A constraint can be added to a project prioritization problem()
to ensure that solutions exhibit a specific characteristic.
The following constraints can be added to a project prioritization
problem():
add_locked_in_constraints()Add constraints to ensure that certain actions are prioritized for funding.
add_locked_out_constraints()Add constraints to ensure that certain actions are not prioritized for funding.
# load data
data(sim_projects, sim_features, sim_actions)
# build problem with maximum richness objective and $150 budget
p1 <- problem(sim_projects, sim_actions, sim_features,
"name", "success", "name", "cost", "name") %>%
add_max_richness_objective(budget = 150) %>%
add_binary_decisions()
# print problem
print(p1)
#> Project Prioritization Problem
#> actions F1_action, F2_action, F3_action, ... (6 actions)
#> projects F1_project, F2_project, F3_project, ... (6 projects)
#> features F1, F2, F3, ... (5 features)
#> action costs: min: 0, max: 103.22583
#> project success: min: 0.81379, max: 1
#> objective: Maximum richness objective [budget (150)]
#> targets: none
#> weights: default
#> decisions Binary decision
#> constraints: <none>
#> solver: default
# build another problem, and lock in the third action
p2 <- p1 %>%
add_locked_in_constraints(c(3))
# print problem
print(p2)
#> Project Prioritization Problem
#> actions F1_action, F2_action, F3_action, ... (6 actions)
#> projects F1_project, F2_project, F3_project, ... (6 projects)
#> features F1, F2, F3, ... (5 features)
#> action costs: min: 0, max: 103.22583
#> project success: min: 0.81379, max: 1
#> objective: Maximum richness objective [budget (150)]
#> targets: none
#> weights: default
#> decisions Binary decision
#> constraints: <Locked in actions [1 locked units]>
#> solver: default
# build another problem, and lock out the second action
p3 <- p1 %>%
add_locked_out_constraints(c(2))
# print problem
print(p3)
#> Project Prioritization Problem
#> actions F1_action, F2_action, F3_action, ... (6 actions)
#> projects F1_project, F2_project, F3_project, ... (6 projects)
#> features F1, F2, F3, ... (5 features)
#> action costs: min: 0, max: 103.22583
#> project success: min: 0.81379, max: 1
#> objective: Maximum richness objective [budget (150)]
#> targets: none
#> weights: default
#> decisions Binary decision
#> constraints: <Manually locked actions [1 locked units]>
#> solver: default
# \dontrun{
# solve problems
s1 <- solve(p1)
#> Set parameter Username
#> Set parameter TimeLimit to value 2147483647
#> Set parameter MIPGap to value 0
#> Set parameter NumericFocus to value 3
#> Set parameter Presolve to value 2
#> Set parameter Threads to value 1
#> Set parameter PoolSolutions to value 1
#> Set parameter PoolSearchMode to value 2
#> Academic license - for non-commercial use only - expires 2025-04-21
#> Gurobi Optimizer version 11.0.2 build v11.0.2rc0 (linux64 - "Ubuntu 22.04.4 LTS")
#>
#> CPU model: 11th Gen Intel(R) Core(TM) i7-1185G7 @ 3.00GHz, instruction set [SSE2|AVX|AVX2|AVX512]
#> Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
#>
#> Optimize a model with 47 rows, 47 columns and 102 nonzeros
#> Model fingerprint: 0xf97d9094
#> Variable types: 0 continuous, 42 integer (42 binary)
#> Semi-Variable types: 5 continuous, 0 integer
#> Coefficient statistics:
#> Matrix range [9e-02, 1e+02]
#> Objective range [1e+00, 1e+00]
#> Bounds range [1e+00, 1e+00]
#> RHS range [1e+00, 2e+02]
#> Found heuristic solution: objective 1.4456093
#> Presolve removed 16 rows and 12 columns
#> Presolve time: 0.00s
#> Presolved: 31 rows, 35 columns, 65 nonzeros
#> Variable types: 0 continuous, 35 integer (35 binary)
#> Root relaxation presolved: 31 rows, 35 columns, 65 nonzeros
#>
#>
#> Root relaxation: objective 1.680145e+00, 11 iterations, 0.00 seconds (0.00 work units)
#>
#> Nodes | Current Node | Objective Bounds | Work
#> Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
#>
#> * 0 0 0 1.6801450 1.68015 0.00% - 0s
#>
#> Explored 1 nodes (11 simplex iterations) in 0.00 seconds (0.00 work units)
#> Thread count was 1 (of 8 available processors)
#>
#> Solution count 1: 1.68015
#> No other solutions better than 1.68015
#>
#> Optimal solution found (tolerance 0.00e+00)
#> Best objective 1.680145013696e+00, best bound 1.680145013696e+00, gap 0.0000%
s2 <- solve(p2)
#> Set parameter Username
#> Set parameter TimeLimit to value 2147483647
#> Set parameter MIPGap to value 0
#> Set parameter NumericFocus to value 3
#> Set parameter Presolve to value 2
#> Set parameter Threads to value 1
#> Set parameter PoolSolutions to value 1
#> Set parameter PoolSearchMode to value 2
#> Academic license - for non-commercial use only - expires 2025-04-21
#> Gurobi Optimizer version 11.0.2 build v11.0.2rc0 (linux64 - "Ubuntu 22.04.4 LTS")
#>
#> CPU model: 11th Gen Intel(R) Core(TM) i7-1185G7 @ 3.00GHz, instruction set [SSE2|AVX|AVX2|AVX512]
#> Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
#>
#> Optimize a model with 47 rows, 47 columns and 102 nonzeros
#> Model fingerprint: 0xaace6374
#> Variable types: 0 continuous, 42 integer (42 binary)
#> Semi-Variable types: 5 continuous, 0 integer
#> Coefficient statistics:
#> Matrix range [9e-02, 1e+02]
#> Objective range [1e+00, 1e+00]
#> Bounds range [1e+00, 1e+00]
#> RHS range [1e+00, 2e+02]
#> Found heuristic solution: objective 1.4456093
#> Presolve removed 42 rows and 41 columns
#> Presolve time: 0.00s
#> Presolved: 5 rows, 6 columns, 10 nonzeros
#> Variable types: 0 continuous, 6 integer (6 binary)
#>
#> Explored 0 nodes (0 simplex iterations) in 0.00 seconds (0.00 work units)
#> Thread count was 1 (of 8 available processors)
#>
#> Solution count 1: 1.44561
#> No other solutions better than 1.44561
#>
#> Optimal solution found (tolerance 0.00e+00)
#> Best objective 1.445609277954e+00, best bound 1.445609277954e+00, gap 0.0000%
s3 <- solve(p3)
#> Set parameter Username
#> Set parameter TimeLimit to value 2147483647
#> Set parameter MIPGap to value 0
#> Set parameter NumericFocus to value 3
#> Set parameter Presolve to value 2
#> Set parameter Threads to value 1
#> Set parameter PoolSolutions to value 1
#> Set parameter PoolSearchMode to value 2
#> Academic license - for non-commercial use only - expires 2025-04-21
#> Gurobi Optimizer version 11.0.2 build v11.0.2rc0 (linux64 - "Ubuntu 22.04.4 LTS")
#>
#> CPU model: 11th Gen Intel(R) Core(TM) i7-1185G7 @ 3.00GHz, instruction set [SSE2|AVX|AVX2|AVX512]
#> Thread count: 4 physical cores, 8 logical processors, using up to 1 threads
#>
#> Optimize a model with 47 rows, 47 columns and 102 nonzeros
#> Model fingerprint: 0x80197d20
#> Variable types: 0 continuous, 42 integer (42 binary)
#> Semi-Variable types: 5 continuous, 0 integer
#> Coefficient statistics:
#> Matrix range [9e-02, 1e+02]
#> Objective range [1e+00, 1e+00]
#> Bounds range [1e+00, 1e+00]
#> RHS range [1e+00, 2e+02]
#> Found heuristic solution: objective 1.4456093
#> Presolve removed 22 rows and 19 columns
#> Presolve time: 0.00s
#> Presolved: 25 rows, 28 columns, 52 nonzeros
#> Variable types: 0 continuous, 28 integer (28 binary)
#> Root relaxation presolved: 25 rows, 28 columns, 52 nonzeros
#>
#>
#> Root relaxation: objective 1.575441e+00, 9 iterations, 0.00 seconds (0.00 work units)
#>
#> Nodes | Current Node | Objective Bounds | Work
#> Expl Unexpl | Obj Depth IntInf | Incumbent BestBd Gap | It/Node Time
#>
#> * 0 0 0 1.5754408 1.57544 0.00% - 0s
#>
#> Explored 1 nodes (9 simplex iterations) in 0.00 seconds (0.00 work units)
#> Thread count was 1 (of 8 available processors)
#>
#> Solution count 1: 1.57544
#> No other solutions better than 1.57544
#>
#> Optimal solution found (tolerance 0.00e+00)
#> Best objective 1.575440809243e+00, best bound 1.575440809243e+00, gap 0.0000%
# print the actions selected for funding in each of the solutions
print(s1[, sim_actions$name])
#> # A tibble: 1 × 6
#> F1_action F2_action F3_action F4_action F5_action baseline_action
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 0 1 0 0 0 1
print(s2[, sim_actions$name])
#> # A tibble: 1 × 6
#> F1_action F2_action F3_action F4_action F5_action baseline_action
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 0 0 1 0 0 1
print(s3[, sim_actions$name])
#> # A tibble: 1 × 6
#> F1_action F2_action F3_action F4_action F5_action baseline_action
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 0 0 0 0 1
# }