Add feature weights

Add weights to the features in a project prioritization problem.

Usage

add_feature_weights(x, weights)

# S4 method for class 'ProjectProblem,numeric'
add_feature_weights(x, weights)

# S4 method for class 'ProjectProblem,character'
add_feature_weights(x, weights)

Arguments

x: problem() object.
weights: Object that specifies the weights for each feature. See the Details section for more information.

Value

A problem() with the weights added to it.

Details

Weights are used to specify the relative importance of particular features. For budget constrained problems (e.g., add_max_wtd_sum_objective()), these weights could be used to specify which features are more important than other features according to evolutionary or cultural metrics. Specifically, features with a higher weight value are considered more important. It is generally best to ensure that weight values range between 0.001 and 1,000 to reduce the time required to solve problems using exact algorithm solvers. As a consequence, you might have to rescale the feature weights if the largest or smallest values occur outside this range (excluding zeros). If you want to ensure that certain features conserved in the solutions, it is strongly recommended to lock in the actions for these features instead of setting really high weights for these features. Please note that a warning will be thrown if you attempt to solve problems with weights when an objective has been specified that does not use weights. Currently, all objectives – except for the minimum set objective (i.e., add_min_set_objective()) – can use weights.

The weights for a problem can be specified in several different ways:

numeric vector: Values specify a weight for each feature. These numeric values should correspond to each row in the argument to features for problem().
character value: The value specifies the name of a column in the feature data (i.e., argument to features in problem()). The column must have numeric values, and these used to weight the features.

Examples

# load data
data(sim_projects, sim_features, sim_actions)

# print feature data
print(sim_features)
#> # A tibble: 5 × 2
#>   name  weight
#>   <chr>  <dbl>
#> 1 F1     0.211
#> 2 F2     0.211
#> 3 F3     0.221
#> 4 F4     0.630
#> 5 F5     1.59 

# build problem with maximum weighted sum objective, $300 budget,
# and no weights
p1 <-
  problem(
    sim_projects, sim_actions, sim_features,
    "name", "success", "name", "cost", "name"
  ) %>%
  add_max_wtd_sum_objective(budget = 200) %>%
  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:    continuous values (between 0 and 103.226)
#> project success: proportion values (between 0.814 and 1)
#> objective:       maximum weighted sum objective
#> targets:         none specified
#> weights:         none specified
#> constraints:     none specified
#> decisions:       binary decision
#> solver:          none specified

# build another problem, and specify feature weights using the values in the
# "weight" column of the sim_features table by specifying the column
# name "weight"
p2 <- p1 %>% add_feature_weights("weight")

# 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:    continuous values (between 0 and 103.226)
#> project success: proportion values (between 0.814 and 1)
#> objective:       maximum weighted sum objective
#> targets:         none specified
#> weights:         feature weights
#> constraints:     none specified
#> decisions:       binary decision
#> solver:          none specified

# build another problem, and specify feature weights using the
# values in the "weight column of the sim_features table, but
# actually input the values rather than specifying the column name
# "weights" column of the sim_features table
p3 <- p1 %>% add_feature_weights(sim_features$weight)

# 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:    continuous values (between 0 and 103.226)
#> project success: proportion values (between 0.814 and 1)
#> objective:       maximum weighted sum objective
#> targets:         none specified
#> weights:         feature weights
#> constraints:     none specified
#> decisions:       binary decision
#> solver:          none specified

# solve the problems
s1 <- solve(p1)
#> Set parameter Username
#> Set parameter LicenseID to value 2806834
#> Set parameter TimeLimit to value 2147483647
#> Set parameter MIPGap to value 0
#> Set parameter ScaleFlag to value 2
#> Set parameter NumericFocus to value 1
#> 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 2027-04-14
#> Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04.2 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
#> 
#> Non-default parameters:
#> TimeLimit  2147483647
#> MIPGap  0
#> ScaleFlag  2
#> NumericFocus  1
#> Presolve  2
#> Threads  1
#> PoolSolutions  1
#> PoolSearchMode  2
#> 
#> Optimize a model with 27 rows, 27 columns and 62 nonzeros (Max)
#> Model fingerprint: 0x3c076626
#> Model has 5 linear objective coefficients
#> Variable types: 5 continuous, 22 integer (22 binary)
#> Coefficient statistics:
#>   Matrix range     [9e-02, 1e+02]
#>   Objective range  [1e+00, 1e+00]
#>   Bounds range     [5e-01, 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: 11 rows, 15 columns, 25 nonzeros
#> Variable types: 0 continuous, 15 integer (15 binary)
#> Root relaxation presolved: 11 rows, 15 columns, 25 nonzeros
#> 
#> 
#> Root relaxation: objective 2.190381e+00, 12 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       2.1903807    2.19038  0.00%     -    0s
#> 
#> Explored 1 nodes (12 simplex iterations) in 0.00 seconds (0.00 work units)
#> Thread count was 1 (of 8 available processors)
#> 
#> Solution count 1: 2.19038 
#> No other solutions better than 2.19038
#> 
#> Optimal solution found (tolerance 0.00e+00)
#> Best objective 2.190380737245e+00, best bound 2.190380737245e+00, gap 0.0000%
s2 <- solve(p2)
#> Set parameter Username
#> Set parameter LicenseID to value 2806834
#> Set parameter TimeLimit to value 2147483647
#> Set parameter MIPGap to value 0
#> Set parameter ScaleFlag to value 2
#> Set parameter NumericFocus to value 1
#> 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 2027-04-14
#> Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04.2 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
#> 
#> Non-default parameters:
#> TimeLimit  2147483647
#> MIPGap  0
#> ScaleFlag  2
#> NumericFocus  1
#> Presolve  2
#> Threads  1
#> PoolSolutions  1
#> PoolSearchMode  2
#> 
#> Optimize a model with 27 rows, 27 columns and 62 nonzeros (Max)
#> Model fingerprint: 0x641970bf
#> Model has 5 linear objective coefficients
#> Variable types: 5 continuous, 22 integer (22 binary)
#> Coefficient statistics:
#>   Matrix range     [9e-02, 1e+02]
#>   Objective range  [2e-01, 2e+00]
#>   Bounds range     [5e-01, 1e+00]
#>   RHS range        [1e+00, 2e+02]
#> 
#> Found heuristic solution: objective 0.6654645
#> Presolve removed 16 rows and 12 columns
#> Presolve time: 0.00s
#> Presolved: 11 rows, 15 columns, 25 nonzeros
#> Variable types: 0 continuous, 15 integer (15 binary)
#> Root relaxation presolved: 11 rows, 15 columns, 25 nonzeros
#> 
#> 
#> Root relaxation: objective 1.511230e+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       1.5112297    1.51123  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: 1.51123 
#> No other solutions better than 1.51123
#> 
#> Optimal solution found (tolerance 0.00e+00)
#> Best objective 1.511229665304e+00, best bound 1.511229665304e+00, gap 0.0000%
s3 <- solve(p3)
#> Set parameter Username
#> Set parameter LicenseID to value 2806834
#> Set parameter TimeLimit to value 2147483647
#> Set parameter MIPGap to value 0
#> Set parameter ScaleFlag to value 2
#> Set parameter NumericFocus to value 1
#> 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 2027-04-14
#> Gurobi Optimizer version 13.0.1 build v13.0.1rc0 (linux64 - "Ubuntu 24.04.2 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
#> 
#> Non-default parameters:
#> TimeLimit  2147483647
#> MIPGap  0
#> ScaleFlag  2
#> NumericFocus  1
#> Presolve  2
#> Threads  1
#> PoolSolutions  1
#> PoolSearchMode  2
#> 
#> Optimize a model with 27 rows, 27 columns and 62 nonzeros (Max)
#> Model fingerprint: 0x641970bf
#> Model has 5 linear objective coefficients
#> Variable types: 5 continuous, 22 integer (22 binary)
#> Coefficient statistics:
#>   Matrix range     [9e-02, 1e+02]
#>   Objective range  [2e-01, 2e+00]
#>   Bounds range     [5e-01, 1e+00]
#>   RHS range        [1e+00, 2e+02]
#> 
#> Found heuristic solution: objective 0.6654645
#> Presolve removed 16 rows and 12 columns
#> Presolve time: 0.00s
#> Presolved: 11 rows, 15 columns, 25 nonzeros
#> Variable types: 0 continuous, 15 integer (15 binary)
#> Root relaxation presolved: 11 rows, 15 columns, 25 nonzeros
#> 
#> 
#> Root relaxation: objective 1.511230e+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       1.5112297    1.51123  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: 1.51123 
#> No other solutions better than 1.51123
#> 
#> Optimal solution found (tolerance 0.00e+00)
#> Best objective 1.511229665304e+00, best bound 1.511229665304e+00, gap 0.0000%

# print solutions
print(s1)
#> # A tibble: 1 × 21
#>   solution status   cost   obj F1_action F2_action F3_action F4_action F5_action
#>      <int> <chr>   <dbl> <dbl> <lgl>     <lgl>     <lgl>     <lgl>     <lgl>    
#> 1        1 OPTIMAL  195.  2.19 TRUE      TRUE      FALSE     FALSE     FALSE    
#> # ℹ 12 more variables: baseline_action <lgl>, F1_project <lgl>,
#> #   F2_project <lgl>, F3_project <lgl>, F4_project <lgl>, F5_project <lgl>,
#> #   baseline_project <lgl>, F1 <dbl>, F2 <dbl>, F3 <dbl>, F4 <dbl>, F5 <dbl>
print(s2)
#> # A tibble: 1 × 21
#>   solution status   cost   obj F1_action F2_action F3_action F4_action F5_action
#>      <int> <chr>   <dbl> <dbl> <lgl>     <lgl>     <lgl>     <lgl>     <lgl>    
#> 1        1 OPTIMAL  199.  1.51 FALSE     FALSE     FALSE     TRUE      TRUE     
#> # ℹ 12 more variables: baseline_action <lgl>, F1_project <lgl>,
#> #   F2_project <lgl>, F3_project <lgl>, F4_project <lgl>, F5_project <lgl>,
#> #   baseline_project <lgl>, F1 <dbl>, F2 <dbl>, F3 <dbl>, F4 <dbl>, F5 <dbl>
print(s3)
#> # A tibble: 1 × 21
#>   solution status   cost   obj F1_action F2_action F3_action F4_action F5_action
#>      <int> <chr>   <dbl> <dbl> <lgl>     <lgl>     <lgl>     <lgl>     <lgl>    
#> 1        1 OPTIMAL  199.  1.51 FALSE     FALSE     FALSE     TRUE      TRUE     
#> # ℹ 12 more variables: baseline_action <lgl>, F1_project <lgl>,
#> #   F2_project <lgl>, F3_project <lgl>, F4_project <lgl>, F5_project <lgl>,
#> #   baseline_project <lgl>, F1 <dbl>, F2 <dbl>, F3 <dbl>, F4 <dbl>, F5 <dbl>

# plot solutions
plot(p1, s1)

plot(p2, s2)

plot(p3, s3)

Usage

Arguments

Value

Details

See also

Examples