Journal of Systems Engineering and Electronics

• SYSTEMS ENGINEERING • Previous Articles     Next Articles

Uncertain bilevel knapsack problem and its solution

Junjie Xue1,*, Ying Wang1, and Jiyang Xiao2   

  1. 1. College of Equipment Management and Safety Engineering, Air Force Engineering University, Xi’an 710051, China;
    2. Science Research Center, Air Force Engineering University, Xi’an 710051, China
  • Online:2017-08-25 Published:2010-01-03


This paper aims at providing an uncertain bilevel knapsack problem (UBKP) model, which is a type of BKPs involving uncertain variables. And then an uncertain solution for the UBKP is proposed by defining PE Nash equilibrium and PE Stackelberg Nash equilibrium. In order to improve the computational efficiency of the uncertain solution, several operators (binary coding distance, inversion operator, explosion operator and binary back learning operator) are applied to the basic fireworks algorithm to design the binary backward fireworks algorithm (BBFWA), which has a good performance in solving the BKP. As an illustration, a case study of the UBKP model and the PE uncertain solution is applied to an armaments transportation problem.

Key words: uncertainty, bilevel programming, knapsack problem, binary backward fireworks algorithm