.

The following portfolios can be added to a conservation planning problem():

add_default_portfolio

Generate a single solution.

add_extra_portfolio()

Generate a portfolio of solutions by storing feasible solutions found during the optimization process. This method is useful for quickly obtaining multiple solutions, but does not provide any guarantees on the number of solutions, or the quality of solutions. Note that it requires the Gurobi solver.

add_top_portfolio()

Generate a portfolio of solutions by finding a pre-specified number of solutions that are closest to optimality (i.e the top solutions). This is useful for examining differences among near-optimal solutions. It can also be used to generate multiple solutions and, in turn, to calculate selection frequencies for small problems. Note that it requires the Gurobi solver.

add_gap_portfolio()

Generate a portfolio of solutions 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). Note that it requires the Gurobi solver.

add_cuts_portfolio()

Generate a portfolio of distinct solutions within a pre-specified optimality gap using Bender's cuts. This is recommended as a replacement for add_top_portfolio() when the Gurobi software is not available.

add_shuffle_portfolio()

Generate a portfolio of solutions by randomly reordering the data prior to attempting to solve the problem. This is recommended as a replacement for add_gap_portfolio() when the Gurobi software is not available.

See also

constraints, decisions, objectives penalties, problem(), solvers, targets.

Examples

# load data
data(sim_pu_raster, sim_features)

# create problem
p <- problem(sim_pu_raster, sim_features) %>%
     add_min_set_objective() %>%
     add_relative_targets(0.1) %>%
     add_binary_decisions() %>%
     add_default_solver(gap = 0.02, verbose = FALSE)

# create problem with cuts portfolio with 4 solutions
p1 <- p %>% add_cuts_portfolio(4)

# create problem with shuffle portfolio with 4 solutions
p2 <- p %>% add_shuffle_portfolio(4)
# \dontrun{
# create problem with extra portfolio
p3 <- p %>% add_extra_portfolio()

# create problem with top portfolio with 4 solutions
p4 <- p %>% add_top_portfolio(4)

# create problem with gap portfolio with 4 solutions within 50% of optimality
p5 <- p %>% add_gap_portfolio(4, 0.5)

# solve problems and create solution portfolios
s <- list(solve(p1), solve(p2), solve(p3), solve(p4), solve(p5))

# plot solutions from extra portfolio
plot(stack(s[[1]]), axes = FALSE, box = FALSE)

# plot solutions from top portfolio
plot(stack(s[[2]]), axes = FALSE, box = FALSE)

# plot solutions from gap portfolio
plot(stack(s[[3]]), axes = FALSE, box = FALSE)

# plot solutions from cuts portfolio
plot(stack(s[[4]]), axes = FALSE, box = FALSE)

# plot solutions from shuffle portfolio
plot(stack(s[[5]]), axes = FALSE, box = FALSE)

# }