Maximal-Sum submatrix search using a hybrid contraint programming/linear programming approach

•The Maximum-Sum Submatrix problem aims at finding submatrices of maximum sum.•Two upper bounds are proposed for the problem, both based on linear relaxations.•A reduced-cost filtering algorithm is proposed for constraint programming solvers.•Large instances are tackled using Large Neighborhood Sear...

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Bibliographic Details
Published in:European journal of operational research Vol. 297; no. 3; pp. 853 - 865
Main Authors: Derval, Guillaume, Schaus, Pierre
Format: Journal Article
Language:English
Published: Elsevier B.V 16.03.2022
Subjects:
Combinatorial optimization
Constraint programming
Linear relaxation
Maximum-sum submatrix
Linear relaxation
Combinatorial optimization
Constraint programming
Maximum-sum submatrix
ISSN:0377-2217, 1872-6860
Online Access:Get full text
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Summary:•The Maximum-Sum Submatrix problem aims at finding submatrices of maximum sum.•Two upper bounds are proposed for the problem, both based on linear relaxations.•A reduced-cost filtering algorithm is proposed for constraint programming solvers.•Large instances are tackled using Large Neighborhood Search.•Improved performance of CP on synthetic and real-word instances against MIP solvers. A Maximal-Sum Submatrix (MSS) maximizes the sum of the entries corresponding to the Cartesian product of a subset of rows and columns from an original matrix (with positive and negative entries). Despite being NP-hard, this recently introduced problem was already proven to be useful for practical data-mining applications. It was used for identifying bi-clusters in gene expression data or to extract a submatrix that is then visualized in a circular plot. The state-of-the-art results for MSS are obtained using an advanced Constraint Programing approach that combines a custom filtering algorithm with a Large Neighborhood Search. We improve the state-of-the-art approach by introducing new upper bounds based on linear and mixed-integer programming formulations, along with dedicated pruning algorithms. We experiment on both synthetic and real-life data, and show that our approach outperforms the previous methods.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2021.06.008