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In this study, a mixed-integer linear programming (MILP) formulation for obtaining the operating points of hybrid electric vehicle (HEV) powertrains is proposed. This study focuses on linearizing the nonlinear terms, such as an engine fuel consumption map, or bilinear terms represented by the energy of the motor. To address this problem, a conventional piecewise linear (PWL) method and a multi-layer perceptron (MLP) regression approach are adopted. Although the optimal solution cannot be determined using a PWL approximation for the fuel consumption map, it can be obtained using an MLP regression. Furthermore, the PWL method achieves better results than the MLP approach in terms of the accuracy of its bilinear approximation. Obtaining the optimal solution using MILP helps in acquiring a Lagrange multiplication of the design variables by solving the dual problem, which allows an efficient design revision strategy to be obtained.

Optimization for the minimum fuel consumption problem of a hybrid electric vehicle using mixed-integer linear programming