# MSc project – Stochastic optimisation for calibration of a land use-transport integrated model

Keywords :

• calibration, optimization, stochastic programming,
• Land use / transport models, integrated modelling, sustainable development.

Topic:The aim of STEEP lab is to develop mathematical and computational decision-making tools to support decision makers in the implementation of the transition to sustainability.To do so, we use and implement various energy / environment / land-use / transport models. These models are designed to simulate the effects of a given policy, or to optimize a policy choice under constraints.

In particular, we are interested in TRANUS, which is a land use and transport integrated (LUTI) model http://www.modelistica.com/tranus_english.htm. Tranus simulates the location of activities in space, the real estate market and the transportation system. TRANUS applies to urban as well as regional scales. It is specially designed to assess the impacts of various envisaged projects and policies in cities and regions. It allows to evaluate their effects from economic, financial and environmental points of view. TRANUS proceeds by solving a system of deterministic nonlinear equations and inequalities containing a number of economic parameters (e.g. demand elasticity parameters, location dispersion parameters, etc.). The solution of such a system represents an economic equilibrium between supply and demand.

The overall calibration (estimation) of the parameters that drive the equations implemented in the model is a vital step. However, current LUTI models are usually calibrated by hand. The calibration can typically take up to 6 months for a medium size LUTI model (about 100 geographic zones, about 10 sectors including economic sectors, population and employment categories). This clearly emphasizes the need to further investigate and at least semi-automate the calibration process. Parameter estimation requires numerical optimization. The general state-of-the-art on optimization procedures is extremely large and mature, covering many different types of optimization problems, in terms of size (number of parameters and data) and type of cost function(s) and constraints. Depending on the characteristics of the considered models in terms of dimension, non linearity, data availability and quality, deterministic or stochastic methods can be implemented. The aim of this internship is therefore to evaluate the potential of using stochastic optimisation algorithms (for exemple, Metropolis Hasting algorithm, Gibbs sampling, Population Monte Carlo, particle swarm optimization, stochastic gradient) in the context of LUTI model calibration.
After a state of the art on these algorithms, they will be tested in a TRANUS model that has been developed for the city of Grenoble in collaboration with IDDRI (Institut du développement durable et des relations internationales).

T. de la Barra, 2005. Integrated Land Use and Transport Modelling: Decision Chains and Hierarchies, Cambridge University Press
N. Bartoli and P. Del Moral, 2001. Simulation et algorithmes stochastiques. Cépaduès-éditions
James C. Spall, 2003. Introdution to stohastic searh and optimization. Wiley

Environment: The project will be carried out in STEEP lab (INRIA Rhône-Alpes / LJK), in close collaboration with MOISE lab (INRIA Rhône-Alpes / LJK) under the supervision of Dr. Elise Arnaud and Dr. Clémentine Prieur. This position is offered at the Rhône-Alpes Research Unit of INRIA, located near Grenoble and Lyon. The Unit includes more than 700 people, within 34 research teams and 10 support services.

Profile and conditions for applicants:

• We are looking for qualified and motivated applicants with strong skills in applied mathematics and computer science. Knowledge in stochastic optimisation is desirable. Knowledge of programming languages will be appreciated (python, R, Matlab). Interest in the application is also highly desirable.

Duration: 6 months. a PhD thesis is planned to follow the internship

Application:

• To apply online, please follow the steps described in the INRIA web pages for the internships
• French students : To apply, please send a pdf file containing a complete CV, your publication list, a cover letter and a list of two references (with telephone numbers and postal and e-mail addresses) to Elise Arnaud.