8

It's not exactly the same thing, but very close: in goal programming, using a weighted combination of the deviations from goals is often called "Archimedean" (as in "Archimedean" goal programming, or using "Archimedean weights"). I'm not sure what the origin of that was. An example appears here.


7

The act of moving soft constraint into the objective function using penalties is closely related to Lagrangian Relaxation and Lagrangian Multipliers. The method penalizes violations of [...] constraints using a Lagrange multiplier, which imposes a cost on violations. These added costs are used instead of the strict [...] constraints in the optimization. ...


6

This problem is addressed in some detail in Section 2.1 of the paper Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems by Watson and Woodruff (a non-paywall version is given here). In general, proper selection can be quite tricky and is highly problem-specific. I recommend trying some of the tricks in the ...


4

I’m not sure I’ve heard a canonical name, but that sounds like a multi-objective optimization problem where you’re minimizing the sum of weighted deviations. The weights are based on the constraint priorities. I’ve run into this a lot with nurse scheduling models - eg many types of constraints that can’t all be simultaneously satisfied (eg union rules, staff ...


4

One common way I've seen in the literature to deal with such cases is to multiply the priority constraint by a big weight and add it into the fitness function alongside the lower priority constraint. You are likely to want greater complexity than that, see below. What is the canonical name of this practice? Suggestion: representation of a category. A ...


3

We can't modify the optimisation problem while it's being solved. What you could try instead is to solve once (maybe with a lax convergence criterion), add/update the constraints based on that solution, and then re-solve by warm-starting the problem using the solution from the previous step.


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