11h30 - 11h55
A new variable selection strategy for the parallel space decomposition in derivative-free optimization.
The current parallel space decomposition of the Mesh Adaptive Direct Search algorithm (PSD-MADS) is an asynchronous parallel method that uses a simple generic strategy to decompose a problem into smaller dimension subproblems. The present work explores new strategies for selecting the subset of variables defining subproblems to be explored in parallel. These strategies are based on ranking the variables using statistical tools to determine the most influential ones. The statistical approach improves the decomposition of the problem into smaller more relevant subproblems. This work aims to improve the use of available processors.
11h55 - 12h20
A Trust Region Method for Solving Derivative-Free Problems with Binary and Continuous Variables Part 1: the underlying algorithm
Trust region methods are used to solve various black-box optimization problems, especially when no derivative information is available. In this talk, we will consider an extension of trust region methods for mixed-integer nonlinear programming (MINLP). There are both theoretical and computational innovations to handle the binary variables, including restricting the quadratic model, solving mixed integer quadratic problems and handling well-poisedness. Whereas, of necessity, we address globality with respect to the binary variables, we are content to obtain good local minima for the continuous variables, at least in part because our typical context involves expensive simulations.
12h20 - 12h45
A Trust Region Method for Solving Derivative-Free Problems with Binary and Continuous Variables - Part 2: applications in the energy domain
Optimization takes place in many IFPEN applications: inferring the parameters of numerical models from experimental data (earth sciences, combustion in engines, chemical process), design optimization (wind turbine, risers, networks of oil pipelines), optimizing the settings of experimental devices (calibration of engines, catalysis). These typically require minimizing a functional that is complex (nonlinearities, depending on mixed continuous and integer/discrete variables) and expensive to estimate (solution of a numerical model based on differential systems), and for which derivatives are often not available.
In this talk, we illustrate the potential of the proposed trust region method adapted to binary and continuous variables on several applications in the energy domain.