Optimistic versus Pessimistic Discrete Robust Optimization Approaches: Opportunities and Challenges

The objective of a discrete robust optimisation approach e.g., budget uncertainty (Bertsimas and Sim, 2003&2004) is to find a solution that optimises against all scenarios in which up "a" number of coefficients that maximally influence the objective vary. Therefore, a solution produced by such method is optimal when exactly "a" coefficients are subject to change and it is feasible for other cases. This view of robustness could be regarded as "pessimistic" robust optimisation approach as the value of the objective reflects the worst-case scenario for a given budget of uncertainty. Building upon the concept of pessimistic robust optimisation, in this research we present an approach that we call "optimistic" robust optimisation. For a given problem with uncertain data in the objective function, the optimistic robust optimisation approach aims to find a solution in which exactly "b" number of coefficients with "minimum" impact on the objective are subject to change. We present examples and discuss opportunities and challenges pertain to the use of such (optimistic)robust optimisation approach.