Uncertainty Handling in Bilevel Optimization for Robust and Reliable Solutions

Uncertainties in variables and parameters cause optimization problems to move away from globally-optimal and uncertain solutions. Practitioners resort to finding robust and reliable solutions in su...

[1]  Lorenz T. Biegler,et al.  Mathematical programs with equilibrium constraints (MPECs) in process engineering , 2003, Comput. Chem. Eng..

[2]  Kalyanmoy Deb,et al.  Reliability-Based Optimization Using Evolutionary Algorithms , 2009, IEEE Transactions on Evolutionary Computation.

[3]  L. N. Vicente,et al.  Descent approaches for quadratic bilevel programming , 1994 .

[4]  Timothy W. Simpson,et al.  Multidisciplinary Robust Design Optimization of an Internal Combustion Engine , 2003 .

[5]  Kalyanmoy Deb,et al.  A population-based fast algorithm for a billion-dimensional resource allocation problem with integer variables , 2017, Eur. J. Oper. Res..

[6]  G. Lei,et al.  Robust Design Optimization of PM-SMC Motors for Six Sigma Quality Manufacturing , 2013, IEEE Transactions on Magnetics.

[7]  Mikkel T. Jensen,et al.  Generating robust and flexible job shop schedules using genetic algorithms , 2003, IEEE Trans. Evol. Comput..

[8]  J. Herskovits,et al.  Contact shape optimization: a bilevel programming approach , 2000 .

[9]  Randy B Machemehl,et al.  Bi-Level Optimization Model for Public Transportation Network Redesign Problem , 2011 .

[10]  Tapabrata Ray,et al.  An Enhanced Memetic Algorithm for Single-Objective Bilevel Optimization Problems , 2016, Evolutionary Computation.

[11]  M. Patriksson,et al.  Stochastic bilevel programming in structural optimization , 2001 .

[12]  Mariano Luque,et al.  Optimization of the size of a solar thermal electricity plant by means of genetic algorithms , 2011 .

[13]  Kalyanmoy Deb,et al.  Introducing Robustness in Multi-Objective Optimization , 2006, Evolutionary Computation.

[14]  Robert H. Storer,et al.  Robustness Measures and Robust Scheduling for Job Shops , 1994 .

[15]  Yu Liu,et al.  A Unified Framework for Integrated Optimization Under Uncertainty , 2010 .

[16]  Seungjae Lee,et al.  Stochastic multi-objective models for network design problem , 2010, Expert Syst. Appl..

[17]  Tapabrata Ray,et al.  A Surrogate Assisted Approach for Single-Objective Bilevel Optimization , 2017, IEEE Transactions on Evolutionary Computation.

[18]  Tapabrata Ray,et al.  Six-Sigma Robust Design Optimization Using a Many-Objective Decomposition-Based Evolutionary Algorithm , 2015, IEEE Transactions on Evolutionary Computation.

[19]  Gerald G. Brown,et al.  Defending Critical Infrastructure , 2006, Interfaces.

[20]  I. K. Altinel,et al.  Competitive facility location problem with attractiveness adjustment of the follower: A bilevel programming model and its solution , 2011, Eur. J. Oper. Res..

[21]  Shigeyoshi Tsutsui,et al.  Genetic algorithms with a robust solution searching scheme , 1997, IEEE Trans. Evol. Comput..

[22]  R. Kevin Wood,et al.  Shortest‐path network interdiction , 2002, Networks.

[23]  Kalyanmoy Deb,et al.  Evolutionary algorithm for bilevel optimization using approximations of the lower level optimal solution mapping , 2017, Eur. J. Oper. Res..

[24]  Robert F. Stengel,et al.  Robust control system design using random search and genetic algorithms , 1997, IEEE Trans. Autom. Control..

[25]  Mahyar A. Amouzegar,et al.  Determining optimal pollution control policies: An application of bilevel programming , 1999, Eur. J. Oper. Res..

[26]  Steven T Waller,et al.  Integrated Network Capacity Expansion and Traffic Signal Optimization Problem: Robust Bi-level Dynamic Formulation , 2010 .

[27]  B. Mordukhovich,et al.  New necessary optimality conditions in optimistic bilevel programming , 2007 .

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

[29]  Kalyanmoy Deb,et al.  A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications , 2017, IEEE Transactions on Evolutionary Computation.

[30]  Andy J. Keane,et al.  Robust-Optimal Design of a Lightweight Space Structure Using a Genetic Algorithm , 2003 .

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

[32]  Guangyao Li,et al.  Crashworthiness design of vehicle by using multiobjective robust optimization , 2011 .