Application of the Plant Propagation Algorithm and NSGA-II to Multiple Objective Linear Programming

Paschal Bisong Nyiam; Abdellah Salhi

doi:doi:10.11648/j.mcs.20230801.13

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Application of the Plant Propagation Algorithm and NSGA-II to Multiple Objective Linear Programming

Paschal Bisong Nyiam, Abdellah Salhi

Published in Mathematics and Computer Science (Volume 8, Issue 1)

Received: 3 May 2022 Accepted: 31 May 2022 Published: 10 February 2023

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Abstract

Multiple Objective Linear Programming (MOLP) problems are usually solved by exact methods. However, nature-inspired population based stochastic algorithms such as the plant propagation algorithm are becoming more and more prominent. This paper applies the multiple objective plant propagation algorithm (MOPPA) and nondominated sorting genetic algorithm II (NSGA-II) for the first time to MOLP and compares their outcomes with those of prominent exact methods. Computational results from a collection of 51 existing MOLP instances suggests that MOPPA compares favourably with four of the most prominent exact methods namely extended multiple objective simplex algorithm (EMSA), affine scaling interior MOLP algorithm (ASIMOLP), Benson’s outer-approximation algorithm (BOA) and parametric simplex algorithm (PSA), and returns best nondominated points which are of higher quality than those returned by NSGA-II. However, the nondominated points approximated by NSGA-II are evenly distributed across the nondominated front. The methods compare well with the four exact methods especially on the large instances which the exact methods failed to solve even when given generous amounts of computation times.

Published in	Mathematics and Computer Science (Volume 8, Issue 1)
DOI	10.11648/j.mcs.20230801.13
Page(s)	19-38
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2023. Published by Science Publishing Group

Keywords

Multiple Objective Linear Programming, Plant Propagation Algorithm, Nondominated Sorting Genetic Algorithm II, Penalty Function Method, Best Nondominated Point

References

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Paschal Bisong Nyiam, Abdellah Salhi. (2023). Application of the Plant Propagation Algorithm and NSGA-II to Multiple Objective Linear Programming. Mathematics and Computer Science, 8(1), 19-38. https://doi.org/10.11648/j.mcs.20230801.13

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Paschal Bisong Nyiam; Abdellah Salhi. Application of the Plant Propagation Algorithm and NSGA-II to Multiple Objective Linear Programming. Math. Comput. Sci. 2023, 8(1), 19-38. doi: 10.11648/j.mcs.20230801.13

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Paschal Bisong Nyiam, Abdellah Salhi. Application of the Plant Propagation Algorithm and NSGA-II to Multiple Objective Linear Programming. Math Comput Sci. 2023;8(1):19-38. doi: 10.11648/j.mcs.20230801.13

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@article{10.11648/j.mcs.20230801.13,
  author = {Paschal Bisong Nyiam and Abdellah Salhi},
  title = {Application of the Plant Propagation Algorithm and NSGA-II to Multiple Objective Linear Programming},
  journal = {Mathematics and Computer Science},
  volume = {8},
  number = {1},
  pages = {19-38},
  doi = {10.11648/j.mcs.20230801.13},
  url = {https://doi.org/10.11648/j.mcs.20230801.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20230801.13},
  abstract = {Multiple Objective Linear Programming (MOLP) problems are usually solved by exact methods. However, nature-inspired population based stochastic algorithms such as the plant propagation algorithm are becoming more and more prominent. This paper applies the multiple objective plant propagation algorithm (MOPPA) and nondominated sorting genetic algorithm II (NSGA-II) for the first time to MOLP and compares their outcomes with those of prominent exact methods. Computational results from a collection of 51 existing MOLP instances suggests that MOPPA compares favourably with four of the most prominent exact methods namely extended multiple objective simplex algorithm (EMSA), affine scaling interior MOLP algorithm (ASIMOLP), Benson’s outer-approximation algorithm (BOA) and parametric simplex algorithm (PSA), and returns best nondominated points which are of higher quality than those returned by NSGA-II. However, the nondominated points approximated by NSGA-II are evenly distributed across the nondominated front. The methods compare well with the four exact methods especially on the large instances which the exact methods failed to solve even when given generous amounts of computation times.},
 year = {2023}
}

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TY  - JOUR
T1  - Application of the Plant Propagation Algorithm and NSGA-II to Multiple Objective Linear Programming
AU  - Paschal Bisong Nyiam
AU  - Abdellah Salhi
Y1  - 2023/02/10
PY  - 2023
N1  - https://doi.org/10.11648/j.mcs.20230801.13
DO  - 10.11648/j.mcs.20230801.13
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 19
EP  - 38
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20230801.13
AB  - Multiple Objective Linear Programming (MOLP) problems are usually solved by exact methods. However, nature-inspired population based stochastic algorithms such as the plant propagation algorithm are becoming more and more prominent. This paper applies the multiple objective plant propagation algorithm (MOPPA) and nondominated sorting genetic algorithm II (NSGA-II) for the first time to MOLP and compares their outcomes with those of prominent exact methods. Computational results from a collection of 51 existing MOLP instances suggests that MOPPA compares favourably with four of the most prominent exact methods namely extended multiple objective simplex algorithm (EMSA), affine scaling interior MOLP algorithm (ASIMOLP), Benson’s outer-approximation algorithm (BOA) and parametric simplex algorithm (PSA), and returns best nondominated points which are of higher quality than those returned by NSGA-II. However, the nondominated points approximated by NSGA-II are evenly distributed across the nondominated front. The methods compare well with the four exact methods especially on the large instances which the exact methods failed to solve even when given generous amounts of computation times.
VL  - 8
IS  - 1
ER  -

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Author Information

Paschal Bisong Nyiam

Department of Mathematical Sciences, University of Essex, Colchester, United Kingdom
Abdellah Salhi

Department of Mathematical Sciences, University of Essex, Colchester, United Kingdom

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Paschal Bisong Nyiam, Abdellah Salhi. (2023). Application of the Plant Propagation Algorithm and NSGA-II to Multiple Objective Linear Programming. Mathematics and Computer Science, 8(1), 19-38. https://doi.org/10.11648/j.mcs.20230801.13

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ACS Style

Paschal Bisong Nyiam; Abdellah Salhi. Application of the Plant Propagation Algorithm and NSGA-II to Multiple Objective Linear Programming. Math. Comput. Sci. 2023, 8(1), 19-38. doi: 10.11648/j.mcs.20230801.13

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AMA Style

Paschal Bisong Nyiam, Abdellah Salhi. Application of the Plant Propagation Algorithm and NSGA-II to Multiple Objective Linear Programming. Math Comput Sci. 2023;8(1):19-38. doi: 10.11648/j.mcs.20230801.13

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@article{10.11648/j.mcs.20230801.13,
  author = {Paschal Bisong Nyiam and Abdellah Salhi},
  title = {Application of the Plant Propagation Algorithm and NSGA-II to Multiple Objective Linear Programming},
  journal = {Mathematics and Computer Science},
  volume = {8},
  number = {1},
  pages = {19-38},
  doi = {10.11648/j.mcs.20230801.13},
  url = {https://doi.org/10.11648/j.mcs.20230801.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20230801.13},
  abstract = {Multiple Objective Linear Programming (MOLP) problems are usually solved by exact methods. However, nature-inspired population based stochastic algorithms such as the plant propagation algorithm are becoming more and more prominent. This paper applies the multiple objective plant propagation algorithm (MOPPA) and nondominated sorting genetic algorithm II (NSGA-II) for the first time to MOLP and compares their outcomes with those of prominent exact methods. Computational results from a collection of 51 existing MOLP instances suggests that MOPPA compares favourably with four of the most prominent exact methods namely extended multiple objective simplex algorithm (EMSA), affine scaling interior MOLP algorithm (ASIMOLP), Benson’s outer-approximation algorithm (BOA) and parametric simplex algorithm (PSA), and returns best nondominated points which are of higher quality than those returned by NSGA-II. However, the nondominated points approximated by NSGA-II are evenly distributed across the nondominated front. The methods compare well with the four exact methods especially on the large instances which the exact methods failed to solve even when given generous amounts of computation times.},
 year = {2023}
}

Copy | Download

TY  - JOUR
T1  - Application of the Plant Propagation Algorithm and NSGA-II to Multiple Objective Linear Programming
AU  - Paschal Bisong Nyiam
AU  - Abdellah Salhi
Y1  - 2023/02/10
PY  - 2023
N1  - https://doi.org/10.11648/j.mcs.20230801.13
DO  - 10.11648/j.mcs.20230801.13
T2  - Mathematics and Computer Science
JF  - Mathematics and Computer Science
JO  - Mathematics and Computer Science
SP  - 19
EP  - 38
PB  - Science Publishing Group
SN  - 2575-6028
UR  - https://doi.org/10.11648/j.mcs.20230801.13
AB  - Multiple Objective Linear Programming (MOLP) problems are usually solved by exact methods. However, nature-inspired population based stochastic algorithms such as the plant propagation algorithm are becoming more and more prominent. This paper applies the multiple objective plant propagation algorithm (MOPPA) and nondominated sorting genetic algorithm II (NSGA-II) for the first time to MOLP and compares their outcomes with those of prominent exact methods. Computational results from a collection of 51 existing MOLP instances suggests that MOPPA compares favourably with four of the most prominent exact methods namely extended multiple objective simplex algorithm (EMSA), affine scaling interior MOLP algorithm (ASIMOLP), Benson’s outer-approximation algorithm (BOA) and parametric simplex algorithm (PSA), and returns best nondominated points which are of higher quality than those returned by NSGA-II. However, the nondominated points approximated by NSGA-II are evenly distributed across the nondominated front. The methods compare well with the four exact methods especially on the large instances which the exact methods failed to solve even when given generous amounts of computation times.
VL  - 8
IS  - 1
ER  -

Copy | Download