  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.

Computational Engineering, Finance, and Science