A Differential Evolution Algorithm to Semivectorial Bilevel Problems

  • Maria João AlvesEmail author
  • Carlos Henggeler Antunes
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10710)


Semivectorial bilevel problems (SVBLP) deal with the optimization of a single function at the upper level and multiple objective functions at the lower level of hierarchical decisions. Therefore, a set of nondominated solutions to the lower level decision maker (the follower) exists and should be exploited for each setting of decision variables controlled by the upper level decision maker (the leader). This paper presents a new algorithmic approach based on differential evolution to compute a set of four extreme solutions to the SVBLP. These solutions capture not just the optimistic vs. pessimistic leader’s attitude but also possible follower’s reactions more or less favorable to the leader within the lower level nondominated solution set. The differential evolution approach is compared with a particle swarm optimization algorithm. In this experimental comparison we draw attention to pitfalls associated with the interpretation of results and assessment of the performance of algorithms in SVBLP.


Semivectorial bilevel problems Differential evolution Particle swarm optimization Optimistic/pessimistic frontiers Optimistic/deceiving solutions Pessimistic/rewarding solutions 



This work was supported by projects UID/MULTI/00308/2013 and SAICTPAC/0004/2015-POCI-01-0145-FEDER-016434.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Maria João Alves
    • 1
    • 3
    Email author
  • Carlos Henggeler Antunes
    • 2
    • 3
  1. 1.CeBER and Faculty of EconomicsUniversity of CoimbraCoimbraPortugal
  2. 2.DEECUniversity of CoimbraCoimbraPortugal
  3. 3.INESC CoimbraCoimbraPortugal

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