Open AccessDOMINO: Data-driven Optimization of bi-level Mixed-Integer NOnlinear Problems
Author(s) -
Burcu Beykal,
Styliani Avraamidou,
Ioannis P. E. Pistikopoulos,
Melis Onel,
Efstratios N. Pistikopoulos
Publication year - 2020
Publication title -
journal of global optimization
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.861
H-Index - 86
eISSN - 1573-2916
pISSN - 0925-5001
DOI - 10.1007/s10898-020-00890-3
Subject(s) - mathematical optimization , global optimization , solver , nonlinear programming , integer programming , domino , optimization problem , mathematics , integer (computer science) , benchmark (surveying) , nonlinear system , discrete optimization , computer science , biochemistry , chemistry , physics , quantum mechanics , programming language , catalysis , geodesy , geography
The Data-driven Optimization of bi-level Mixed-Integer NOnlinear problems (DOMINO) framework is presented for addressing the optimization of bi-level mixed-integer nonlinear programming problems. In this framework, bi-level optimization problems are approximated as single-level optimization problems by collecting samples of the upper-level objective and solving the lower-level problem to global optimality at those sampling points. This process is done through the integration of the DOMINO framework with a grey-box optimization solver to perform design of experiments on the upper-level objective, and to consecutively approximate and optimize bi-level mixed-integer nonlinear programming problems that are challenging to solve using exact methods. The performance of DOMINO is assessed through solving numerous bi-level benchmark problems, a land allocation problem in Food-Energy-Water Nexus, and through employing different data-driven optimization methodologies, including both local and global methods. Although this data-driven approach cannot provide a theoretical guarantee to global optimality, we present an algorithmic advancement that can guarantee feasibility to large-scale bi-level optimization problems when the lower-level problem is solved to global optimality at convergence.