Improve logs

[tbittar]

• Add total duration in logs from standard output (and possibly to out.json)
• There is a difference between run_duration in out.json and the Benders run time printed in the standard output, we should investigate this difference and correct it
• It could be nice to uniformize the different printings of duration time in the standard output logs (optional)
• We should add the total number of iterations done a the end of the logs so that the user can get this information in a blink of an eye:
  • In the file out.json
  • In the standard output log just before best iteration..., add a line Total number of iterations done : xx
• The field solution[problem_status] in out.json is misleading. It corresponds to the status of the resolution of the subproblems or the master of the corresponding iteration (we should check) but it does not indicate the status of the global Xpansion problem. We may create an indicator xpansion_status that reflects the state of the global Xpansion problem and that can take the following values:
  • optimal if the algorithm stops because the relaxed or absolute optimality gap is reached
  • convergence to be checked (or a better name ?) if the algorithm stops because of a timelimit or a maximum iteration number
  • None (or not converged) if the algorithm has not stopped