A Branch and Bound Algorithm for the Bilevel Programming Problem

1990 ◽  
Vol 11 (2) ◽  
pp. 281-292 ◽  
Author(s):  
Jonathan F. Bard ◽  
James T. Moore
Keyword(s):  
Programming Problem ◽  
Branch And Bound ◽  
Bilevel Programming ◽  
Branch And Bound Algorithm ◽  
Bilevel Programming 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.

scholarly journals A Deterministic Method for Solving the Sum of Linear Ratios Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Zhenping Wang ◽  
Yonghong Zhang ◽  
Paolo Manfredi
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Branch And Bound ◽  
Nonconvex Programming ◽  
Real Life ◽  
Branch And Bound Algorithm ◽  
Separation Technique ◽  
Linear Programming Relaxation ◽  
Deterministic Method ◽  
Linearization Technique

Since the sum of linear ratios problem (SLRP) has many applications in real life, for globally solving it, an efficient branch and bound algorithm is presented in this paper. By utilizing the characteristic of the problem (SLRP), we propose a convex separation technique and a two-part linearization technique, which can be used to generate a sequence of linear programming relaxation of the initial nonconvex programming problem. For improving the convergence speed of this algorithm, a deleting rule is presented. The convergence of this algorithm is established, and some experiments are reported to show the feasibility and efficiency of the proposed algorithm.

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