1

When we solve an optimization problem, containing in his objective function an uncertain parameter (i.e. random variable), using robust optimization techniques such as the max-min approach, we first solve the problem for the worst case of the uncertain parameter, hence the min part of the max-min approach (in this step the decision variables are constant). Next, we solve the original optimization problem after fixing the random variable with the previously found worst value. My question is maybe simple, why taking always the worst case in robust optimization, we can as well work with the average or the median case. I feel that focusing on the worst scenario is a bit pessimistic.

omar
  • 11
  • You're questioning the definition of Robust Optimization, which is sometimes equated with worst case analysis where its roots lie. If you want stochastic optimization you would use different techniques. If you use different techniques you aren't doing robust optimization. – Jeff Snider Jan 21 '14 at 18:43
  • That right !! they are different techniques. But here, I'm just wondering about the idea or the reasons behind choosing the worst case of the uncertain parameter (for robust optimization). Is it for convenience or we can prove that the worst-case carrie in it some additional robustness. – omar Jan 22 '14 at 06:59

1 Answers1

0

It is a solution that is best possible in the worst case scenario. Different approach produces different 'robust' solutions. It all depends on how robustness is defined. I do agree that it is not easy to quantify how much more 'robust' solution can become, since usually the quality (i.e., the objective function value) of this max-min solution is not as good. However, there are other definitions such as lightly robustness where additional constraints are introduced to guarantee certain quality of the solutions.

user415922
  • 1
  • Thank you. I do also agree, robustness and quality are contradictory objectives. The definition of quality is very clear, but that of robustness seems to be not always evident. – omar Feb 14 '17 at 13:55