Natural Computing

, Volume 13, Issue 2, pp 145–156 | Cite as

Robust swarm optimisation for fuzzy open shop scheduling

  • Juan José Palacios
  • Inés González-RodríguezEmail author
  • Camino R. Vela
  • Jorge Puente


In this paper we consider a variant of the open shop problem where task durations are allowed to be uncertain and where uncertainty is modelled using fuzzy numbers. Solutions to this problem are fuzzy schedules, which we argue should be seen as predictive schedules, thus establishing links with the concept of robustness and a measure thereof. We propose a particle swarm optimization (PSO) approach to minimise the schedule’s expected makespan, using priorities to represent particle position, as well as a decoding algorithm to generate schedules in a subset of possibly active ones. Our proposal is evaluated on a varied set of several benchmark problems. The experimental study includes a parametric analysis, results of the PSO compared with the state-of-the-art, and an empirical study of the robustness of taking into account uncertainty along the scheduling process.


Open shop scheduling Fuzzy durations Particle swarm optimisation Robustness 



This work Has been funded by the Spanish Ministry of Science and Education under research grants MEC-FEDER TIN2010-20976-C02-02 and MTM2010-16051 and by the Principality of Asturias (Spain) under grant Severo Ochoa BP13106.

Supplementary material

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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  • Juan José Palacios
    • 1
  • Inés González-Rodríguez
    • 2
    Email author
  • Camino R. Vela
    • 1
  • Jorge Puente
    • 1
  1. 1.Department of Computer ScienceUniversity of OviedoOviedoSpain
  2. 2.Department of Mathematics, Statistics and ComputingUniversity of CantabriaSantanderSpain

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