Black-Box Optimization

Since 2011 During my PostDoc I have done at the Institute of Mathematics of Toulouse and GERAD in Montreal, I was able to expand my area of expertise by considering more general problems.Indeed, nowadays, more and more simulation codes and modeling are used by researchers, but also by industry. However, after modeling and simulation of the problem, the next step is its optimization. So, the objective function and the constraints can come from several hours of CPU time or a black-Box.

To solve this problem, genetic algorithms are so often used, because they are simple to implement and do not require advanced knowledge in optimization.Unfortunately, this approach does not guarantee the results. Other approaches may be considered.

• • A first approach is to make these approaches more user-friendly. For example, methods Derivative-Free Optimization (DFO) and Direct Search (MADS) are techniques that have proven effective and have made ​​great breakthrough in recent years. In addition, they can prove the local optimality of the solutions and some versions can minimize the number of calls to the black box. I worked on an algorithm combining the two approaches (MADS-DFO), by integrating approximations by quadratic models in an algorithm Patern Search (NOMAD).

  • On the other hand, to overcome this difficulty, many analytical models have been developed to eliminate completely or partially the numerical simulations. A new type of algorithm can be considered, combining MADS-DFO algorithm to solve the black box part of the problem and a global optimization algorithm to solve the explicit part.