Memetic Computing

, Volume 11, Issue 4, pp 391–406 | Cite as

Project portfolio selection and scheduling under a fuzzy environment

  • Xiaoxiong ZhangEmail author
  • Keith W. Hipel
  • Yuejin Tan
Regular Research Paper


The problem of integrated project portfolio selection and scheduling (PPSS) is among the most important and highly pursed subjects in project management. In this study, a mathematical model and algorithm are designed specifically to assist decision makers decide which projects are to be chosen and when these projects are to be undertaken. More specifically, the PPSS problem is first formulated as a nonlinear multi-objective model with simultaneous consideration of benefit and risk factors. Due to the complexity and uncertainty involved in most real life situations, fuzzy numbers are incorporated into the model, which can provide decision makers with more flexibility. Then, an inverse modeling based multi-objective evolutionary algorithm using a Gaussian Process is presented to obtain the Pareto set. Finally, an illustrative example is used to demonstrate the high efficacy of the foregoing approach, which can provide decision makers with valuable insights into the PPSS process. The proposed algorithm is found to be more effective compared with two other popular algorithms.


Project portfolio selection and planning Multi-objective optimization Fuzzy numbers Inverse modeling Gaussian process 



This work was supported in part by the National Natural Science Foundation of China under Grants 71690233, 71501182, and 71571185. The authors would like to thank the editor and three anonymous reviewers for their constructive comments that helped us to improve the quality of this paper.


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Copyright information

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

Authors and Affiliations

  1. 1.The Sixty-third Research InstituteNational University of Defense TechnologyNanjingChina
  2. 2.Department of Systems Design EngineeringUniversity of WaterlooWaterlooCanada
  3. 3.Centre for International Governance InnovationWaterlooCanada
  4. 4.Balsillie School of International AffairsWaterlooCanada
  5. 5.College of Systems EngineeringNational University of Defense TechnologyChangshaChina

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