scholarly journals Genetic algorithm based on simplex method for solving linear-quadratic bilevel programming problem

2008 ◽  
Vol 56 (10) ◽  
pp. 2550-2555 ◽  
Author(s):  
Guangmin Wang ◽  
Zhongping Wan ◽  
Xianjia Wang ◽  
Yibing Lv
Keyword(s):  
Genetic Algorithm ◽  
Programming Problem ◽  
Bilevel Programming ◽  
Simplex Method ◽  
Linear Quadratic ◽  
Bilevel Programming Problem

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.

A Genetic Algorithm for Solving Linear-Quadratic Bilevel Program-Ming Problems

2011 ◽  
Vol 186 ◽  
pp. 626-630
Author(s):  
He Cheng Li ◽  
Yu Ping Wang
Keyword(s):  
Genetic Algorithm ◽  
Nonlinear Programming ◽  
Programming Problem ◽  
Original Problem ◽  
Nonlinear Programming Problem ◽  
Linear Quadratic ◽  
Bilevel Programming Problem ◽  
Equivalent Problem ◽  
Bilevel Program ◽  
Two Phases

In this paper, we focus on a special linear-quadratic bilevel programming problem in which the follower’s problem is a convex-quadratic programming, whereas the leader’s functions are linear. At first, based on Karush-Kuhn-Tucher(K-K-T) conditions, the original problem is transformed into an equivalent nonlinear programming problem in which the objective and constraint functions are linear except for the complementary slack conditions. Then, a genetic algorithm is proposed to solve the equivalent problem. In the proposed algorithm, the individuals are encoded in two phases. Finally, the efficiency of the approach is demonstrated by an example.

Genetic algorithm for solving quadratic bilevel programming problem

2007 ◽  
Vol 12 (3) ◽  
pp. 421-425 ◽  
Author(s):  
Guangmin Wang ◽  
Zhongping Wan ◽  
Xianjia Wang ◽  
Debin Fang
Keyword(s):  
Genetic Algorithm ◽  
Programming Problem ◽  
Bilevel Programming ◽  
Bilevel Programming Problem

Genetic Algorithm Based on Duality Principle for Bilevel Programming Problem in Steel-making Production

2014 ◽  
Vol 22 (7) ◽  
pp. 742-747 ◽  
Author(s):  
Shuo Lin ◽  
Fangjun Luan ◽  
Zhonghua Han ◽  
Xisheng Lü ◽  
Xiaofeng Zhou ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Programming Problem ◽  
Bilevel Programming ◽  
Duality Principle ◽  
Bilevel Programming Problem ◽  
Steel Making
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