, Volume 101, Issue 6, pp 499–529 | Cite as

A multi-objective invasive weed optimization algorithm for robust aggregate production planning under uncertain seasonal demand

  • Alireza Goli
  • Erfan Babaee Tirkolaee
  • Behnam Malmir
  • Gui-Bin Bian
  • Arun Kumar SangaiahEmail author


This paper addresses a robust multi-objective multi-period aggregate production planning (APP) problem based on different scenarios under uncertain seasonal demand. The main goals are to minimize the total cost including in-house production, outsourcing, workforce, holding, shortage and employment/unemployment costs, and maximize the customers’ satisfaction level. To deal with demand uncertainty, robust optimization approach is applied to the proposed mixed integer linear programming model. A goal programming method is then implemented to cope with the multi-objectiveness and validate the suggested robust model. Since APP problems are classified as NP-hard, two solution methods of non-dominated sorting genetic algorithm II (NSGA-II) and multi-objective invasive weed optimization algorithm (MOIWO) are designed to solve the problem. Moreover, Taguchi design method is implemented to increase the efficiency of the algorithms by adjusting the algorithms’ parameters optimally. Finally, several numerical test problems are generated in different sizes to evaluate the performance of the algorithms. The results obtained from different comparison criteria demonstrate the high quality of the proposed solution methods in terms of speed and accuracy in finding optimal solutions.


Aggregate production planning Uncertain seasonal demand Multi-objective invasive weed optimization algorithm (MOIWO) NSGA-II Robust optimization 

Mathematics Subject Classification

90B30 90B50 68Txx 90C59 


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Industrial EngineeringYazd UniversityYazdIran
  2. 2.Department of Industrial EngineeringMazandaran University of Science and TechnologyBabolIran
  3. 3.Young Researchers and Elite Club, Ayatollah Amoli BranchIslamic Azad UniversityAmolIran
  4. 4.Department of Systems and Information EngineeringUniversity of VirginiaCharlottesvilleUSA
  5. 5.State Key Laboratory of Management and Control for Complex Systems, Institute of AutomationChinese Academy of SciencesBeijingChina
  6. 6.School of Computing Science and EngineeringVellore Institute of TechnologyVelloreIndia

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