createWeights: Das and Dennis's structured weight generation, normal...

In MaOEA: Many Objective Evolutionary Algorithm

Description

Generate a set of weights following Das and Dennis's method. Each column returned is a weight vector.

Usage

createWeights(nDim, axisDivision = nDim + 2, noZero = FALSE)

Arguments

nDim	The dimensionality of the problem. In EA, usually this is used in the objective space, hence nDim = nObjective
axisDivision	Used only when no weights are supplied. An input for the structured weight distribution. This defines how many division are created in each axis.
noZero	Default to false. If set to TRUE, reference vector containing zero, e.g. (1,0,0) will be removed. Used to generate weight in modified tch method.

Value

The function return a set of weight vectors.

References

Indraneel Das and J. E. Dennis. 1998. Normal-Boundary Intersection: A New Method for Generating the Pareto Surface in Nonlinear Multicriteria Optimization Problems. SIAM Journal on Optimization 1998 8:3, 631-657.

Examples

nObjective <- 3
axisDiv <- 6

createWeights(nObjective,axisDiv)

Example output

Check required python modules:
reticulate::py_module_available('numpy') and reticulate::py_module_available('pygmo').
If not available, try using MaOEA::install_python_dependencies()
or follow the instructions in https://esa.github.io/pagmo2/install.html
and call MaOEA::load_python_dependencies().
     [,1]      [,2]      [,3]      [,4]      [,5]      [,6]      [,7]      [,8]
[1,]    1 0.9805807 0.9805807 0.8944272 0.9428090 0.8944272 0.7071068 0.8017837
[2,]    0 0.1961161 0.0000000 0.4472136 0.2357023 0.0000000 0.7071068 0.5345225
[3,]    0 0.0000000 0.1961161 0.0000000 0.2357023 0.4472136 0.0000000 0.2672612
          [,9]     [,10]     [,11]     [,12]     [,13]     [,14]     [,15]
[1,] 0.8017837 0.7071068 0.4472136 0.5345225 0.5773503 0.5345225 0.4472136
[2,] 0.2672612 0.0000000 0.8944272 0.8017837 0.5773503 0.2672612 0.0000000
[3,] 0.5345225 0.7071068 0.0000000 0.2672612 0.5773503 0.8017837 0.8944272
         [,16]     [,17]     [,18]     [,19]     [,20]     [,21] [,22]
[1,] 0.1961161 0.2357023 0.2672612 0.2672612 0.2357023 0.1961161     0
[2,] 0.9805807 0.9428090 0.8017837 0.5345225 0.2357023 0.0000000     1
[3,] 0.0000000 0.2357023 0.5345225 0.8017837 0.9428090 0.9805807     0
         [,23]     [,24]     [,25]     [,26]     [,27] [,28]
[1,] 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000     0
[2,] 0.9805807 0.8944272 0.7071068 0.4472136 0.1961161     0
[3,] 0.1961161 0.4472136 0.7071068 0.8944272 0.9805807     1

MaOEA documentation built on Aug. 31, 2020, 5:07 p.m.