1 research outputs found
A Stochastic Benders Decomposition Scheme for Large-Scale Data-Driven Network Design
Network design problems involve constructing edges in a transportation or
supply chain network to minimize construction and daily operational costs. We
study a data-driven version of network design where operational costs are
uncertain and estimated using historical data. This problem is notoriously
computationally challenging, and instances with as few as fifty nodes cannot be
solved to optimality by current decomposition techniques. Accordingly, we
propose a stochastic variant of Benders decomposition that mitigates the high
computational cost of generating each cut by sampling a subset of the data at
each iteration and nonetheless generates deterministically valid cuts (as
opposed to the probabilistically valid cuts frequently proposed in the
stochastic optimization literature) via a dual averaging technique. We
implement both single-cut and multi-cut variants of this Benders decomposition
algorithm, as well as a k-cut variant that uses clustering of the historical
scenarios. On instances with 100-200 nodes, our algorithm achieves 4-5%
optimality gaps, compared with 13-16% for deterministic Benders schemes, and
scales to instances with 700 nodes and 50 commodities within hours. Beyond
network design, our strategy could be adapted to generic two-stage stochastic
mixed-integer optimization problems where second-stage costs are estimated via
a sample average