Decomposition Based Refinement for the Network Interdiction Problem

TL;DR

This paper presents a hybrid decomposition algorithm for the NP-hard shortest path network interdiction problem, leveraging Ising Processing Units and classical solvers to improve scalability and computational efficiency.

Contribution

Introduces a novel hybrid decomposition approach combining IPUs and classical solvers for large-scale SPNI problems.

Findings

Achieves comparable solution quality to existing methods.

Reduces computational time for large instances.

Enables parallel processing of sub-problems.

Abstract

The shortest path network interdiction (SPNI) problem poses significant computational challenges due to its NP-hardness. Current solutions, primarily based on integer programming methods, are inefficient for large-scale instances. In this paper, we introduce a novel hybrid algorithm that can utilize Ising Processing Units (IPUs) alongside classical solvers. This approach decomposes the problem into manageable sub-problems, which are then offloaded to the slow but high-quality classical solvers or IPU. Results are subsequently recombined to form a global solution. Our method demonstrates comparable quality to existing whole problem solvers while reducing computational time for large-scale instances. Furthermore, our approach is amenable to parallelization, allowing for simultaneous processing of decomposed sub-problems.