Single-level reformulations of a specific non-smooth bilevel programming problem and their applications

2019 ◽  
Vol 14 (6) ◽  
pp. 1393-1406
Author(s):  
Xide Zhu ◽  
Peijun Guo
Keyword(s):  
Programming Problem ◽  
Bilevel Programming ◽  
Bilevel Programming Problem ◽  
Single Level

AN ITERATIVE ALGORITHM FOR A CLASS OF NONLINEAR INTEGER BILEVEL PROGRAMMING PROBLEMS WITH BOX CONSTRAINTS

2012 ◽  
Vol 05 (03) ◽  
pp. 1250032
Author(s):  
Kalpana Dahiya ◽  
Vikas Sharma ◽  
Vanita Verma
Keyword(s):  
Programming Problem ◽  
Iterative Algorithm ◽  
Bilevel Programming ◽  
Box Constraints ◽  
Bilevel Programming Problem ◽  
Single Level ◽  
Bilevel Programming Problems ◽  
Indefinite Quadratic ◽  
Feasible Points ◽  
Fractional Function

The bilevel programming problem is a leader–follower game in which two players try to maximize their own objective functions over a common constraint region. This paper discusses an integer nonlinear bilevel programming problem with box constraints by exploiting the quasimonotone character of the indefinite quadratic fractional function, considered as leader's objective. By making use of the duality theory, given nonlinear bilevel programming problem is transformed into single level programming problem. Various cuts have been discussed in this paper which successively rank and scan all integer feasible points of the single level programming problem in the decreasing value of objective function. An iterative algorithm is proposed, which by making use of these cuts repeatedly, solves the problem.

scholarly journals Bi-Objective Bilevel Programming Problem: A Fuzzy Approach

2015 ◽  
Vol 11 (2) ◽  
pp. 97-115 ◽  
Author(s):  
S. Haseen ◽  
A. Bari
Keyword(s):  
Programming Problem ◽  
Bilevel Programming ◽  
Decision Model ◽  
Stackelberg Game ◽  
Fuzzy Approach ◽  
Fuzzy Decision ◽  
Bilevel Programming Problem ◽  
Decision Variables ◽  
Fuzzy Decision Model ◽  
Fuzzy Cost

Abstract In this paper, a likely situation of a set of decision maker’s with bi-objectives in case of fuzzy multi-choice goal programming is considered. The problem is then carefully formulated as a bi-objective bilevel programming problem (BOBPP) with multiple fuzzy aspiration goals, fuzzy cost coefficients and fuzzy decision variables. Using Ranking method the fuzzy bi-objective bilevel programming problem (FBOBPP) is converted into a crisp model. The transformed problem is further solved by adopting a two level Stackelberg game theory and fuzzy decision model of Sakawa. A numerical with hypothetical values is also used to illustrate the problem.

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