Michaël Thémans

Forecasting the Demand for Electric Vehicles: Accounting for Attitudes and Perceptions

In the context of the arrival of electric vehicles on the car market, new mathematical models are needed to understand and predict the impact on the market shares. This research provides a comprehensive methodology to forecast the demand of a technology that is not widespread yet, such as electric cars. It aims at providing contributions regarding three issues related to the prediction of the demand for electric vehicles: survey design, model estimation, and forecasting. We develop a stated preferences SP survey with personalized choice situations involving standard gasoline/diesel cars and electric cars. We specify a hybrid choice model accounting for attitudes toward leasing contracts or practical aspects of a car in the decision-making process. A forecasting analysis based on the collected SP data and additional market information is performed to evaluate the future demand for electric cars.

A Heuristic for Nonlinear Global Optimization

We propose a new heuristic for nonlinear global optimization combining a variable neighborhood search framework with a modified trust-region algorithm as local search. The proposed method presents the capability to prematurely interrupt the local search if the iterates are converging to a local minimum that has already been visited or if they are reaching an area where no significant improvement can be expected. The neighborhoods, as well as the neighbors selection procedure, are exploiting the curvature of the objective function. Numerical tests are performed on a set of unconstrained nonlinear problems from the literature. Results illustrate that the new method significantly outperforms existing heuristics from the literature in terms of success rate, CPU time, and number of function evaluations.

A multi-iterate method to solve systems of nonlinear equations

We propose an extension of secant methods for nonlinear equations using a population of previous iterates. Contrarily to classical secant methods, where exact interpolation is used, we prefer a least squares approach to calibrate the linear model. We propose an explicit control of the numerical stability of the method. We show that our approach can lead to an update formula. In that case, we prove the local convergence of the corresponding undamped quasi-Newton method. Finally, computational comparisons with classical quasi-Newton methods highlight a significant improvement in terms of robustness and number of function evaluations. We also present numerical tests showing the robust behavior of our method in the presence of noise.

Dealing with singularities in nonlinear unconstrained optimization

We propose a new trust region based optimization algorithm for solving unconstrained nonlinear problems whose second derivatives matrix is singular at a local solution. We give a theoretical characterization of the singularity in this context and we propose an iterative procedure which allows to identify a singularity in the objective function during the course of the optimization algorithm, and artificially adds curvature to the objective function. Numerical tests are performed on a set of unconstrained nonlinear problems, both singular and non-singular. Results illustrate the significant performance improvement compared to classical trust region and filter algorithms proposed in the literature. The approach is also shown to be competitive with tensor methods in terms of efficiency while reaching a higher level of robustness.