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An Efficient Local Search Solver for Mixed Integer Programming

Authors Peng Lin , Mengchuan Zou , Shaowei Cai

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Author Details

Peng Lin
  • Key Laboratory of System Software (Chinese Academy of Sciences) and State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China
  • School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing, China
Mengchuan Zou
  • Key Laboratory of System Software (Chinese Academy of Sciences) and State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China
Shaowei Cai
  • Key Laboratory of System Software (Chinese Academy of Sciences) and State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing, China
  • School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing, China

Funding

This work is supported by National Key R&D Program of China (2023YFA1009500).

Cite AsGet BibTex

Peng Lin, Mengchuan Zou, and Shaowei Cai. An Efficient Local Search Solver for Mixed Integer Programming. In 30th International Conference on Principles and Practice of Constraint Programming (CP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 307, pp. 19:1-19:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.CP.2024.19

Abstract

Mixed integer programming (MIP) is a fundamental model in operations research. Local search is a powerful method for solving hard problems, but the development of local search solvers for MIP still needs to be explored. This work develops an efficient local search solver for solving MIP, called Local-MIP. We propose two new operators for MIP to adaptively modify variables for optimizing the objective function and satisfying constraints, respectively. Furthermore, we design a new weighting scheme to dynamically balance the priority between the objective function and each constraint, and propose a two-level scoring function structure to hierarchically guide the search for high-quality feasible solutions. Experiments are conducted on seven public benchmarks to compare Local-MIP with state-of-the-art MIP solvers, which demonstrate that Local-MIP significantly outperforms CPLEX, HiGHS, SCIP and Feasibility Jump, and is competitive with the most powerful commercial solver Gurobi. Moreover, Local-MIP establishes 4 new records for MIPLIB open instances.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Integer programming
  • Theory of computation → Randomized local search
  • Applied computing → Operations research
Keywords
  • Mixed Integer Programming
  • Local Search
  • Operator
  • Scoring Function

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