N2N: A Parallel Framework for Large-Scale MILP under Distributed Memory

2025-11-23

AI Summary

Addressing challenges in large-scale distributed-memory environments for mixed-integer linear programming (MILP) solving—including difficulty in parallelizing branch-and-bound (B&B), deep coupling of algorithmic components in existing solvers, and weak determinism guarantees—this paper proposes N2N, a scalable distributed-memory parallel framework. Its core contributions are: (1) a lightweight B&B scheduling architecture based on node-to-compute-node mapping; (2) a novel sliding-window mechanism ensuring strong deterministic execution order; and (3) adaptive solving strategies and communication optimizations enabling seamless integration with multiple solvers (e.g., SCIP, HiGHS). Evaluated on a 1,000-core MPI cluster, N2N achieves a speedup of 22.52× under nondeterministic mode—outperforming ParaSCIP by 2.08×—and maintains significant performance advantages even under strict determinism, demonstrating high efficiency, scalability, and solver generality.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Parallelization has emerged as a promising approach for accelerating MILP solving. However, the complexity of the branch-and-bound (B&B) framework and the numerous effective algorithm components in MILP solvers make it difficult to parallelize. In this study, a scalable parallel framework, N2N (a node-to-node framework that maps the B&B nodes to distributed computing nodes), was proposed to solve large-scale problems in a distributed memory computing environment. Both deterministic and nondeterministic modes are supported, and the framework is designed to be easily integrated with existing solvers. Regarding the deterministic mode, a novel sliding-window-based algorithm was designed and implemented to ensure that tasks are generated and solved in a deterministic order. Moreover, several advanced techniques, such as the utilization of CP search and general primal heuristics, have been developed to fully utilize distributed computing resources and capabilities of base solvers. Adaptive solving and data communication optimization were also investigated. A popular open-source MILP solver, SCIP, was integrated into N2N as the base solver, yielding N2N-SCIP. Extensive computational experiments were conducted to evaluate the performance of N2N-SCIP compared to ParaSCIP, which is a state-of-the-art distributed parallel MILP solver under the UG framework. The nondeterministic N2N-SCIP achieves speedups of 22.52 and 12.71 with 1,000 MPI processes on the Kunpeng and x86 computing clusters, which is 1.98 and 2.08 times faster than ParaSCIP, respectively. In the deterministic mode, N2N-SCIP also shows significant performance improvements over ParaSCIP across different process numbers and computing clusters. To validate the generality of N2N, HiGHS, another open-source solver, was integrated into N2N. The related results are analyzed, and the requirements of N2N on base solvers are also concluded.

Problem

• Solving large-scale MILP problems efficiently in distributed memory computing environments
• Overcoming parallelization difficulties in branch-and-bound framework for MILP solving
• Developing scalable parallel framework that integrates with existing MILP solvers

Innovation

• Parallel framework maps B&B nodes to distributed computing nodes
• Sliding-window algorithm ensures deterministic task execution order
• Integrates advanced techniques like CP search and primal heuristics