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Mathematical optimization is a valuable tool since it allows to maximize or minimize the quantities we want, depending on the variables, parameters, and constraints of a given problem. The main ingredient of optimization algorithms is the gradient. However, in realistic engineering and various mathematical applications such as hyperparameter optimization in machine learning, the gradient does not exist or cannot be computed. It is under these conditions, among others, that optimization without derivatives must be considered.

In other words and circumstances, this type of optimization can also be very useful for optimizing functions that require computer simulations that are expensive to evaluate and whose characteristics are not known or exploitable.

Here are some other examples of potential applications (credit: Juliane Mueller):

• Reliability Redundancy Optimization - maximizing system reliability
• Global climate model - calibrating methane model parameters
• Sail design - maximizing lift and minimizing drag simultaneously
• Watershed management - agricultural land set-aside to reduce pH
• Setting the physical event generator - matching simulations with observations
• Engine efficiency - designing better engines and fuels
• Renewable energy - optimizing the energy produced by kites, hydroelectricity, etc.
• Scheduling - how to assemble products online in the most efficient way possible
• And many more...

This seminar will introduce the basics of optimization and then describe how derivative-free optimization works without the gradient via a so-called "direct search" algorithm called MADS, which is used via the free NOMAD software.

Algorithms and software tools will be presented, then examples of applications at Hydro-Québec where derivative-free optimization was the winning option will be discussed.

Language: slides in English, presentation in French.

Agenda:

13:00-13:45
Presentation by Sébastien Le Digabel - Member, GERAD, Full Professor, Department of Mathematics and Industrial Engineering, Polytechnique Montréal, Canada

13:45-14:00
Presentation of applications developed at Hydro-Québec by Stéphane Alarie, Associate Member of GERAD - Researcher, Institut de recherche d'Hydro-Québec, Canada

14:00-14:30
Question and answer period

14:30-14:45
Discussion on the possible deployment of a consortium project