Network Flow Models for Robust Binary Optimization with Selective Adaptability
arxiv(2024)
摘要
Adaptive robust optimization problems have received significant attention in
recent years, but remain notoriously difficult to solve when recourse decisions
are discrete in nature. In this paper, we propose new reformulation techniques
for adaptive robust binary optimization (ARBO) problems with objective
uncertainty. Without loss of generality, we focus on ARBO problems with
"selective adaptability", a term we coin to describe a common class of linking
constraints between first-stage and second-stage solutions. Our main
contribution revolves around a collection of exact and approximate network flow
reformulations for the ARBO problem, which we develop by building upon ideas
from the decision diagram literature. Our proposed models can generate feasible
solutions, primal bounds and dual bounds, while their size and approximation
quality can be precisely controlled through user-specified parameters.
Furthermore, and in contrast with existing solution methods, these models are
easy to implement and can be solved directly with standard off-the-shelf
solvers. Through an extensive set of computational experiments, we show that
our models can generate high-quality solutions and dual bounds in significantly
less time than popular benchmark methods, often by orders of magnitude.
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