[IDEA] Modeling problems for external MILP and non-linear MIP solvers

[gialmisi]

• What is the current behavior?
  In the past, we have assumed that the problems we solve in DESDEO have been defined, and are available as, Python objects. This makes it hard to utilize solvers that expect a more algebraic format of the problem, limiting our access to basic MILP and non-linear MIP solvers.

• Describe the solution you'd like
  Since we have moved to a new way to define the problems in DESDEO (in json format), this format can be readily parsed into various other formats. I would like to discuss a potential format that would be understood by most of the popular solvers.

• What is the motivation/use case for changing the behavior?
  In the past, we have lacked support for (mixed-)integer problems.

• Describe alternatives you've considered
  We could utilize AMPL, which basically allows us to parse problems into an .nl-format. This format is understood by most solvers. Alternatively, we could just model (and solve!) the problems (based on the json representation) as pyomoo models, which also gives us access to a plethora of solvers, and also outputs .nl-files, if needed.

• Additional context
  pyomoo works well with problems that depend a lot on data, e.g., many data-based parameters. While AMPL seems to be widely accepted, it is not fully open source. Pyomoo allows redistribution and is as permissive as the MIT license. However, I am not exactly sure what part of AMPL is proprietary and what is open source, perhaps I have misunderstood this.