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Linear bilevel programming solution by genetic algorithm

S.R. Hejazi, A. Memariani, G. Jahanshahloo, M.M. Sepehri
2002 Computers & Operations Research  
Bilevel programming has been proved to be NP-hard problem. Numerous algorithms have been developed so far for solving bilevel programming problem.  ...  Bilevel programming, a tool for modeling decentralized decisions, consists of the objective of the leader at its ÿrst level and that of the follower at the second level.  ...  Acknowledgements The authors would like to thank the anonymous referees whose comments and suggestions improved the algorithm and the quality of presentation.  ... 
doi:10.1016/s0305-0548(01)00066-1 fatcat:cmlgfajgpndxpbaa2tfmdhzjey

A new methodological development for solving linear bilevel integer programming problems in hybrid fuzzy environment

Animesh Biswas, Arnab Kumar De
2016 New Trends in Mathematical Sciences  
A method of defuzzification of fuzzy numbers using α−cut has been adopted to reduce the problem into a linear bilevel integer programming problem.  ...  This paper deals with fuzzy goal programming approach to solve fuzzy linear bilevel integer programming problems with fuzzy probabilistic constraints following Pareto distribution and Frechet distribution  ...  The authors are thankful to the anonymous reviewers for the constructive comments and suggestions in improving the quality of the article.  ... 
doi:10.20852/ntmsci.2016217828 fatcat:osulor22pvecndjqlbxeaorpry

Parametric Integer Programming Algorithm for Bilevel Mixed Integer Programs

M. Köppe, M. Queyranne, C. T. Ryan
2010 Journal of Optimization Theory and Applications  
We consider discrete bilevel optimization problems where the follower solves an integer program with a fixed number of variables.  ...  Using recent results in parametric integer programming, we present polynomial time algorithms for pure and mixed integer bilevel problems.  ...  The second is due to Deng [18] , who develops a polynomial time algorithm for bilevel linear programs when the number of decision variables of the follower is fixed.  ... 
doi:10.1007/s10957-010-9668-3 fatcat:zwas47utrbgchfbt5lldmdbjoy

A Trust-Region Method for Nonlinear Bilevel Programming: Algorithm and Computational Experience

Benoît Colson, Patrice Marcotte, Gilles Savard
2005 Computational optimization and applications  
We consider the approximation of nonlinear bilevel mathematical programs by solvable programs of the same type, i.e., bilevel programs involving linear approximations of the upper-level objective and all  ...  constraintdefining functions, as well as a quadratic approximation of the lower-level objective.  ...  More precisely, our approach consists in approximating a nonlinear bilevel program by a solvable problem of the same type, namely, a bilevel program of the linear-quadratic type.  ... 
doi:10.1007/s10589-005-4612-4 fatcat:zh65gjokrne6nmkh6z2nn4d7ay

A Bilevel Approach to Frequency Optimization in Public Transportation Systems

Agustin Arizti, Antonio Mauttone, Maria E. Urquhart, Michael Wagner
2018 Algorithmic Approaches for Transportation Modeling, Optimization, and Systems  
The resulting formulation is bilevel, and is transformed into a mixed integer linear programming formulation (MILP) that can be solved to optimality for small-sized problem instances, using standard MILP  ...  We study different variants of the same formulation to better understand the bilevel nature of the model and its application to real settings.  ...  Acknowledgements The authors would like to thank to four reviewers, whose comments have improved the manuscript. This work is partially funded by PEDECIBA.  ... 
doi:10.4230/oasics.atmos.2018.7 dblp:conf/atmos/AriztiMU18 fatcat:3qhzqhve2zci7di5pndtiha7gu

An Exact Algorithm for Bilevel 0-1 Knapsack Problems

Raid Mansi, Cláudio Alves, J. M. Valério de Carvalho, Saïd Hanafi
2012 Mathematical Problems in Engineering  
We describe a polynomial time procedure to solve the linear relaxation of the bilevel 0-1 knapsack problem.  ...  We propose a new exact method for solving bilevel 0-1 knapsack problems. A bilevel problem models a hierarchical decision process that involves two decision makers called the leader and the follower.  ...  The authors would like to thank the anonymous referees for their constructive comments, which helped improving the quality of the paper.  ... 
doi:10.1155/2012/504713 fatcat:tv4ahufv2jbw3f6aluaqs3kvrq

A local convergence analysis of bilevel decomposition algorithms

Victor DeMiguel, Walter Murray
2006 Optimization and Engineering  
A popular approach to MDO problems is bilevel decomposition algorithms. These algorithms use nonlinear optimization techniques to solve both the master problem and the subproblems.  ...  In this paper, we propose two new bilevel decomposition algorithms and analyze their properties.  ...  We thank the Associate Editors and three referees for their detailed comments and sugges-tions. We are grateful to R.W. Cottle, M.P. Friedlander, M.A. Saunders, S. Scholtes for many helpful comments.  ... 
doi:10.1007/s11081-006-6835-3 fatcat:z5gahplzlje6jd25kmdfhfbuoy

Solving the Bilevel Facility Location Problem under Preferences by a Stackelberg-Evolutionary Algorithm

José-Fernando Camacho-Vallejo, Álvaro Eduardo Cordero-Franco, Rosa G. González-Ramírez
2014 Mathematical Problems in Engineering  
An evolutionary algorithm based on the equilibrium in a Stackelberg's game is proposed to solve the bilevel model.  ...  Also, two reformulations of the bilevel model are presented, reducing it into a mixed-integer single-level problem.  ...  Acknowledgments This research has been partially supported by the Secretariat of Public Education (SEP by its acronym in Spanish) as a part of the Teachers Improvement Program and the Project named PROMEP  ... 
doi:10.1155/2014/430243 fatcat:tehvoo4fsvcr7jhl2g6oat5gfq

Sequential Competitive Facility Location: Exact and Approximate Algorithms [article]

Mingyao Qi, Ruiwei Jiang, Siqian Shen
2022 arXiv   pre-print
This process is a Stackelberg game and admits a bilevel mixed-integer nonlinear program (MINLP) formulation.  ...  We use the two valid inequalities in a branch-and-cut algorithm to find globally optimal solutions.  ...  All the authors thank the Department Editor, Associate Editor, and three reviewers for making helpful suggestions and comments to improve the work.  ... 
arXiv:2103.04259v3 fatcat:gowqekoapvgftgpucqwczvblyu

A globally convergent sequential linear programming algorithm for mathematical programs with linear complementarity constraints

Jean Bosco Etoa Etoa
2010 Journal of Information and Optimization Sciences  
This paper presents a sequential linear programming algorithm for computing a stationary point of a mathematical program with linear equilibrium constraints.  ...  Keywords: mathematical program with linear equilibrium constraints, linear complementarity problem, perturbed Fisher-Burmeister functional, sequential linear programming algorithm.  ...  Acknowledgments We are grateful to professor Gilles Savard 3 and professor Patrice Marcotte 4 for their constructive review and useful comments.  ... 
doi:10.1080/02522667.2010.10700008 fatcat:3ecxk46hxjcpjpfzyrukta6qpi

A multi-parametric programming algorithm for special classes of non-convex multilevel optimization problems

Abay Molla Kassa, Semu Mitiku Kassa
2013 An International Journal of Optimization and Control: Theories & Applications  
A branch-and-bound procedure is employed until a pre-specified positive tolerance is satisfied. Moreover, a ϵ−convergence proof is given for the algorithm.  ...  programming approach.  ...  The authors also would like to thank the three anonymous reviewers for their valuable comments and suggestions to improve the earlier version of the manuscript.  ... 
doi:10.11121/ijocta.01.2013.00156 fatcat:x4cjyjvr5rakpl2rdpbbhwiuvy

A Scatter Search Algorithm for Solving a Bilevel Optimization Model for Determining Highway Tolls

José Luis González Velarde, José Fernando Camacho Vallejo, Gabriel Pinto Serrano
2015 Journal of Computacion y Sistemas  
The problem is formulated as a bilevel optimization problem where the upper level consists of an administrator who establishes tolls in some arcs of a network, while the lower level is represented by a  ...  The problem of determining optimal tolls established on a subset of arcs in a multicommodity capacitated transportation network is presented.  ...  The authors also gratefully acknowledge the comments and suggestions of the reviewers.  ... 
doi:10.13053/cys-19-1-1916 fatcat:tcdf267vmvdldl3hx7y5tltf2u

A Mathematical Model and Descent Algorithm for Bilevel Traffic Management

Michael Patriksson, R. Tyrrell Rockafellar
2002 Transportation Science  
W e provide a new mathematical model for strategic traffic management, formulated and analyzed as a mathematical program with equilibrium constraints (MPEC).  ...  For this model, we also propose and analyze a descent algorithm.  ...  Table 1 A 1 Descent Algorithm 0.  ... 
doi:10.1287/trsc. fatcat:lrmyngbzlrgh5c6ytmehwzenz4

Branch-and-Sandwich: a deterministic global optimization algorithm for optimistic bilevel programming problems. Part I: Theoretical development

Polyxeni-Margarita Kleniati, Claire S. Adjiman
2014 Journal of Global Optimization  
We present a global optimization algorithm, Branch-and-Sandwich, for optimistic bilevel programming problems that satisfy a regularity condition in the inner problem.  ...  To achieve this, the well-known features of branch-and-bound algorithms are customized appropriately.  ...  We also thank two anonymous referees for their thorough and insightful comments that helped us to improve the paper.  ... 
doi:10.1007/s10898-013-0121-7 fatcat:mmnkstzwhbawhpngbbwhrwtrme

Proximal algorithms with Bregman distances for bilevel equilibrium problems with application to the problem of "how routines form and change" in Economics and Management Sciences [article]

G. C. Bento, J. X. Cruz Neto, P.A. Soares Jr, A. Soubeyran
2016 arXiv   pre-print
Using Bregman distances on Hadamard manifolds we propose a framework for to analyse the convergence of a proximal point algorithm to solve this bilevel equilibrium problem.  ...  In this paper we present the bilevel equilibrium problem under conditions of pseudomonotonicity.  ...  In the linear setting, several authors have presented iterative processes to approximate a solution of Bilevel problems.  ... 
arXiv:1401.4865v2 fatcat:df5oafudgbb4rn7arsen54nk7m
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