Algorithms - Pareto Archived DDS (PADDS)

The OSTRICH Pareto Archived DDS multi-objective optimization algorithm

Initial Publication:

Modified:

The following optional group will configure the multi-objective Pareto Archived DDS algorithm and will be processed if [ProgramType] is set to “PADDS”. 

BeginPADDSAlg
PerturbationValue      [r_val]
MaxIterations          [budget]
SelectionMetric        [metric]
EndPADDSAlg

BeginPADDSAlg
PerturbationValue      0.2
MaxIterations          50
SelectionMetric        Random
EndPADDSAlg

Figure 1: General Format (left) and Example (right) of the PADDS Group

Where BeginPADDSAlg and EndPADDSAlg are parsing tags that wrap a set of algorithm configuration variables. Alternatively, BeginPADDS and EndPADDS may be used as the parsing tags. PADDS configuration variables are described below:

  • PerturbationValue: This parameter defines the standard deviation of the decision variable perturbations as follows: PerturbationValue = StdDev / DV_Range. The allowable range is 0 to 1. As the value increases, the sampling becomes more and more spread out from the current best value of the decision variable. The default and recommended value is 0.2.
  • MaxIterations: The computational budget in terms of the number of objective function evaluations. Users need to set this input for each problem according to how long each objective function evaluation takes and how quickly an answer is needed. The more objective functions you use, the better your estimate of the globally optimal solution will be. The default value is 50.

  • SelectionMetric: This metric for scoring non-dominated solutions when seeding DDS trials within the overall PADDS algorithm. Values currently supported are listed below:

    • Random
    • CrowdingDistance
    • EstimatedHyperVolumeContribution
    • ExactHyperVolumeContribution

    The default selection metric value is “ExactHyperVolumeContribution”. For a discussion on choosing the appropriate selection metric see Asadzadeh and Tolson (2013).

References

Asadzadeh, M.,Tolson, B. A. Year. "A new multi-objective algorithm, Pareto archived DDS." Paper presented at the Proceedings of the 11th Annual Conference Companion on Genetic and Evolutionary Computation Conference: Late Breaking Papers, 2009.

Asadzadeh, M.,Tolson, B. 2013. Pareto archived dynamically dimensioned search with hypervolume-based selection for multi-objective optimization. Engineering Optimization 45, 1489-1509.