Adaptive Benders decomposition and enhanced SDDP for multistage stochastic programs with block-separable multistage recourse

TL;DR

This paper introduces a novel algorithm combining Adaptive Benders decomposition and enhanced SDDP to efficiently solve multistage stochastic programs with block-separable recourse, demonstrated on power system planning.

Contribution

It presents the first algorithm for this class of problems, integrating adaptive Benders decomposition with enhanced SDDP for improved efficiency and convergence.

Findings

The algorithm efficiently solves the power system investment problem.

Stochastic wind modeling affects investment decisions.

Deterministic wind modeling underestimates the objective.

Abstract

This paper proposes an algorithm to efficiently solve multistage stochastic programs with block separable recourse where each recourse problem is a multistage stochastic program with stage-wise independent uncertainty. The algorithm first decomposes the full problem into a reduced master problem and subproblems using Adaptive Benders decomposition. The subproblems are then solved by an enhanced SDDP. The enhancement includes (1) valid bounds at each iteration, (2) a path exploration rule, (3) cut sharing among subproblems, and (4) guaranteed {\delta}-optimal convergence. The cuts for the subproblems are then shared by calling adaptive oracles. The key contribution of the paper is the first algorithm for solving this class of problems. The algorithm is demonstrated on a power system investment planning problem with multi-timescale uncertainty. The case study results show that (1) the proposed algorithm can efficiently solve this type of problem, (2) deterministic wind modelling underestimate the objective function, and (3) stochastic modelling of wind leads to different investment decisions.