Polynomial-time local-improvement algorithm for Consecutive Block Minimization

Haddadi, Salim; Chenche, S.; Cheraitia, Meryem; Guessoum, F.

doi:10.1016/j.ipl.2015.02.010

Cited by 8 publications

(4 citation statements)

References 15 publications

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“…A basic GA is proposed with many new fitness functions and FF5 is chosen to solve the C1S problem. The minimum consecutive blocks or CBM in [3] is also solved using the GA. We applied our algorithm to a large number of randomly generated matrices and real-world instances. The results show that large submatrices with C1P can be found for matrices with small sizes.…”

Section: Discussionmentioning

confidence: 99%

“…Haddadi and others found a polynomial-time local-improvement heuristic for the CBM. They introduced two ( ) size local neighborhood search, where the blocks number of a neighbor is provided in ( ) operations [2,3].…”

Section: Polynomial-time Local-improvement Heuristic For Cbmmentioning

confidence: 99%

“…A block of 1's (block of 0's) in a binary matrix A is any maximal set of consecutive one entries (zero entries) appearing in the same row [2]. A binary matrix A is said to have the Consecutive Ones Property (C1P) if the ones in every row appear consecutively [3].…”

Section: Introductionmentioning

confidence: 99%

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A Metaheuristic Approach to the C1S Problem

Abo-Alsabeh

Salhi

2021

eijs

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Given a binary matrix, finding the maximum set of columns such that the resulting submatrix has the Consecutive Ones Property (C1P) is called the Consecutive Ones Submatrix (C1S) problem. There are solution approaches for it, but there is also a room for improvement. Moreover, most of the studies of the problem use exact solution methods. We propose an evolutionary approach to solve the problem. We also suggest a related problem to C1S, which is the Consecutive Blocks Minimization (CBM). The algorithm is then performed on real-world and randomly generated matrices of the set covering type.

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Section: Discussionmentioning

confidence: 99%

Section: Polynomial-time Local-improvement Heuristic For Cbmmentioning

confidence: 99%

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A Metaheuristic Approach to the C1S Problem

Abo-Alsabeh

Salhi

2021

eijs

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“…It is run on a Dell Optiplex i3-2120 @3.30 GHz with 2 GB RAM and tested on a benchmark dataset. This set of instances was constructed by Haddadi et al (2015) by fixing the number of rows, the number of columns, and the matrix density, with the requirement that each column contains at least one nonzero entry and each row has at least two 1s (see the table below for more details). There are five instances of each of the nine types.…”

Section: Methodsmentioning

confidence: 99%

Exponential neighborhood search for consecutive block minimization

Haddadi

2021

Int Trans Operational Res

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Given binary matrix A$A$, the term A(π)$A^{(\pi )}$ refers to the matrix obtained by permuting the columns of A$A$ according to permutation π$\pi$. A 1‐block in a binary matrix is any maximal sequence of consecutive 1s situated on the same row. Given binary matrix A$A$, consecutive block minimization (CBM) is a combinatorial optimization problem that seeks a permutation π$\pi$ of A$A$ columns such that the number of 1‐blocks in A(π)$A^{(\pi )}$ is minimum. Since CBM is NP‐hard, we solve it by iterating local search where the neighborhood is exponential in the instance size and is always constructed in the vicinity of the best current solution. Seeking a local optimum in the exponential neighborhood amounts to solving a small traveling salesman problem (TSP). Instead, we obtain a good near local optimal solution using an implementation of Lin–Kernighan heuristic. Our method is compared with a recently published iterated local search metaheuristic as well as with two TSP solvers. The comparison shows that the proposed method provides better quality solutions.

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