A hybrid machine-learning and optimization method to solve bi-level problems
Journal article, 2018

Bi-level optimization has widespread applications in many disciplines including management, economy, energy, and transportation. Because it is by nature a NP-hard problem, finding an efficient and reliable solution method tailored to large sized cases of specific types is of the highest importance. To this end, we develop a hybrid method based on machine-learning and optimization. For numerical tests, we set up a highly challenging case: a nonlinear discrete bi-level problem with equilibrium constraints in transportation science, known as the discrete network design problem. The hybrid method transforms the original problem to an integer linear programing problem based on a supervised learning technique and a tractable nonlinear problem. This methodology is tested using a real dataset in which the results are found to be highly promising. For the machine learning tasks we employ MATLAB and to solve the optimization problems, we use GAMS (with CPLEX solver).

Discrete network design problem

Machine learning


Supervised learning

Integer linear programming


Saeed Asadi Bagloee

University of Melbourne

Majid Sarvi

University of Melbourne

Michael Patriksson

University of Gothenburg

Chalmers, Mathematical Sciences

M. Asadi

University of Saskatchewan

Expert Systems with Applications

0957-4174 (ISSN)

Vol. 95 1 142-152

Driving Forces

Sustainable development

Areas of Advance



Subject Categories

Computational Mathematics

Other Mathematics


Basic sciences



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