BOLIB: Bilevel Optimization LIBrary of Test Problems

To help accelerate the development of numerical solvers for bilevel optimization, BOLIB aims at presenting a collection of academic and real-world applications or case studies on the problem. This first version of the library is made of 124 academic examples of nonlinear bilevel optimization problems, tidied up from a wide range of publications. To the best of our knowledge, this is the first time that such a scale of examples are provided to render a uniform basis on which algorithms proposed to deal with nonlinear bilevel optimization can be tested and compared. All the collected examples are programmed via Matlab and the library will be made freely available online.

[1]  Claire S. Adjiman,et al.  Branch-and-Sandwich: a deterministic global optimization algorithm for optimistic bilevel programming problems. Part II: Convergence analysis and numerical results , 2014, Journal of Global Optimization.

[2]  Wayne F. Bialas,et al.  Two-Level Linear Programming , 1984 .

[3]  S. Dempe.  First-Order Necessary Optimality Conditions for General Bilevel Programming Problems , 1997 .

[4]  Sanjo Zlobec.  Bilevel Programming: Optimality Conditions and Duality , 2009, Encyclopedia of Optimization.

[5]  A. Ciric,et al.  A dual temperature simulated annealing approach for solving bilevel programming problems , 1998 .

[6]  Efstratios N. Pistikopoulos,et al.  A Decomposition-Based Global Optimization Approach for Solving Bilevel Linear and Quadratic Programs , 1996 .

[7]  Le Dung Muu,et al.  A Global Optimization Method for Solving Convex Quadratic Bilevel Programming Problems , 2003, J. Glob. Optim..

[8]  Benoît Colson.  BIPA (BIlevel Programming with Approximation methods): Software guide and test problems , 2002 .

[9]  Kalyanmoy Deb,et al.  An improved bilevel evolutionary algorithm based on Quadratic Approximations , 2014, 2014 IEEE Congress on Evolutionary Computation (CEC).

[10]  R. Henrion,et al.  On calmness conditions in convex bilevel programming , 2011 .

[11]  Ue-Pyng Wen,et al.  A hybrid neural network approach to bilevel programming problems , 2007, Appl. Math. Lett..

[12]  Johannes P. Schlöder,et al.  Regularizing Bilevel Nonlinear Programs by Lifting , 2013 .

[13]  D. White,et al.  A solution method for the linear static Stackelberg problem using penalty functions , 1990 .

[14]  Yuping Wang,et al.  An evolutionary algorithm for solving nonlinear bilevel programming based on a new constraint-handling scheme , 2005, IEEE Transactions on Systems, Man, and Cybernetics, Part C (Applications and Reviews).

[15]  Paul H. Calamai,et al.  Generating quadratic bilevel programming test problems , 1994, TOMS.

[16]  Stephan Dempe,et al.  Linear bilevel programming with upper level constraints depending on the lower level solution , 2006, Appl. Math. Comput..

[17]  Patrice Marcotte,et al.  A Trust-Region Method for Nonlinear Bilevel Programming: Algorithm and Computational Experience , 2005, Comput. Optim. Appl..

[18]  Gui-Hua Lin,et al.  On solving simple bilevel programs with a nonconvex lower level program , 2014, Math. Program..

[19]  S. Scholtes,et al.  Nondifferentiable and two-level mathematical programming , 1997 .

[20]  Boris S. Mordukhovich,et al.  Sensitivity Analysis for Two-Level Value Functions with Applications to Bilevel Programming , 2012, SIAM J. Optim..

[21]  Jonathan F. Bard,et al.  An explicit solution to the multi-level programming problem , 1982, Comput. Oper. Res..

[22]  J. Mirrlees.  The Theory of Moral Hazard and Unobservable Behaviour: Part I , 1999 .

[23]  Lorenzo Lampariello,et al.  A Bridge Between Bilevel Programs and Nash Games , 2015, J. Optim. Theory Appl..

[24]  S. Dempe.  A necessary and a sufficient optimality condition for bilevel programming problems , 1992 .

[25]  Claire S. Adjiman,et al.  Branch-and-Sandwich: a deterministic global optimization algorithm for optimistic bilevel programming problems. Part I: Theoretical development , 2014, Journal of Global Optimization.

[26]  Wan Zhongping,et al.  A dual-relax penalty function approach for solving nonlinear bilevel programming with linear lower level problem , 2011 .

[27]  E. Aiyoshi,et al.  A solution method for the static constrained Stackelberg problem via penalty method , 1984 .

[28]  Georg Still,et al.  Solving bilevel programs with the KKT-approach , 2012, Mathematical Programming.

[29]  Stephan Dempe,et al.  Optimality Conditions for a Simple Convex Bilevel Programming Problem , 2010 .

[30]  Athanasios Migdalas,et al.  A novel approach to Bilevel nonlinear programming , 2007, J. Glob. Optim..

[31]  Wilfred Candler,et al.  A linear two-level programming problem, , 1982, Comput. Oper. Res..

[32]  Arthur W. Westerberg,et al.  Bilevel programming for steady-state chemical process design—I. Fundamentals and algorithms , 1990 .

[33]  Arthur W. Westerberg,et al.  Bilevel programming for steady-state chemical process design , 1990 .

[34]  P. Mehlitz,et al.  Optimality conditions for the simple convex bilevel programming problem in Banach spaces , 2018 .

[35]  Herminia I. Calvete,et al.  The bilevel linear/linear fractional programming problem , 1999, Eur. J. Oper. Res..

[36]  Francisco Facchinei,et al.  A smoothing method for mathematical programs with equilibrium constraints , 1999, Math. Program..

[37]  Charles E. Blair,et al.  Computational Difficulties of Bilevel Linear Programming , 1990, Oper. Res..

[38]  Eitaro Aiyoshi,et al.  Double penalty method for bilevel optimization problems , 1992, Ann. Oper. Res..

[39]  Jonathan F. Bard,et al.  Algorithms for nonlinear bilevel mathematical programs , 1991, IEEE Trans. Syst. Man Cybern..

[40]  Peter Gritzmann,et al.  On the Complexity of some Basic Problems in Computational Convexity: II. Volume and mixed volumes , 1994, Universität Trier, Mathematik/Informatik, Forschungsbericht.

[41]  Jonathan F. BARD,et al.  Convex two-level optimization , 1988, Math. Program..

[42]  DEPENDENCE OF BILEVEL PROGRAMMING ON IRRELEVANT DATA , 2011 .

[43]  J. M. Henderson,et al.  Microeconomic Theory: A Mathematical Approach. , 1959 .

[44]  J. G. Ecker,et al.  Solving Bilevel Linear Programs Using Multiple Objective Linear Programming , 2009 .

[45]  Peter Värbrand,et al.  A quasiconcave minimization method for solving linear two-level programs , 1994, J. Glob. Optim..

[46]  Fioravante Patrone,et al.  Stackelberg Problems: Subgame Perfect Equilibria via Tikhonov Regularization , 2006 .

[47]  Zwei-Ebenen-Optimierungsaufgaben mit nichtkonvexer Zielfunktion in der unteren Ebene , 2001 .

[48]  C. Floudas.  Handbook of Test Problems in Local and Global Optimization , 1999 .

[49]  J. Bard.  Some properties of the bilevel programming problem , 1991 .

[50]  Kalyanmoy Deb,et al.  Robust and Reliable Solutions in Bilevel Optimization Problems Under Uncertainties , 2016 .

[51]  Christodoulos A. Floudas,et al.  Global Optimization of Nonlinear Bilevel Programming Problems , 2001, J. Glob. Optim..

[52]  Jirí V. Outrata,et al.  On Optimization Problems with Variational Inequality Constraints , 1994, SIAM J. Optim..

[53]  Claire S. Adjiman,et al.  BASBL: Branch-And-Sandwich BiLevel solver. Implementation and computational study with the BASBLib test set , 2020, Comput. Chem. Eng..

[54]  Tiesong Hu,et al.  A neural network approach for solving linear bilevel programming problem , 2010, Knowl. Based Syst..

[55]  Jane J. Ye,et al.  New Necessary Optimality Conditions for Bilevel Programs by Combining the MPEC and Value Function Approaches , 2010, SIAM J. Optim..

[56]  Stephan Dempe,et al.  Is bilevel programming a special case of a mathematical program with complementarity constraints? , 2012, Math. Program..

[57]  Jonathan F. Bard,et al.  Practical Bilevel Optimization , 1998 .

[58]  E. Aiyoshi,et al.  A new computational method for Stackelberg and min-max problems by use of a penalty method , 1981 .

[59]  万仲平,et al.  A DUAL-RELAX PENALTY FUNCTION APPROACH FOR SOLVING NONLINEAR BILEVEL PROGRAMMING WITH LINEAR LOWER LEVEL PROBLEM , 2011 .

[60]  Christodoulos A. Floudas,et al.  Optimality and Duality in Parametric Convex Lexicographic Programming , 1998 .

[61]  Charles M. Macal,et al.  Dependence of bilevel mathematical programs on irrelevant constraints , 1997, Comput. Oper. Res..

[62]  Lorenzo Lampariello,et al.  Numerically tractable optimistic bilevel problems , 2020, Comput. Optim. Appl..

[63]  Yi-Hsin Liu,et al.  Characterizing an optimal solution to the linear bilevel programming problem , 1994 .

[64]  Peter Värbrand,et al.  A global optimization approach for the linear two-level program , 1993, J. Glob. Optim..

[65]  Yekini Shehu,et al.  An inertial extrapolation method for convex simple bilevel optimization , 2018, Optim. Methods Softw..

[66]  Jirí Vladimír Outrata,et al.  On the numerical solution of a class of Stackelberg problems , 1990, ZOR Methods Model. Oper. Res..

[67]  Jonathan F. Bard,et al.  Practical Bilevel Optimization: Algorithms and Applications , 1998 .

[68]  Oliver Stein,et al.  Solving Semi-Infinite Optimization Problems with Interior Point Techniques , 2003, SIAM J. Control. Optim..

[69]  J. Outrata.  Necessary optimality conditions for Stackelberg problems , 1993 .

[70]  A. Westerberg,et al.  A note on the optimality conditions for the bilevel programming problem , 1988 .

[71]  Le Thi Hoai An,et al.  DC programming techniques for solving a class of nonlinear bilevel programs , 2009, J. Glob. Optim..

[72]  Alain Haurie,et al.  A Note on: An Efficient Point Algorithm for a Linear Two-Stage Optimization Problem , 1987, Oper. Res..

[73]  J. Bard.  Optimality conditions for the bilevel programming problem , 1984 .

[74]  Jiří V. Outrata,et al.  On the implicit programming approach in a class of mathematical programs with equilibrium constraints , 2009 .

[75]  Jiming Liu,et al.  On bilevel programming, Part I: General nonlinear cases , 1995, Math. Program..

[77]  Stephan Dempe,et al.  Solution algorithm for an optimistic linear Stackelberg problem , 2014, Comput. Oper. Res..

[78]  Li Wang,et al.  Bilevel Polynomial Programs and Semidefinite Relaxation Methods , 2015, SIAM J. Optim..

[79]  Gerd Wachsmuth,et al.  Weak and strong stationarity in generalized bilevel programming and bilevel optimal control , 2016 .

[80]  R. Lucchetti,et al.  Existence theorems of equilibrium points in stackelberg , 1987 .