A local search-based generalized normal distribution algorithm for permutation flow shop scheduling

Mohamed Abdel-Basset, Reda Mohamed, Mohamed Abouhawwash*, Victor Chang, S. S. Askar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


This paper studies the generalized normal distribution algorithm (GNDO) performance for tackling the permutation flow shop scheduling problem (PFSSP). Because PFSSP is a discrete problem and GNDO generates continuous values, the largest ranked value rule is used to convert those continuous values into discrete ones to make GNDO applicable for solving this discrete problem. Additionally, the discrete GNDO is effectively integrated with a local search strategy to improve the quality of the best-so-far solution in an abbreviated version of HGNDO. More than that, a new improvement using the swap mutation operator applied on the best-so-far solution to avoid being stuck into local optima by accelerating the convergence speed is effectively applied to HGNDO to propose a new version, namely a hybrid-improved GNDO (HIGNDO). Last but not least, the local search strategy is improved using the scramble mutation operator to utilize each trial as ideally as possible for reaching better outcomes. This improved local search strategy is integrated with IGNDO to produce a new strong algorithm abbreviated as IHGNDO. Those proposed algorithms are extensively compared with a number of well-established optimization algorithms using various statistical analyses to estimate the optimal makespan for 41 well-known instances in a reasonable time. The findings show the benefits and speedup of both IHGNDO and HIGNDO over all the compared algorithms, in addition to HGNDO.

Original languageEnglish
Article number4837
JournalApplied Sciences (Switzerland)
Issue number11
Publication statusPublished - 25 May 2021

Bibliographical note

© 2021 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
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Funding Information:
This project is funded by King Saud University, Riyadh, Saudi Arabia. Research Supporting Project number (RSP?2021/167), King Saud University, Riyadh, Saudi Arabia.


  • Generalized normal distribution optimization algorithm
  • Local search strategy
  • Makespan
  • Permutation flow shop scheduling


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