[TASK] Constraints for Samplers

[sprapp-inl]

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Issue Description

Is your feature request related to a problem? Please describe.

At the moment, it appears to be impossible to constrain the input space from a sampler (Monte Carlo, for example) using a constraint function like the ones possible in optimizers.

Describe the solution you'd like

Additional optional fields to specify constraint functions (<Constraint>) or implicit constraint functions (<ImplicitConstraint>) for use in Samplers where the inclusion of constraints would be applicable should the user need it. These would operate in the same way as the constraints for sampling input space for optimizers.

Describe alternatives you've considered

At the moment, the only features considered have been variable sampling functions or a Custom Sampling strategy, but the use of these relies on the user to provide a lot more data, where RAVEN could generate it automatically. A partial workaround is included below.

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Example

As an example of the problem, the initialization of a Genetic Algorithm optimizer samples the input space of all variables using a sampler that is pulled from outside the optimizer for the first generation. This results in any defined constraints in the Genetic Algorithm optimizer to be ignored and a possibility that a portion of the initial population falls outside constraints, reducing diversity.

An example where 3 independent variables are constrained by their sum (the sum does not need to be sampled in RAVEN so a sampling function would be inapplicable):

• Suppose you have a set of variables (genes) x, y, and z that have continuous distributions A, B, and C.
• Suppose you want to apply a constraint such that the sum of x, y, and z is less than a constant value S.
• The distributions A, B, and C. allow the sum to exceed S if the input space is not constrained (i.e. there exist values possible for x, y, and z such that their sum is greater than S).
• A solution to this is to take x, y, and z and add a fourth variable w that is sampled from a distribution that has maximum value S and minimum value (max(x) + max(y)).
• Then, you can calculate z in the driven code (or RAVEN function) as z = w - (x + y).
• If this method is applied, the initial sample of the Genetic Algorithm will always be within the input space.
• The drawbacks of this approach is that you must reduce the domain of w such that w is always greater than (x + y), which reduces the domain of the sum of x, y, and z from [0, S] to [max(x) + max(y), S]

This constraint is trivial to apply when sampled from within the optimizer, however the initial generation does not use the defined constraints if provided.

I do not know who would be best suited to be assigned to this, so I'm mentioning the following according to the contributing guidelines: @wangcj05 @PaulTalbot-INL @mandd

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• 1. Is it tagged with a type: defect or task?
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• 5. Is a rationale provided? (Such as explaining why the improvement is needed or why current code is wrong.)

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For Change Control Board: Issue Closure

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• 1. If the issue is a defect, is the defect fixed?
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• 5. If the issue is being closed without a pull request, has an explanation of why it is being closed been provided?

[PaulTalbot-INL]

Hm, this is a good point. While I don't generally think most samplers can make good use of constraints when being used for statistical workflows, certainly if a sampler is used to prepopulate an optimizer, that sampler should follow the same constraints that we impose on the optimization itself. Good point!