A Novel Technique for Solving Integer Linear Bilevel Programming Problems

2021 ◽  
Vol 23 (08) ◽  
pp. 326-333
Author(s):  
Alaa Mokhtar Morsy ◽  
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Bilevel Programming ◽  
Feasible Region ◽  
Global Optimality ◽  
Bilevel Programming Problem ◽  
Novel Technique ◽  
Linear Bilevel Programming ◽  
Linear Programming Problems ◽  
Upper Level

A novel technique that addresses the solution of the general integer linear bilevel programming problem to global optimality is presented i.e. the general case of bilevel linear programming problems where each decision maker has objective functions conflicting with each other. We introduce linear programming problem of which resolution can permit to generate the whole feasible set of the upper level decisions. The approach is based on the relaxation of the feasible region by convex underestimation. Finally, we illustrate our approach with a numerical example.

Genetic Algorithm for FGP Model of a Multiobjective Bilevel Programming Problem in Uncertain Environment

2016 ◽  
pp. 870-888
Author(s):  
Debjani Chakraborti ◽  
Valentina E. Balas ◽  
Bijay Baran Pal
Keyword(s):  
Genetic Algorithm ◽  
Programming Problem ◽  
Bilevel Programming ◽  
Chance Constraints ◽  
Proper Solution ◽  
Bilevel Programming Problem ◽  
Uncertain Environment ◽  
Degree Of Satisfaction ◽  
Objective Function Values ◽  
Upper Level

This chapter describes a Genetic Algorithm (GA) based Fuzzy Goal Programming (FGP) model to solve a Multiobjective Bilevel Programming Problem (MOBLPP) with a set of chance constraints within a structure of decentralized decision problems. To formulate the model, the chance constraints are converted first to their crisp equivalents to employ FGP methodology. Then, the tolerance membership functions associated with fuzzily described goals of the objective functions are defined to measure the degree of satisfaction of Decision Makers (DMs) with achievement of objective function values and also to obtain the degree of optimality of vector of decision variables controlled by upper-level DM in the decision system. In decision-making process, a GA scheme is adopted to solve the problem and thereby to obtain a proper solution for balancing execution powers of DMs in uncertain environment. A numerical example is provided to illustrate the method.

scholarly journals The Backpropagation Artificial Neural Network Based on Elite Particle Swam Optimization Algorithm for Stochastic Linear Bilevel Programming Problem

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Tao Zhang ◽  
Xiaofei Li
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Programming Problem ◽  
Optimization Algorithm ◽  
Bilevel Programming ◽  
Bilevel Programming Problem ◽  
Simulation Experiments ◽  
Linear Bilevel Programming ◽  
Artificial Neural ◽  
Backpropagation Artificial Neural Network

For a class of stochastic linear bilevel programming problem, we firstly transform it into a deterministic linear bilevel covariance programming problem. Then, the deterministic bilevel covariance programming problem is solved by backpropagation artificial neural network based on elite particle swam optimization algorithm (BPANN-PSO). Finally, we perform the simulation experiments and the results show that the computational efficiency of the proposed algorithm has a potential upside compared with the classical algorithm.

scholarly journals A new method for strong-weak linear bilevel programming problem

2015 ◽  
Vol 11 (2) ◽  
pp. 529-547 ◽  
Author(s):  
Yue Zheng ◽  
◽  
Zhongping Wan ◽  
Shihui Jia ◽  
Guangmin Wang ◽  
...  
Keyword(s):  
Programming Problem ◽  
Bilevel Programming ◽  
New Method ◽  
Bilevel Programming Problem ◽  
Linear Bilevel Programming
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