Local optima and weight distribution in the number partitioning problem

Khulood Alyahya; Jonathan E. Rowe

doi:10.1007/978-3-319-10762-2

Local optima and weight distribution in the number partitioning problem

Khulood Alyahya, Jonathan E. Rowe

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

1 Citation (Scopus)

Abstract

This paper investigates the relation between the distribution of the weights and the number of local optima in the Number Partitioning Problem (NPP). The number of local optima in the 1-bit flip landscape was found to be strongly and negatively correlated with the coefficient of variation (CV) of the weights. The average local search cost using the 1- bit flip operator was also found to be strongly and negatively correlated with the CV of the weights. A formula based on the CV of the weights for estimating the average number of local optima in the 1-bit flip landscape is proposed in the paper. The paper also shows that the CV of the weights has a potentially useful application in guiding the choice of heuristic search algorithm.

Original language	English
Title of host publication	Parallel Problem Solving from Nature – PPSN XIII
Subtitle of host publication	13th International Conference, Ljubljana, Slovenia, September 13-17, 2014. Proceedings
Editors	Thomas Bartz-Beielstein, Jurgen Branke, Bogdan Filipic, Jim Smith
Publisher	Springer
Pages	862-871
Number of pages	10
Volume	8672
ISBN (Electronic)	9783319107622
ISBN (Print)	9783319107615
DOIs	https://doi.org/10.1007/978-3-319-10762-2
Publication status	Published - 2014
Event	13th International Conference on Parallel Problem Solving from Nature (PPSN XIII) - - Ljublijana, Slovenia Duration: 13 Sept 2014 → 17 Sept 2014

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer-Verlag
Volume	8672
ISSN (Print)	0302-9743

Conference

Conference	13th International Conference on Parallel Problem Solving from Nature (PPSN XIII) -
Country/Territory	Slovenia
Period	13/09/14 → 17/09/14

Keywords

Combinatorial optimisation
Fitness landscape
Makespan scheduling
Partitioning problem
Phase transition

ASJC Scopus subject areas

General Computer Science
Theoretical Computer Science

Access to Document

10.1007/978-3-319-10762-2

Cite this

Alyahya, K., & Rowe, J. E. (2014). Local optima and weight distribution in the number partitioning problem. In T. Bartz-Beielstein, J. Branke, B. Filipic, & J. Smith (Eds.), Parallel Problem Solving from Nature – PPSN XIII : 13th International Conference, Ljubljana, Slovenia, September 13-17, 2014. Proceedings (Vol. 8672, pp. 862-871). (Lecture Notes in Computer Science ; Vol. 8672). Springer. https://doi.org/10.1007/978-3-319-10762-2

Alyahya, Khulood ; Rowe, Jonathan E. / Local optima and weight distribution in the number partitioning problem. Parallel Problem Solving from Nature – PPSN XIII : 13th International Conference, Ljubljana, Slovenia, September 13-17, 2014. Proceedings. editor / Thomas Bartz-Beielstein ; Jurgen Branke ; Bogdan Filipic ; Jim Smith. Vol. 8672 Springer, 2014. pp. 862-871 (Lecture Notes in Computer Science ).

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abstract = "This paper investigates the relation between the distribution of the weights and the number of local optima in the Number Partitioning Problem (NPP). The number of local optima in the 1-bit flip landscape was found to be strongly and negatively correlated with the coefficient of variation (CV) of the weights. The average local search cost using the 1- bit flip operator was also found to be strongly and negatively correlated with the CV of the weights. A formula based on the CV of the weights for estimating the average number of local optima in the 1-bit flip landscape is proposed in the paper. The paper also shows that the CV of the weights has a potentially useful application in guiding the choice of heuristic search algorithm.",

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Alyahya, K & Rowe, JE 2014, Local optima and weight distribution in the number partitioning problem. in T Bartz-Beielstein, J Branke, B Filipic & J Smith (eds), Parallel Problem Solving from Nature – PPSN XIII : 13th International Conference, Ljubljana, Slovenia, September 13-17, 2014. Proceedings. vol. 8672, Lecture Notes in Computer Science , vol. 8672, Springer, pp. 862-871, 13th International Conference on Parallel Problem Solving from Nature (PPSN XIII) - , Slovenia, 13/09/14. https://doi.org/10.1007/978-3-319-10762-2

Local optima and weight distribution in the number partitioning problem. / Alyahya, Khulood; Rowe, Jonathan E.
Parallel Problem Solving from Nature – PPSN XIII : 13th International Conference, Ljubljana, Slovenia, September 13-17, 2014. Proceedings. ed. / Thomas Bartz-Beielstein; Jurgen Branke; Bogdan Filipic; Jim Smith. Vol. 8672 Springer, 2014. p. 862-871 (Lecture Notes in Computer Science ; Vol. 8672).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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Alyahya K, Rowe JE. Local optima and weight distribution in the number partitioning problem. In Bartz-Beielstein T, Branke J, Filipic B, Smith J, editors, Parallel Problem Solving from Nature – PPSN XIII : 13th International Conference, Ljubljana, Slovenia, September 13-17, 2014. Proceedings. Vol. 8672. Springer. 2014. p. 862-871. (Lecture Notes in Computer Science ). doi: 10.1007/978-3-319-10762-2

Local optima and weight distribution in the number partitioning problem

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Keywords

ASJC Scopus subject areas

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