A Solution Methodology of Bi-Level Linear Programming Based on Genetic Algorithm

Abstract

Problem statement:We deal with the bi-level linear programming problem. A bi-level programming problem is formulated for a problem in which two Decision-Makers (DMs) make decisions successively. Approach: In this research we studied and designs a Genetic Algorithm (GA) of Bi-Level Linear Programming Problems (BLPP) by constructing the fitness function of the upperlevel programming problems based on the definition of the feasible degree. This GA avoids the use of penalty function to deal with the constraints, by changing the randomly generated initial population into an initial population satisfying the constraints in order to improve the ability of the GA to deal with the constraints. Also we designed software to solve this problem. A comparative study between proposed method and previous methods through numerical results of some examples. Finally, parametric information of the GA was introduced. Results: Results of the study showed that the proposed method is feasible and more efficient to solve (BLPP), also there exist package to solve (BLPP) problem. Conclusion: This GA avoids the use of penalty function to deal with the constraints, by changing the randomly generated initial population into an initial population satisfying the constraints in order to improve the ability of the GA to deal with the constraints.

Pareto Evolutionary Optimization of Joint Network Design and Pricing Strategies Related to Emissions in Urban Networks

“…When dealing with multi-objective optimization problems, where the solution of problem is composed of conflicting objectives, the optimality conditions correspond to a compromise among them (Osman, Abd El-Wahed, El Shafei & Abd El Wahab, 2010;Deb & Sinha 2010;Abraham, Jaim & Goldberg, 2005;Tan, Khor, & Lee, 2005). The determination of the set of optimal tradeoffs among conflicting objectives composes the so-called PF (see Section 2).…”

An Evolutionary Algorithmic Approach based Optimal Web Service Selection for Composition with Quality of Service

“…Genetic Algorithms (GAs) (Goldberg, 1989) are search methods which were developed by John Holland and are based on the principles of natural selection (Osman et al, 2009) Genetic Algorithm is proposed as a search algorithm and has proven to be powerful in rapidly discovering good solutions for some difficult problems (Ismail and Irhamah, 2008) especially when the search space is large, complex and poorly understood. GA can be applied to the optimal service selection optimization problem (Yu and Lin, 2004).…”

A New Approach for Solving Linear Bilevel Programming Using Differential Evolution

“…Therefore, for LBP problem meta heuristics algorithms seem to be necessary since these have proved to be robust in finding good solutions to complex optimization problems and are able to solve large problems in reasonable computational time [2]. Up to now, these algorithms include genetic algorithms [2], [5], [7], simulated annealing algorithms [9], particle swarm optimization(PSO) [6], etc.…”