HEC Montréal, Canada, May 2 - 4, 2011

2011 Optimization Days

HEC Montréal, Canada, 2 — 4 May 2011

Schedule Authors My Schedule

MA4 Programmation dynamique approchée : théorie et applications / Approximate Dynamic Programming: Theory and Applications

May 2, 2011 10:30 AM – 12:10 PM

Location: Cogeco

Chaired by Michel Denault

4 Presentations

  • 10:30 AM - 10:55 AM

    A Bayesian Approach to the Exploration/Exploitation Dilemma

    • Ilya Ryzhov, presenter, Princeton University
    • Warren Powell, Princeton University

    We use a correlated Bayesian belief model to represent our uncertainty about the value function in ADP. Correlations between the values of different states allow us to learn about multiple states from a single decision. We apply the knowledge gradient concept from optimal learning to create a new exploration strategy.

  • 10:55 AM - 11:20 AM

    Optimal Control of a Two Dam Hydroelectric Facility Under Time Varying Prices

    • Matt Davison, presenter, Departments of Applied Mathematics and Statistical & Actuarial Sciences, Richard Ivey School of Business, The University of Western Ontario

    We investigate optimal control strategies for the variable price electricity market operations of a hydro-electric facility comprising two dams linked in series by a common reservoir which receives the outflow from the first dam and supplies the inflow to the second dam. Using a dynamic programming approach, we are able to obtain some interesting insights about the behaviour of these plants and compare the similarities and differences of the pump-wait-release cycle of this two dam system to a similar one dam system. In particular, we show that the electricity price plays a more important role in a two dam system than in a one dam system.

  • 11:20 AM - 11:45 AM

    Extending the Simulations and Regressions A.D.P. Approach to Value and Control a Hydropower System

    • Michel Denault, presenter, GERAD - HEC Montréal
    • Mathieu Rousseau, KPMG
    • Jean-Guy Simonato, HEC Montréal
    • Lars Stentoft, HEC Montréal

    We solve a control problem by using simulations and regressions, a common approach in approximate dynamic programming. Specifically, in a hydropower system problem, we have one exogeneous stochastic state variable, power price, and one endogeneous state variable, the water level in the dam. Neither is discretized.

  • 11:45 AM - 12:10 PM

    The Optimization Strategy of the Model-Based Analysis of Cell Divisions in Arabidopsis Leaf

    • Leila Kheibarshekan, presenter, Ghent University

    We studied the temporal control of epidermal cell divisions in the Arabidopsis leaf. We built a mathematical model with several parameters to study the rules whereby different cell types divide and expand. To optimize the parameters, the experimental data were fitted into a computational model by the downhill simplex method or Nelder-Mead method.