Formulate master pulp by columns

As mentioned here, for the diving heuristic to work, for some speed up, it would be good to rework master_solve_pulp.py such that it doesn’t have to be reformulated in every iteration of the column generation procedure.

For a column generation friendly way of updating the constraints, one can formulate the problem by columns (seen an example).

The idea is to

1. create empty constraints using pulp.LpConstraintVar, with only the sign (<=, >=) and RHS specified.
2. Then place variables pulp.LpVariable in already existing constraints with the appropriate coefficient, using the e parameter. Here, one can use pulp operations like pulp.lpSum to add variables to multiple constraints at once (this can be seen in the example)

To update the constraints throughout the column generation procedure, the constraints has have to preserved. For example as a dictionary in an attribute.

Constraints Converted

• Set Covering
• Vehicle bound

Variables Converted

• route selecting (y)
  • Simplest case
  • With vehicle bound
• Drop
• Artificial

[torressa]

@Kuifje02 @Halvaros Just ran the new version on the Solomon instance and comparing with the old (OLD) comp results from https://github.com/Kuifje02/vrpy/issues/8#issuecomment-612176272. We get some pretty amazing speed up! Average of over 10,000% faster and scales a lot better! Needs more testing but definitely faster

[Kuifje02]

Excellent idea !

Another very simple example with explanations can be found here.