A stabilised Benders decomposition with adaptive oracles applied to
investment planning of multi-region power systems with short-term and
long-term uncertainty
Benders decomposition with adaptive oracles was proposed to solve large-scale
optimisation problems with a column bounded block-diagonal structure, where
subproblems differ on the right-hand side and cost coefficients. Adaptive
Benders reduces computational effort significantly by iteratively building
inexact cutting planes and valid upper and lower bounds. However, Adaptive
Benders and standard Benders may suffer severe oscillation when solving a
multi-region investment planning problem. Therefore, we propose stabilising
Adaptive Benders with the level set method and adaptively selecting the
subproblems to solve per iteration for more accurate information. Furthermore,
we propose a dynamic level set method to improve the robustness of stabilised
Adaptive Benders by adjusting the level set per iteration. We compare
stabilised Adaptive Benders with the unstabilised versions of Adaptive Benders
with one subproblem solved per iteration and standard Benders on a multi-region
long-term power system investment planning problem with short-term and
long-term uncertainty. The problem is formulated as multi-horizon stochastic
programming. Four algorithms were implemented to solve linear programming with
up to 1 billion variables and 4.5 billion constraints. The computational
results show that: a) for a 1.00% convergence tolerance, the proposed
stabilised method is up to 113.7 times faster than standard Benders and 2.14
times faster than unstabilised Adaptive Benders; b) for a 0.10% convergence
tolerance, the proposed stabilised method is up to 45.5 times faster than
standard Benders and unstabilised Adaptive Benders cannot solve the largest
instance to convergence tolerance due to severe oscillation and c) dynamic
level set method makes stabilisation more robust