Title: Estimates Pareto-Optimal Solution for Hiring with 3 Objectives
Version: 1.0.1
Description: Estimates Pareto-optimal solution for personnel selection with 3 objectives using Normal Boundary Intersection (NBI) algorithm introduced by Das and Dennis (1998) <doi:10.1137/S1052623496307510>. Takes predictor intercorrelations and predictor-objective relations as input and generates a series of solutions containing predictor weights as output. Accepts between 3 and 10 selection predictors. Maximum 2 objectives could be adverse impact objectives. Partially modeled after De Corte (2006) TROFSS Fortran program https://users.ugent.be/~wdecorte/trofss.pdf and updated from 'ParetoR' package described in Song et al. (2017) <doi:10.1037/apl0000240>. For details, see Study 3 of Zhang et al. (2023).
License: MIT + file LICENSE
Encoding: UTF-8
RoxygenNote: 7.2.1
Suggests: knitr, rmarkdown, testthat (≥ 3.0.0)
VignetteBuilder: knitr
Imports: graphics, grDevices, nloptr, stats
Config/testthat/edition: 3
NeedsCompilation: no
Packaged: 2023-11-08 20:34:13 UTC; kimye
Author: Chelsea Song ORCID iD [aut, cre], Yesuel Kim ORCID iD [ctb]
Maintainer: Chelsea Song <qianqisong@gmail.com>
Repository: CRAN
Date/Publication: 2023-11-08 23:00:02 UTC

rMOST: Estimates Pareto-Optimal Solution for Hiring with 3 Objectives

Description

Estimates Pareto-optimal solution for personnel selection with 3 objectives using Normal Boundary Intersection (NBI) algorithm introduced by Das and Dennis (1998) doi:10.1137/S1052623496307510. Takes predictor intercorrelations and predictor-objective relations as input and generates a series of solutions containing predictor weights as output. Accepts between 3 and 10 selection predictors. Maximum 2 objectives could be adverse impact objectives. Partially modeled after De Corte (2006) TROFSS Fortran program https://users.ugent.be/~wdecorte/trofss.pdf and updated from 'ParetoR' package described in Song et al. (2017) doi:10.1037/apl0000240. For details, see Study 3 of Zhang et al. (in press).

Author(s)

Maintainer: Chelsea Song qianqisong@gmail.com (ORCID)

Other contributors:

MOST

Description

Optimizes 3 objectives with normal boundary intersection algorithm

Usage

MOST(optProb, Rx, Rxy1, Rxy2, Rxy3, sr, prop1, prop2, d1, d2, Spac = 10)

Arguments

optProb

Optimization problem. "3C" = no adverse impact objectives and three non-adverse impact objectives; "2C_1AI" = one adverse impact objective and two non-adverse impact objectives; "1C_2AI" = two adverse impact objectives and one non-adverse impact objective.

Rx

Predictor intercorrelation matrix

Rxy1

Needs to specify for all three types of optimization problems (optProb). Predictor criterion-related validity for non-adverse impact objective 1 (i.e., correlation between each predictor and non-adverse impact objective 1)

Rxy2

Only specify if optimization problem is "3C" or "2C_1AI". Predictor criterion-related validity for non-adverse impact objective 2 (i.e., correlation between each predictor and non-adverse impact objective 2)

Rxy3

Only specify if optimization problem is "3C". Predictor criterion-related validity for non-adverse impact objective 3 (i.e., correlation between each predictor and non-adverse impact objective 3)

sr

Only specify if optimization problem is "2C_1AI" or "1C_2AI". Overall selection ratio.

prop1

Only specify if optimization problem is "2C_1AI" or "1C_2AI". Proportion of minority1 in the applicant pool; prop1 = (# of minority1 applicants)/(total # of applicants)

prop2

Only specify if optimization problem is "1C_2AI". Proportion of minority2 in the applicant pool; prop2 = (# of minority2 applicants)/(total # of applicants)

d1

Only specify if optimization problem is "2C_1AI" or "1C_2AI". Vector of standardized group-mean differences between majority and minority 1 for each predictor; d1 = avg_majority - avg_minority1

d2

Only specify if optimization problem is "1C_2AI". Vector of standardized group-mean differences between majority and minority 2 for each predictor; d2 = avg_majority - avg_minority2

Spac

Determines the number of solutions.

Details

# Inputs required by optimization problems Different types of optimization problems require different input parameters: * optProb = "3C": MOST(optProb, Rx, Rxy1, Rxy2, Rxy3) * optProb = "2C_1AI": MOST(optProb, Rx, Rxy1, Rxy2, sr, prop1, d1) * optProb = "1C_2AI": MOST(optProb, Rx, Rxy1, sr, prop1, d1, prop2, d2)

# Notes regarding the inputs * For personnel selection applications, all predictor-intercorrelations and criterion-related validity inputs should be corrected for range restriction and criterion unreliability to reflect the relations in the applicant sample. * For optimization problems with 2 adverse impact objectives (i.e., optProb = "1C_2AI"), d1 and d2 should be the standardized mean difference between a minority group and the same reference group (e.g., Black-White and Hispanic-White, not Black-White and female-male)

# Optimization * Optimization may take several minutes to run. * Optimization may fail in some applications due to non-convergence.

For more details, please consult the vignette.

Value

Pareto-Optimal solutions with objective values (e.g., C1, AI1) and the corresponding predictor weights (e.g., P1, P2)

Examples

# A sample optimization problem with 3 non-adverse impact objectives and 3 predictors
# For more examples, please consult the vignette.

# Specify inputs
# Predictor inter-correlation matrix (Rx)
Rx <- matrix(c(1,  .50, .50,
               .50,  1, .50,
               .50, .50,  1), 3, 3)

# Predictor-objective relation vectors (Rxy1, Rxy2, Rxy3)
# Criterion-related validities
## Criterion 1
Rxy1 <- c(-.30, 0, .30)
## Criterion 2
Rxy2 <- c(0, .30, -.30)
## Criterion 3
Rxy3 <- c(.30, -.30, 0)

# Get Pareto-optimal solutions

out <- MOST(optProb = "3C", Rx = Rx, Rxy1 = Rxy1, Rxy2 = Rxy2, Rxy3 = Rxy3, Spac = 10)
out

NBI Main Function

Description

Main function for obtaining pareto-optimal solution via normal boundary intersection.

Usage

NBI_1C_1AIR(
  X0,
  Spac,
  Fnum,
  VLB = vector(),
  VUB = vector(),
  TolX = 1e-04,
  TolF = 1e-04,
  TolCon = 1e-07,
  graph = TRUE
)

Arguments

X0

Initial input for predictor weight vector

Spac

Number of Pareto spaces (i.e., number of Pareto points minus one)

Fnum

Number of criterions

VLB

Lower boundary for weight vector estimation

VUB

Upper boundary for weight vector estimation

TolX

Tolerance index for estimating weight vector, default is 1e-4

TolF

Tolerance index for estimating criterion, default is 1e-4

TolCon

Tolerance index for constraint conditions, default is 1e-7

graph

If TRUE, plots will be generated for Pareto-optimal curve and predictor Weights_1C_1AIR

Value

Pareto-Optimal solutions

NBI Main Function

Description

Main function for obtaining pareto-optimal solution via normal boundary intersection.

Usage

NBI_1C_2AIR(
  X0,
  Spac,
  Fnum,
  VLB = vector(),
  VUB = vector(),
  TolX = 1e-07,
  TolF = 1e-07,
  TolCon = 1e-07
)

Arguments

X0

Initial input for predictor weight vector

Spac

Number of Pareto spaces (i.e., number of Pareto points minus one)

Fnum

Number of criterions

VLB

Lower boundary for weight vector estimation

VUB

Upper boundary for weight vector estimation

TolX

Tolerance index for estimating weight vector, default is 1e-4

TolF

Tolerance index for estimating criterion, default is 1e-4

TolCon

Tolerance index for constraint conditions, default is 1e-7

Value

Pareto-Optimal solutions

NBI Main Function

Description

Main function for obtaining pareto-optimal solution via normal boundary intersection.

Usage

NBI_2C(
  X0,
  Spac,
  Fnum,
  VLB = vector(),
  VUB = vector(),
  TolX = 1e-04,
  TolF = 1e-04,
  TolCon = 1e-07,
  graph = TRUE
)

Arguments

X0

Initial input for predictor weight vector

Spac

Number of Pareto spaces (i.e., number of Pareto points minus one)

Fnum

Number of criterions

VLB

Lower boundary for weight vector estimation

VUB

Upper boundary for weight vector estimation

TolX

Tolerance index for estimating weight vector, default is 1e-4

TolF

Tolerance index for estimating criterion, default is 1e-4

TolCon

Tolerance index for constraint conditions, default is 1e-7

graph

If TRUE, plots will be generated for Pareto-optimal curve and predictor weights

Value

Pareto-Optimal solutions

NBI Main Function

Description

Main function for obtaining pareto-optimal solution via normal boundary intersection.

Usage

NBI_2C_1AIR(
  X0,
  Spac,
  Fnum,
  VLB = vector(),
  VUB = vector(),
  TolX = 1e-04,
  TolF = 1e-04,
  TolCon = 1e-07
)

Arguments

X0

Initial input for predictor weight vector

Spac

Number of Pareto spaces (i.e., number of Pareto points minus one)

Fnum

Number of criterions

VLB

Lower boundary for weight vector estimation

VUB

Upper boundary for weight vector estimation

TolX

Tolerance index for estimating weight vector, default is 1e-4

TolF

Tolerance index for estimating criterion, default is 1e-4

TolCon

Tolerance index for constraint conditions, default is 1e-7

Value

Pareto-Optimal solutions

NBI Main Function

Description

Main function for obtaining pareto-optimal solution via normal boundary intersection.

Usage

NBI_3C(
  X0,
  Spac,
  Fnum,
  VLB = vector(),
  VUB = vector(),
  TolX = 1e-07,
  TolF = 1e-07,
  TolCon = 1e-07
)

Arguments

X0

Initial input for predictor weight vector

Spac

Number of Pareto spaces (i.e., number of Pareto points minus one)

Fnum

Number of criterions

VLB

Lower boundary for weight vector estimation

VUB

Upper boundary for weight vector estimation

TolX

Tolerance index for estimating weight vector, default is 1e-4

TolF

Tolerance index for estimating criterion, default is 1e-4

TolCon

Tolerance index for constraint conditions, default is 1e-7

Value

Pareto-Optimal solutions

ParetoR_1C_1AIR

Description

Command function to optimize 1 non-adverse impact objective and 1 adverse impact objective via NBI algorithm

Usage

ParetoR_1C_1AIR(Rx, Rxy1, sr, prop1, d1, Spac = 10, graph = FALSE)

Arguments

Rx

Matrix with intercorrelations among predictors

Rxy1

Vector with correlation between each predictor and criterion 1

sr

Selection ratio in the full applicant pool

prop1

Proportion of minority applicants in full applicant pool

d1

Subgroup difference; standardized mean differences between minority and majority subgroups on each predictor in full applicant pool

Spac

Number of solutions

graph

If TRUE, plots will be generated for Pareto-optimal curve and predictor Weights_1C_1AIR

Value

out Pareto-Optimal solution with objective outcome values (Criterion) and predictor Weights_1C_1AIR (ParetoWeights)

ParetoR_1C_2AIR

Description

Command function to optimize 1 non-adverse impact objective and 2 adverse impact objectives via NBI algorithm

Usage

ParetoR_1C_2AIR(sr, prop1, prop2, Rx, Rxy1, d1, d2, Spac = 10)

Arguments

sr

Selection ratio in the full applicant pool

prop1

Proportion of minority1 applicants in the full applicant pool

prop2

Proportion of minority2 applicants in the full applicant pool

Rx

Matrix with intercorrelations among predictors

Rxy1

Vector with correlation between each predictor and the non-adverse impact objective

d1

Subgroup difference 1; standardized mean differences between minority1 and majority subgroups on each predictor in full applicant pool

d2

Subgroup difference 2; standardized mean differences between minority2 and majority subgroups on each predictor in full applicant pool

Spac

Number of solutions

Value

out Pareto-Optimal solution with objective outcome values (Criterion) and predictor weights (ParetoWeights)

ParetoR_2C

Description

Command function to optimize 2 non-adverse impact objectives via NBI algorithm

Usage

ParetoR_2C(Rx, Rxy1, Rxy2, Spac = 10, graph = TRUE)

Arguments

Rx

Matrix with intercorrelations among predictors

Rxy1

Vector with correlation between each predictor and non-adverse impact objective 1

Rxy2

Vector with correlation between each predictor and non-adverse impact objective 2

Spac

Number of Pareto points

graph

If TRUE, plots will be generated for Pareto-optimal curve and predictor weights

Value

out Pareto-Optimal solution with objective outcome values (Criterion) and predictor weights (ParetoWeights)

ParetoR_2C_1AIR

Description

Command function to optimize 2 non-adverse impact objectives and 1 adverse impact objective via NBI algorithm

Usage

ParetoR_2C_1AIR(Rx, Rxy1, Rxy2, sr, prop1, d1, Spac = 10)

Arguments

Rx

Matrix with intercorrelations among predictors

Rxy1

Vector with correlation between each predictor and non-adverse impact objective 1

Rxy2

Vector with correlation between each predictor and non-adverse impact objective 2

sr

Selection ratio in full applicant pool

prop1

Proportion of minority applicants in full applicant pool

d1

Subgroup difference; standardized mean differences between minority and majority subgroups on each predictor in full applicant pool

Spac

Number of Pareto points

Value

out Pareto-Optimal solution with objective outcome values (Criterion) and predictor weights (ParetoWeights)

ParetoR_3C

Description

Command function to optimize 3 non-adverse impact objectives via NBI algorithm

Usage

ParetoR_3C(Rx, Rxy1, Rxy2, Rxy3, Spac = 10)

Arguments

Rx

Matrix with intercorrelations among predictors

Rxy1

Vector with correlation between each predictor and non-adverse impact objective 1

Rxy2

Vector with correlation between each predictor and non-adverse impact objective 2

Rxy3

Vector with correlation between each predictor and non-adverse impact objective 3

Spac

Number of solutions

Value

out Pareto-Optimal solution with objective outcome values (Criterion) and predictor weights (ParetoWeights)

Weight_Generate_1C_1AIR

Description

Function intended to test the weight generation scheme for NBI for > 2 objectives

Usage

Weight_Generate_1C_1AIR(n, k)

Arguments

n

Number of objects (i.e., number of predictor and criterion)

k

Number of Pareto points

Value

Weight_Generate_1C_1AIR

Weight_Generate_1C_2AIR

Description

Function intended to test the weight generation scheme for NBI for > 2 objectives

Usage

Weight_Generate_1C_2AIR(n, k)

Arguments

n

Number of objects (i.e., number of predictor and criterion)

k

Number of Pareto points

Value

Weight_Generate_1C_2AIR

Weight_Generate_2C

Description

Function intended to test the weight generation scheme for NBI for > 2 objectives

Usage

Weight_Generate_2C(n, k)

Arguments

n

Number of objects (i.e., number of predictor and criterion)

k

Number of Pareto points

Value

Weight_Generate_2C

Weight_Generate_2C_1AIR

Description

Function intended to test the weight generation scheme for NBI for > 2 objectives

Usage

Weight_Generate_2C_1AIR(n, k)

Arguments

n

Number of objects (i.e., number of predictor and criterion)

k

Number of Pareto points

Value

Weight_Generate_2C_1AIR

Weight_Generate_3C

Description

Function intended to test the weight generation scheme for NBI for > 2 objectives

Usage

Weight_Generate_3C(n, k)

Arguments

n

Number of objects (i.e., number of predictor and criterion)

k

Number of Pareto points

Value

Weight_Generate_3C

WeightsFun_1C_1AIR

Description

Support function, checks input predictor weight vector x

Usage

WeightsFun_1C_1AIR(n, k)

Arguments

n

the number of objectives

k

the inverse of the 1/k, which is the unform spacing between two w_i (k integral)

Value

x Checked and refined input predictor weight vector

WeightsFun_1C_2AIR

Description

Support function, generates all possible weights for NBI subproblems

Usage

WeightsFun_1C_2AIR(n, k)

Arguments

n

Number of objects (i.e., number of predictor and criterion)

k

Number of Pareto points

Value

Weights All possible weights for NBI subproblem

WeightsFun_2C

Description

Support function, generates all possible weights for NBI subproblems

Usage

WeightsFun_2C(n, k)

Arguments

n

Number of objects (i.e., number of predictor and criterion)

k

Number of Pareto points

Value

Weights All possible weights for NBI subproblem

WeightsFun_2C_1AIR

Description

Support function, generates all possible weights for NBI subproblems

Usage

WeightsFun_2C_1AIR(n, k)

Arguments

n

Number of objects (i.e., number of predictor and criterion)

k

Number of Pareto points

Value

Weights All possible weights for NBI subproblem

WeightsFun_3C

Description

Support function, generates all possible weights for NBI subproblems

Usage

WeightsFun_3C(n, k)

Arguments

n

Number of objects (i.e., number of predictor and criterion)

k

Number of Pareto points

Value

Weights All possible weights for NBI subproblem

ai_ratio

Description

Helper function to convert mean subgroup differences to AI ratios (Newman et al., 2007). Called by calc_out().

Usage

ai_ratio(d, sr, p)

Arguments

d

Mean subgroup difference of predictor(s)

sr

Selection ratio in the full applicant pool

p

Proportion of minority group in the full applicant pool

assert_col_vec_1C_1AIR

Description

Support function, refines intermediate variable for use in NBI()

Usage

assert_col_vec_1C_1AIR(v)

Arguments

v

Intermediate variable v

Value

Refined variable v

assert_col_vec_1C_2AIR

Description

Support function, refines intermediate variable for use in NBI()

Usage

assert_col_vec_1C_2AIR(v)

Arguments

v

Intermediate variable v

Value

Refined variable v

assert_col_vec_2C

Description

Support function, refines intermediate variable for use in NBI()

Usage

assert_col_vec_2C(v)

Arguments

v

Intermediate variable v

Value

Refined variable v

assert_col_vec_2C_1AIR

Description

Support function, refines intermediate variable for use in NBI()

Usage

assert_col_vec_2C_1AIR(v)

Arguments

v

Intermediate variable v

Value

Refined variable v

myCon_ineq_3C

Description

Support function, defines inequal constraint condition

Usage

assert_col_vec_3C(v)

Arguments

v

Input predictor weight vector

Value

Inequal constraint condition for use in NBI()

calc_out

Description

Helper function to calculate the expected objective outcome values based on predictor weights solutions. Called by MOST().

Usage

calc_out(x)

Arguments

x

Matrix of predictor weights solutions

Value

Expected objective outcomes

combR_1C_1AIR

Description

Support function to create predictor-criterion matrix

Usage

combR_1C_1AIR(Rx, Ry)

Arguments

Rx

Predictor inter-correlation matrix

Ry

Predictor-criterion correlation (validity)

Value

Rxy Predictor-criterion correlation matrix

combR_1C_2AIR

Description

Support function to create predictor-criterion matrix

Usage

combR_1C_2AIR(Rx, Ry)

Arguments

Rx

Predictor inter-correlation matrix

Ry

Predictor-criterion correlation (validity)

Value

Rxy Predictor-criterion correlation matrix

combR_2C_1AIR

Description

Support function to create predictor-criterion matrix

Usage

combR_2C_1AIR(Rx, Ry)

Arguments

Rx

Predictor inter-correlation matrix

Ry

Predictor-criterion correlation (validity)

Value

Rxy Predictor-criterion correlation matrix

combR_3C

Description

Support function to create predictor-criterion matrix

Usage

combR_3C(Rx, Ry)

Arguments

Rx

Predictor inter-correlation matrix

Ry

Predictor-criterion correlation (validity)

Value

Rxy Predictor-criterion correlation matrix

dimFun_1C_1AIR

Description

Support function, checks input predictor weight vector x

Usage

dimFun_1C_1AIR(x)

Arguments

x

Input predictor weight vector

Value

x Checked and refined input predictor weight vector

dimFun_1C_2AIR

Description

Support function, checks input predictor weight vector x

Usage

dimFun_1C_2AIR(x)

Arguments

x

Input predictor weight vector

Value

x Checked and refined input predictor weight vector

dimFun_2C

Description

Support function, checks input predictor weight vector x

Usage

dimFun_2C(x)

Arguments

x

Input predictor weight vector

Value

x Checked and refined input predictor weight vector

dimFun_2C_1AIR

Description

Support function, checks input predictor weight vector x

Usage

dimFun_2C_1AIR(x)

Arguments

x

Input predictor weight vector

Value

x Checked and refined input predictor weight vector

dimFun_3C

Description

Support function, checks input predictor weight vector x

Usage

dimFun_3C(x)

Arguments

x

Input predictor weight vector

Value

x Checked and refined input predictor weight vector

myCon_eq_1C_1AIR

Description

Support function, defines equal constraint condition

Usage

myCon_eq_1C_1AIR(x)

Arguments

x

Input predictor weight vector

Value

Equal constraint condition for use in NBI_1C_1AIR()

myCon_eq_1C_2AIR

Description

Support function, defines equal constraint condition

Usage

myCon_eq_1C_2AIR(x)

Arguments

x

Input predictor weight vector

Value

Equal constraint condition for use in NBI()

myCon_eq_1_1C_2AIR

Description

Support function, defines equal constraint condition

Usage

myCon_eq_1_1C_2AIR(x)

Arguments

x

Input predictor weight vector

Value

Equal constraint condition for use in NBI()

myCon_eq_2C

Description

Support function, defines equal constraint condition

Usage

myCon_eq_2C(x)

Arguments

x

Input predictor weight vector

Value

Equal constraint condition for use in NBI()

myCon_eq_2C_1AIR

Description

Support function, defines equal constraint condition

Usage

myCon_eq_2C_1AIR(x)

Arguments

x

Input predictor weight vector

Value

Equal constraint condition for use in NBI()

myCon_eq_2_1C_2AIR

Description

Support function, defines equal constraint condition

Usage

myCon_eq_2_1C_2AIR(x)

Arguments

x

Input predictor weight vector

Value

Equal constraint condition for use in NBI()

myCon_ineq_3C

Description

Support function, defines inequal constraint condition

Usage

myCon_eq_3C(x)

Arguments

x

Input predictor weight vector

Value

Inequal constraint condition for use in NBI()

myFM_1C_1AIR

Description

Supporting function, defines criterion space

Usage

myCon_ineq_1C_1AIR(x)

Arguments

x

Input predictor weight vector

Value

f Criterion vector

myCon_ineq_1C_2AIR

Description

Support function, defines inequal constraint condition

Usage

myCon_ineq_1C_2AIR(x)

Arguments

x

Input predictor weight vector

Value

Inequal constraint condition for use in NBI()

myCon_ineq_2C

Description

Support function, defines inequal constraint condition

Usage

myCon_ineq_2C(x)

Arguments

x

Input predictor weight vector

Value

Inequal constraint condition for use in NBI()

myCon_ineq_2C_1AIR

Description

Support function, defines inequal constraint condition

Usage

myCon_ineq_2C_1AIR(x)

Arguments

x

Input predictor weight vector

Value

Inequal constraint condition for use in NBI()

myCon_ineq_3C

Description

Support function, defines inequal constraint condition

Usage

myCon_ineq_3C(x)

Arguments

x

Input predictor weight vector

Value

Inequal constraint condition for use in NBI()

myFM_1C_1AIR

Description

Supporting function, defines criterion space

Usage

myFM_1C_1AIR(x)

Arguments

x

Input predictor weight vector

Value

f Criterion vector

myFM_1C_2AIR

Description

Supporting function, defines criterion space

Usage

myFM_1C_2AIR(x)

Arguments

x

Input predictor weight vector

Value

f Criterion vector

myFM_2C

Description

Supporting function, defines criterion space

Usage

myFM_2C(x)

Arguments

x

Input predictor weight vector

Value

f Criterion vector

myFM_2C_1AIR

Description

Supporting function, defines criterion space

Usage

myFM_2C_1AIR(x)

Arguments

x

Input predictor weight vector

Value

f Criterion vector

myFM_3C

Description

Supporting function, defines criterion space

Usage

myFM_3C(x)

Arguments

x

Input predictor weight vector

Value

f Criterion vector

myLinCom_1C_1AIR

Description

Support function

Usage

myLinCom_1C_1AIR(x)

Arguments

x

Input predictor weight vector

Value

f Criterion vector

myLinCom_1C_2AIR

Description

Support function

Usage

myLinCom_1C_2AIR(x)

Arguments

x

Input predictor weight vector

Value

f Criterion vector

myLinCom_2C

Description

Support function

Usage

myLinCom_2C(x)

Arguments

x

Input predictor weight vector

Value

f Criterion vector

myLinCom_2C_1AIR

Description

Support function

Usage

myLinCom_2C_1AIR(x)

Arguments

x

Input predictor weight vector

Value

f Criterion vector

myLinCom_3C

Description

Support function

Usage

myLinCom_3C(x)

Arguments

x

Input predictor weight vector

Value

f Criterion vector

myTCon_eq_1C_1AIR

Description

Support function, define constraint condition for intermediate step in NBI()

Usage

myTCon_eq_1C_1AIR(x_t)

Arguments

x_t

Temporary input weight vector

Value

ceq Temporary constraint condition

myTCon_eq_1C_2AIR

Description

Support function, define constraint condition for intermediate step in NBI()

Usage

myTCon_eq_1C_2AIR(x_t)

Arguments

x_t

Temporary input weight vector

Value

ceq Temporary constraint condition

myTCon_eq_1_1C_2AIR

Description

Support function, define constraint condition for intermediate step in NBI()

Usage

myTCon_eq_1_1C_2AIR(x_t)

Arguments

x_t

Temporary input weight vector

Value

ceq Temporary constraint condition

myTCon_eq_2C

Description

Support function, define constraint condition for intermediate step in NBI()

Usage

myTCon_eq_2C(x_t)

Arguments

x_t

Temporary input weight vector

Value

ceq Temporary constraint condition

myTCon_eq_2C_1AIR

Description

Support function, define constraint condition for intermediate step in NBI()

Usage

myTCon_eq_2C_1AIR(x_t)

Arguments

x_t

Temporary input weight vector

Value

ceq Temporary constraint condition

myTCon_eq_2_1C_2AIR

Description

Support function, define constraint condition for intermediate step in NBI()

Usage

myTCon_eq_2_1C_2AIR(x_t)

Arguments

x_t

Temporary input weight vector

Value

ceq Temporary constraint condition

myTCon_eq_3C

Description

Support function, define constraint condition for intermediate step in NBI()

Usage

myTCon_eq_3C(x_t)

Arguments

x_t

Temporary input weight vector

Value

ceq Temporary constraint condition

myTCon_ineq_1C_2AIR

Description

Support function, defines inequal constraint condition

Usage

myTCon_ineq_1C_2AIR(x_t)

Arguments

x_t

Input predictor weight vector

Value

Inequal constraint condition for use in NBI()

myTCon_ineq_3C

Description

Support function, defines inequal constraint condition

Usage

myTCon_ineq_3C(x_t)

Arguments

x_t

Input predictor weight vector

Value

Inequal constraint condition for use in NBI()

myT_1C_1AIR

Description

Support function, define criterion space for intermediate step in NBI()

Usage

myT_1C_1AIR(x_t)

Arguments

x_t

Temporary input weight vector

Value

f Temporary criterion space

myT_1C_2AIR

Description

Support function, define criterion space for intermediate step in NBI()

Usage

myT_1C_2AIR(x_t)

Arguments

x_t

Temporary input weight vector

Value

f Temporary criterion space

myT_2C

Description

Support function, define criterion space for intermediate step in NBI()

Usage

myT_2C(x_t)

Arguments

x_t

Temporary input weight vector

Value

f Temporary criterion space

myT_2C_1AIR

Description

Support function, define criterion space for intermediate step in NBI()

Usage

myT_2C_1AIR(x_t)

Arguments

x_t

Temporary input weight vector

Value

f Temporary criterion space

myT_3C

Description

Support function, define criterion space for intermediate step in NBI()

Usage

myT_3C(x_t)

Arguments

x_t

Temporary input weight vector

Value

f Temporary criterion space

plotPareto_1C_1AIR

Description

Function for plotting Pareto-optimal curve and predictor Weights_1C_1AIR

Usage

plotPareto_1C_1AIR(CriterionOutput, ParetoWeights)

Arguments

CriterionOutput

Pareto-Optimal criterion solution

ParetoWeights

Pareto-Optimal predictor weight solution

Value

Plot of Pareto-optimal curve and plot of predictor Weights_1C_1AIR

plotPareto_2C

Description

Function for plotting Pareto-optimal curve and predictor weights

Usage

plotPareto_2C(CriterionOutput, ParetoWeights)

Arguments

CriterionOutput

Pareto-Optimal criterion solution

ParetoWeights

Pareto-Optimal predictor weight solution

Value

Plot of Pareto-optimal curve and plot of predictor weights