On the Solution of Large-Scale Robust Transmission Network Expansion   Planning under Uncertain Demand and Generation Capacity
  Two-stage robust optimization has emerged as a relevant approach to deal with uncertain demand and generation capacity in the transmission network expansion planning problem. Unfortunately, available solution methodologies for the resulting trilevel robust counterpart are unsuitable for large-scale problems. In order to overcome this shortcoming, this paper presents an alternative column-and-constraint generation algorithm wherein the max-min problem associated with the second stage is solved by a novel coordinate descent method. As a major salient feature, the proposed approach does not rely on the transformation of the second-stage problem to a single-level equivalent. As a consequence, bilinear terms involving dual variables or Lagrange multipliers do not arise, thereby precluding the use of computationally expensive big-M-based linearization schemes. Thus, not only is the computational effort reduced, but also the typically overlooked non-trivial tuning of bounding parameters for dual variables or Lagrange multipliers is avoided. The practical applicability of the proposed methodology is confirmed by numerical testing on several benchmarks including a case based on the Polish 2383-bus system, which is well beyond the capability of the robust methods available in the literature. 
Roberto M\'inguez and Raquel Garc\'ia-Bertrand and Jos\'e Manuel   Arroyo and Natalia Alguacil
cs.CE