GPU-based Split algorithm for Large-Scale CVRPSD

TL;DR

This paper presents a GPU-accelerated framework that reformulates dynamic programming recursions as batched min-plus matrix-vector products, enabling the evaluation of over one million uncertainty realizations simultaneously, significantly speeding up large-scale stochastic optimization.

Contribution

The paper introduces a novel GPU-based reformulation of dynamic programming for stochastic programming, allowing massive parallelism and scalability to handle over a million scenarios.

Findings

Achieves 10 to 1000 times speedup over CPU baselines.

Enables evaluation of over one million scenarios in a single GPU pass.

Demonstrates near-linear scaling with the number of scenarios.

Abstract

Dynamic programming (DP) is a cornerstone of combinatorial optimization, yet its inherently sequential structure has long limited its scalability in scenario-based stochastic programming (SP). This paper introduces a GPU-accelerated framework that reformulates a broad class of forward DP recursions as batched min-plus matrix-vector products over layered DAGs, collapsing actions into masked state-to-state transitions that map seamlessly to GPU kernels. Using this reformulation, our approach takes advantage of massive parallelism across both scenarios and transitions, enabling the simultaneous evaluation of \emph{over one million uncertainty realizations} in a single GPU pass -- a scale far beyond the reach of existing methods. We instantiate the framework in two canonical applications: the capacitated vehicle routing problem with stochastic demand and a dynamic stochastic inventory routing problem. In both cases, DP subroutines traditionally considered sequential are redesigned to harness two- or three-dimensional GPU parallelism. Experiments demonstrate near-linear scaling in the number of scenarios and yield one to three orders of magnitude speedups over multithreaded CPU baselines, resulting in tighter SAA estimates and significantly stronger first-stage decisions under fixed time budgets. Beyond these applications, our work establishes a general-purpose recipe for transforming classical DP routines into high-throughput GPU primitives, substantially expanding the computational frontier of stochastic discrete optimization to the million-scenario scale.