Efficient frontier-like analysis

I needed to perform an optimization run of the form:

for different λ’s. Essentially something like an efficient frontier but in this case we have a MINLP (with semi-integer variables), so no smooth curve but instead some points.

In this case f(x) and g(x) were having different units and different magnitudes. In that case it is better to solve first:

and then use:

This will get a (hopefully) better spread of the λ’s. See: http://yetanothermathprogrammingconsultant.blogspot.com/2010/02/efficient-frontiers-in-mip-models.html.

Of course if λ=0 or λ=1 is part of the λ’s we need to trace, then this actually does not require extra models to solve, just a different ordering: first do λ=0 and λ=1 to get f₀ and g₀ and then do the λ’s in between. As the λ’s are user specified, we needed a little bit of logic to handle this.